Control system compensator lag lead
nbahadure
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Jun 30, 2021
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About This Presentation
Necessary of Compensation, Methods of Compensation, Phase Lead Compensation, Phase Lag Compensation, Phase Lag Lead Compensation, and Comparison between lead and lag compensators.
Slide Content
Control System
Lag, Lead, Lag-Lead Compensator
Dr. Nilesh Bhaskarrao Bahadure
[email protected]
https://www.sites.google.com/site/nileshbbahadure/home
June 30, 2021
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 1 / 30
Lag, Lead, Lag-Lead Compensator
Dr. Nilesh Bhaskarrao Bahadure
[email protected]
https://www.sites.google.com/site/nileshbbahadure/home
June 30, 2021
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 1 / 30
Overview
1
Necessary of Compensation
2
Methods of Compensation
3
Phase Lead Compensation
Eect of Phase Lead Compensation
Advantages of Phase Lead Compensation
Disadvantages of Phase Lead Compensation
4
Phase Lag Compensation
Eect of Phase Lag Compensation
Advantages of Phase Lag Compensation
Disadvantages of Phase Lag Compensation
5
Phase Lag Lead Compensation
6
Comparison between lead and lag compensators
7
Thank You
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 2 / 30
1
Necessary of Compensation
2
Methods of Compensation
3
Phase Lead Compensation
Eect of Phase Lead Compensation
Advantages of Phase Lead Compensation
Disadvantages of Phase Lead Compensation
4
Phase Lag Compensation
Eect of Phase Lag Compensation
Advantages of Phase Lag Compensation
Disadvantages of Phase Lag Compensation
5
Phase Lag Lead Compensation
6
Comparison between lead and lag compensators
7
Thank You
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 2 / 30
Necessary of Compensation
1
In order to obtain the desired performance of the system, we use
compensating networks. Compensating networks are applied to the
system in the form of feed forward path gain adjustment.
2
Compensate a unstable system to make it stable.
3
A compensating network is used to minimize overshoot.
4
These compensating networks increase the steady state accuracy of
the system. An important point to be noted here is that the increase
in the steady state accuracy brings instability to the system.
5
Compensating networks also introduces poles and zeros in the system
thereby causes changes in the transfer function of the system. Due to
this, performance specications of the system change.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 3 / 30
1
In order to obtain the desired performance of the system, we use
compensating networks. Compensating networks are applied to the
system in the form of feed forward path gain adjustment.
2
Compensate a unstable system to make it stable.
3
A compensating network is used to minimize overshoot.
4
These compensating networks increase the steady state accuracy of
the system. An important point to be noted here is that the increase
in the steady state accuracy brings instability to the system.
5
Compensating networks also introduces poles and zeros in the system
thereby causes changes in the transfer function of the system. Due to
this, performance specications of the system change.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 3 / 30
Necessary of Compensation
1
In order to obtain the desired performance of the system, we use
compensating networks. Compensating networks are applied to the
system in the form of feed forward path gain adjustment.
2
Compensate a unstable system to make it stable.
3
A compensating network is used to minimize overshoot.
4
These compensating networks increase the steady state accuracy of
the system. An important point to be noted here is that the increase
in the steady state accuracy brings instability to the system.
5
Compensating networks also introduces poles and zeros in the system
thereby causes changes in the transfer function of the system. Due to
this, performance specications of the system change.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 3 / 30
1
In order to obtain the desired performance of the system, we use
compensating networks. Compensating networks are applied to the
system in the form of feed forward path gain adjustment.
2
Compensate a unstable system to make it stable.
3
A compensating network is used to minimize overshoot.
4
These compensating networks increase the steady state accuracy of
the system. An important point to be noted here is that the increase
in the steady state accuracy brings instability to the system.
5
Compensating networks also introduces poles and zeros in the system
thereby causes changes in the transfer function of the system. Due to
this, performance specications of the system change.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 3 / 30
Necessary of Compensation
1
In order to obtain the desired performance of the system, we use
compensating networks. Compensating networks are applied to the
system in the form of feed forward path gain adjustment.
2
Compensate a unstable system to make it stable.
3
A compensating network is used to minimize overshoot.
4
These compensating networks increase the steady state accuracy of
the system. An important point to be noted here is that the increase
in the steady state accuracy brings instability to the system.
5
Compensating networks also introduces poles and zeros in the system
thereby causes changes in the transfer function of the system. Due to
this, performance specications of the system change.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 3 / 30
1
In order to obtain the desired performance of the system, we use
compensating networks. Compensating networks are applied to the
system in the form of feed forward path gain adjustment.
2
Compensate a unstable system to make it stable.
3
A compensating network is used to minimize overshoot.
4
These compensating networks increase the steady state accuracy of
the system. An important point to be noted here is that the increase
in the steady state accuracy brings instability to the system.
5
Compensating networks also introduces poles and zeros in the system
thereby causes changes in the transfer function of the system. Due to
this, performance specications of the system change.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 3 / 30
Necessary of Compensation
1
In order to obtain the desired performance of the system, we use
compensating networks. Compensating networks are applied to the
system in the form of feed forward path gain adjustment.
2
Compensate a unstable system to make it stable.
3
A compensating network is used to minimize overshoot.
4
These compensating networks increase the steady state accuracy of
the system. An important point to be noted here is that the increase
in the steady state accuracy brings instability to the system.
5
Compensating networks also introduces poles and zeros in the system
thereby causes changes in the transfer function of the system. Due to
this, performance specications of the system change.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 3 / 30
1
In order to obtain the desired performance of the system, we use
compensating networks. Compensating networks are applied to the
system in the form of feed forward path gain adjustment.
2
Compensate a unstable system to make it stable.
3
A compensating network is used to minimize overshoot.
4
These compensating networks increase the steady state accuracy of
the system. An important point to be noted here is that the increase
in the steady state accuracy brings instability to the system.
5
Compensating networks also introduces poles and zeros in the system
thereby causes changes in the transfer function of the system. Due to
this, performance specications of the system change.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 3 / 30
Necessary of Compensation
1
In order to obtain the desired performance of the system, we use
compensating networks. Compensating networks are applied to the
system in the form of feed forward path gain adjustment.
2
Compensate a unstable system to make it stable.
3
A compensating network is used to minimize overshoot.
4
These compensating networks increase the steady state accuracy of
the system. An important point to be noted here is that the increase
in the steady state accuracy brings instability to the system.
5
Compensating networks also introduces poles and zeros in the system
thereby causes changes in the transfer function of the system. Due to
this, performance specications of the system change.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 3 / 30
1
In order to obtain the desired performance of the system, we use
compensating networks. Compensating networks are applied to the
system in the form of feed forward path gain adjustment.
2
Compensate a unstable system to make it stable.
3
A compensating network is used to minimize overshoot.
4
These compensating networks increase the steady state accuracy of
the system. An important point to be noted here is that the increase
in the steady state accuracy brings instability to the system.
5
Compensating networks also introduces poles and zeros in the system
thereby causes changes in the transfer function of the system. Due to
this, performance specications of the system change.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 3 / 30
Methods of Compensation
1
Series compensation
2
Feedback compensation
Series Compensation
Connecting compensating circuit between error detector and plants known
as series compensation.
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 4 / 30
1
Series compensation
2
Feedback compensation
Series Compensation
Connecting compensating circuit between error detector and plants known
as series compensation.
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 4 / 30
Methods of Compensation
1
Series compensation
2
Feedback compensation
Series Compensation
Connecting compensating circuit between error detector and plants known
as series compensation.
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 4 / 30
1
Series compensation
2
Feedback compensation
Series Compensation
Connecting compensating circuit between error detector and plants known
as series compensation.
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 4 / 30
Methods of Compensation Feedback Compensation
When a compensator used in a feedback manner called feedback
compensation.
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 5 / 30
When a compensator used in a feedback manner called feedback
compensation.
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 5 / 30
Phase Lead Compensation
A system which has one pole and one dominating zero is known as lead
network.
If we want to add a dominating zero for compensation in control
system then we have to select lead compensation network.The lead compensator is an electrical network which produces a sinusoidal
output having phase lead when a sinusoidal input is applied.
The lead
compensator circuit in the 's' domain is shown in the gure
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 6 / 30
A system which has one pole and one dominating zero is known as lead
network.
If we want to add a dominating zero for compensation in control
system then we have to select lead compensation network.The lead compensator is an electrical network which produces a sinusoidal
output having phase lead when a sinusoidal input is applied.
The lead
compensator circuit in the 's' domain is shown in the gure
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 6 / 30
Phase Lead Compensation
A system which has one pole and one dominating zero is known as lead
network.
If we want to add a dominating zero for compensation in control
system then we have to select lead compensation network.The lead compensator is an electrical network which produces a sinusoidal
output having phase lead when a sinusoidal input is applied.
The lead
compensator circuit in the 's' domain is shown in the gure
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 6 / 30
A system which has one pole and one dominating zero is known as lead
network.
If we want to add a dominating zero for compensation in control
system then we have to select lead compensation network.The lead compensator is an electrical network which produces a sinusoidal
output having phase lead when a sinusoidal input is applied.
The lead
compensator circuit in the 's' domain is shown in the gure
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 6 / 30
Phase Lead Compensation
A system which has one pole and one dominating zero is known as lead
network.
If we want to add a dominating zero for compensation in control
system then we have to select lead compensation network.The lead compensator is an electrical network which produces a sinusoidal
output having phase lead when a sinusoidal input is applied.
The lead
compensator circuit in the 's' domain is shown in the gure
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 6 / 30
A system which has one pole and one dominating zero is known as lead
network.
If we want to add a dominating zero for compensation in control
system then we have to select lead compensation network.The lead compensator is an electrical network which produces a sinusoidal
output having phase lead when a sinusoidal input is applied.
The lead
compensator circuit in the 's' domain is shown in the gure
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 6 / 30
Phase Lead Compensation
A system which has one pole and one dominating zero is known as lead
network.
If we want to add a dominating zero for compensation in control
system then we have to select lead compensation network.The lead compensator is an electrical network which produces a sinusoidal
output having phase lead when a sinusoidal input is applied.
The lead
compensator circuit in the 's' domain is shown in the gure
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 6 / 30
A system which has one pole and one dominating zero is known as lead
network.
If we want to add a dominating zero for compensation in control
system then we have to select lead compensation network.The lead compensator is an electrical network which produces a sinusoidal
output having phase lead when a sinusoidal input is applied.
The lead
compensator circuit in the 's' domain is shown in the gure
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 6 / 30
Phase Lead Compensation
A system which has one pole and one dominating zero is known as lead
network.
If we want to add a dominating zero for compensation in control
system then we have to select lead compensation network.The lead compensator is an electrical network which produces a sinusoidal
output having phase lead when a sinusoidal input is applied.
The lead
compensator circuit in the 's' domain is shown in the gure
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 6 / 30
A system which has one pole and one dominating zero is known as lead
network.
If we want to add a dominating zero for compensation in control
system then we have to select lead compensation network.The lead compensator is an electrical network which produces a sinusoidal
output having phase lead when a sinusoidal input is applied.
The lead
compensator circuit in the 's' domain is shown in the gure
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 6 / 30
Phase Lead Compensation
A system which has one pole and one dominating zero is known as lead
network.
If we want to add a dominating zero for compensation in control
system then we have to select lead compensation network.The lead compensator is an electrical network which produces a sinusoidal
output having phase lead when a sinusoidal input is applied.
The lead
compensator circuit in the 's' domain is shown in the gure
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 6 / 30
A system which has one pole and one dominating zero is known as lead
network.
If we want to add a dominating zero for compensation in control
system then we have to select lead compensation network.The lead compensator is an electrical network which produces a sinusoidal
output having phase lead when a sinusoidal input is applied.
The lead
compensator circuit in the 's' domain is shown in the gure
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 6 / 30
Phase Lead Compensation...
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 7 / 30
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 7 / 30
Phase Lead Compensation...
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 7 / 30
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 7 / 30
Phase Lead Compensation...
From the circuit we get,
I1=C
d
dt
(eieo)
I2=
eieo
R1
I=I1+I2
Also,
I=
eo
R2
Equating above equations we get,
eo
R2
=C
d
dt
(eieo) +
eieo
R1
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 8 / 30
From the circuit we get,
I1=C
d
dt
(eieo)
I2=
eieo
R1
I=I1+I2
Also,
I=
eo
R2
Equating above equations we get,
eo
R2
=C
d
dt
(eieo) +
eieo
R1
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 8 / 30
Phase Lead Compensation...
From the circuit we get,
I1=C
d
dt
(eieo)
I2=
eieo
R1
I=I1+I2
Also,
I=
eo
R2
Equating above equations we get,
eo
R2
=C
d
dt
(eieo) +
eieo
R1
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 8 / 30
From the circuit we get,
I1=C
d
dt
(eieo)
I2=
eieo
R1
I=I1+I2
Also,
I=
eo
R2
Equating above equations we get,
eo
R2
=C
d
dt
(eieo) +
eieo
R1
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 8 / 30
Phase Lead Compensation...
From the circuit we get,
I1=C
d
dt
(eieo)
I2=
eieo
R1
I=I1+I2
Also,
I=
eo
R2
Equating above equations we get,
eo
R2
=C
d
dt
(eieo) +
eieo
R1
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 8 / 30
From the circuit we get,
I1=C
d
dt
(eieo)
I2=
eieo
R1
I=I1+I2
Also,
I=
eo
R2
Equating above equations we get,
eo
R2
=C
d
dt
(eieo) +
eieo
R1
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 8 / 30
Phase Lead Compensation...
From the circuit we get,
I1=C
d
dt
(eieo)
I2=
eieo
R1
I=I1+I2
Also,
I=
eo
R2
Equating above equations we get,
eo
R2
=C
d
dt
(eieo) +
eieo
R1
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 8 / 30
From the circuit we get,
I1=C
d
dt
(eieo)
I2=
eieo
R1
I=I1+I2
Also,
I=
eo
R2
Equating above equations we get,
eo
R2
=C
d
dt
(eieo) +
eieo
R1
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 8 / 30
Phase Lead Compensation...
From the circuit we get,
I1=C
d
dt
(eieo)
I2=
eieo
R1
I=I1+I2
Also,
I=
eo
R2
Equating above equations we get,
eo
R2
=C
d
dt
(eieo) +
eieo
R1
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 8 / 30
From the circuit we get,
I1=C
d
dt
(eieo)
I2=
eieo
R1
I=I1+I2
Also,
I=
eo
R2
Equating above equations we get,
eo
R2
=C
d
dt
(eieo) +
eieo
R1
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 8 / 30
Phase Lead Compensation...
From the circuit we get,
I1=C
d
dt
(eieo)
I2=
eieo
R1
I=I1+I2
Also,
I=
eo
R2
Equating above equations we get,
eo
R2
=C
d
dt
(eieo) +
eieo
R1
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 8 / 30
From the circuit we get,
I1=C
d
dt
(eieo)
I2=
eieo
R1
I=I1+I2
Also,
I=
eo
R2
Equating above equations we get,
eo
R2
=C
d
dt
(eieo) +
eieo
R1
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 8 / 30
Phase Lead Compensation...
From the circuit we get,
I1=C
d
dt
(eieo)
I2=
eieo
R1
I=I1+I2
Also,
I=
eo
R2
Equating above equations we get,
eo
R2
=C
d
dt
(eieo) +
eieo
R1
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 8 / 30
From the circuit we get,
I1=C
d
dt
(eieo)
I2=
eieo
R1
I=I1+I2
Also,
I=
eo
R2
Equating above equations we get,
eo
R2
=C
d
dt
(eieo) +
eieo
R1
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 8 / 30
Phase Lead Compensation...
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage. So taking Laplace transform of both side of
above equations,
Eo(s)
R2
=
1
R1
[Ei(s)Eo(s)] +Cs[Ei(s)Eo(s)]
Eo(s)
Ei(s)
=
1+sCR1
R1
R1+R2+sR1R2C
R2R1
Eo(s)
Ei(s)
=
R2
R1+R2
[
1 +sCR1
1 +
sR1R2C
R1+R2
]
On substituting the=
R1+R2
R2
andT=
R1R2
R1+R2
Where,Tandare respectively the time constant and attenuation
constant, we haveTransfer Function =
Eo(s)
Ei(s)
=
1
[
1 +sT
1 +sT
]
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 9 / 30
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage. So taking Laplace transform of both side of
above equations,
Eo(s)
R2
=
1
R1
[Ei(s)Eo(s)] +Cs[Ei(s)Eo(s)]
Eo(s)
Ei(s)
=
1+sCR1
R1
R1+R2+sR1R2C
R2R1
Eo(s)
Ei(s)
=
R2
R1+R2
[
1 +sCR1
1 +
sR1R2C
R1+R2
]
On substituting the=
R1+R2
R2
andT=
R1R2
R1+R2
Where,Tandare respectively the time constant and attenuation
constant, we haveTransfer Function =
Eo(s)
Ei(s)
=
1
[
1 +sT
1 +sT
]
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 9 / 30
Phase Lead Compensation...
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage. So taking Laplace transform of both side of
above equations,
Eo(s)
R2
=
1
R1
[Ei(s)Eo(s)] +Cs[Ei(s)Eo(s)]
Eo(s)
Ei(s)
=
1+sCR1
R1
R1+R2+sR1R2C
R2R1
Eo(s)
Ei(s)
=
R2
R1+R2
[
1 +sCR1
1 +
sR1R2C
R1+R2
]
On substituting the=
R1+R2
R2
andT=
R1R2
R1+R2
Where,Tandare respectively the time constant and attenuation
constant, we haveTransfer Function =
Eo(s)
Ei(s)
=
1
[
1 +sT
1 +sT
]
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 9 / 30
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage. So taking Laplace transform of both side of
above equations,
Eo(s)
R2
=
1
R1
[Ei(s)Eo(s)] +Cs[Ei(s)Eo(s)]
Eo(s)
Ei(s)
=
1+sCR1
R1
R1+R2+sR1R2C
R2R1
Eo(s)
Ei(s)
=
R2
R1+R2
[
1 +sCR1
1 +
sR1R2C
R1+R2
]
On substituting the=
R1+R2
R2
andT=
R1R2
R1+R2
Where,Tandare respectively the time constant and attenuation
constant, we haveTransfer Function =
Eo(s)
Ei(s)
=
1
[
1 +sT
1 +sT
]
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 9 / 30
Phase Lead Compensation...
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage. So taking Laplace transform of both side of
above equations,
Eo(s)
R2
=
1
R1
[Ei(s)Eo(s)] +Cs[Ei(s)Eo(s)]
Eo(s)
Ei(s)
=
1+sCR1
R1
R1+R2+sR1R2C
R2R1
Eo(s)
Ei(s)
=
R2
R1+R2
[
1 +sCR1
1 +
sR1R2C
R1+R2
]
On substituting the=
R1+R2
R2
andT=
R1R2
R1+R2
Where,Tandare respectively the time constant and attenuation
constant, we haveTransfer Function =
Eo(s)
Ei(s)
=
1
[
1 +sT
1 +sT
]
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 9 / 30
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage. So taking Laplace transform of both side of
above equations,
Eo(s)
R2
=
1
R1
[Ei(s)Eo(s)] +Cs[Ei(s)Eo(s)]
Eo(s)
Ei(s)
=
1+sCR1
R1
R1+R2+sR1R2C
R2R1
Eo(s)
Ei(s)
=
R2
R1+R2
[
1 +sCR1
1 +
sR1R2C
R1+R2
]
On substituting the=
R1+R2
R2
andT=
R1R2
R1+R2
Where,Tandare respectively the time constant and attenuation
constant, we haveTransfer Function =
Eo(s)
Ei(s)
=
1
[
1 +sT
1 +sT
]
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 9 / 30
Phase Lead Compensation...
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage. So taking Laplace transform of both side of
above equations,
Eo(s)
R2
=
1
R1
[Ei(s)Eo(s)] +Cs[Ei(s)Eo(s)]
Eo(s)
Ei(s)
=
1+sCR1
R1
R1+R2+sR1R2C
R2R1
Eo(s)
Ei(s)
=
R2
R1+R2
[
1 +sCR1
1 +
sR1R2C
R1+R2
]
On substituting the=
R1+R2
R2
andT=
R1R2
R1+R2
Where,Tandare respectively the time constant and attenuation
constant, we haveTransfer Function =
Eo(s)
Ei(s)
=
1
[
1 +sT
1 +sT
]
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 9 / 30
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage. So taking Laplace transform of both side of
above equations,
Eo(s)
R2
=
1
R1
[Ei(s)Eo(s)] +Cs[Ei(s)Eo(s)]
Eo(s)
Ei(s)
=
1+sCR1
R1
R1+R2+sR1R2C
R2R1
Eo(s)
Ei(s)
=
R2
R1+R2
[
1 +sCR1
1 +
sR1R2C
R1+R2
]
On substituting the=
R1+R2
R2
andT=
R1R2
R1+R2
Where,Tandare respectively the time constant and attenuation
constant, we haveTransfer Function =
Eo(s)
Ei(s)
=
1
[
1 +sT
1 +sT
]
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 9 / 30
Phase Lead Compensation...
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage. So taking Laplace transform of both side of
above equations,
Eo(s)
R2
=
1
R1
[Ei(s)Eo(s)] +Cs[Ei(s)Eo(s)]
Eo(s)
Ei(s)
=
1+sCR1
R1
R1+R2+sR1R2C
R2R1
Eo(s)
Ei(s)
=
R2
R1+R2
[
1 +sCR1
1 +
sR1R2C
R1+R2
]
On substituting the=
R1+R2
R2
andT=
R1R2
R1+R2
Where,Tandare respectively the time constant and attenuation
constant, we haveTransfer Function =
Eo(s)
Ei(s)
=
1
[
1 +sT
1 +sT
]
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 9 / 30
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage. So taking Laplace transform of both side of
above equations,
Eo(s)
R2
=
1
R1
[Ei(s)Eo(s)] +Cs[Ei(s)Eo(s)]
Eo(s)
Ei(s)
=
1+sCR1
R1
R1+R2+sR1R2C
R2R1
Eo(s)
Ei(s)
=
R2
R1+R2
[
1 +sCR1
1 +
sR1R2C
R1+R2
]
On substituting the=
R1+R2
R2
andT=
R1R2
R1+R2
Where,Tandare respectively the time constant and attenuation
constant, we haveTransfer Function =
Eo(s)
Ei(s)
=
1
[
1 +sT
1 +sT
]
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 9 / 30
Phase Lead Compensation...
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage. So taking Laplace transform of both side of
above equations,
Eo(s)
R2
=
1
R1
[Ei(s)Eo(s)] +Cs[Ei(s)Eo(s)]
Eo(s)
Ei(s)
=
1+sCR1
R1
R1+R2+sR1R2C
R2R1
Eo(s)
Ei(s)
=
R2
R1+R2
[
1 +sCR1
1 +
sR1R2C
R1+R2
]
On substituting the=
R1+R2
R2
andT=
R1R2
R1+R2
Where,Tandare respectively the time constant and attenuation
constant, we haveTransfer Function =
Eo(s)
Ei(s)
=
1
[
1 +sT
1 +sT
]
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 9 / 30
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage. So taking Laplace transform of both side of
above equations,
Eo(s)
R2
=
1
R1
[Ei(s)Eo(s)] +Cs[Ei(s)Eo(s)]
Eo(s)
Ei(s)
=
1+sCR1
R1
R1+R2+sR1R2C
R2R1
Eo(s)
Ei(s)
=
R2
R1+R2
[
1 +sCR1
1 +
sR1R2C
R1+R2
]
On substituting the=
R1+R2
R2
andT=
R1R2
R1+R2
Where,Tandare respectively the time constant and attenuation
constant, we haveTransfer Function =
Eo(s)
Ei(s)
=
1
[
1 +sT
1 +sT
]
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 9 / 30
Phase Lead Compensation...
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage. So taking Laplace transform of both side of
above equations,
Eo(s)
R2
=
1
R1
[Ei(s)Eo(s)] +Cs[Ei(s)Eo(s)]
Eo(s)
Ei(s)
=
1+sCR1
R1
R1+R2+sR1R2C
R2R1
Eo(s)
Ei(s)
=
R2
R1+R2
[
1 +sCR1
1 +
sR1R2C
R1+R2
]
On substituting the=
R1+R2
R2
andT=
R1R2
R1+R2
Where,Tandare respectively the time constant and attenuation
constant, we haveTransfer Function =
Eo(s)
Ei(s)
=
1
[
1 +sT
1 +sT
]
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 9 / 30
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage. So taking Laplace transform of both side of
above equations,
Eo(s)
R2
=
1
R1
[Ei(s)Eo(s)] +Cs[Ei(s)Eo(s)]
Eo(s)
Ei(s)
=
1+sCR1
R1
R1+R2+sR1R2C
R2R1
Eo(s)
Ei(s)
=
R2
R1+R2
[
1 +sCR1
1 +
sR1R2C
R1+R2
]
On substituting the=
R1+R2
R2
andT=
R1R2
R1+R2
Where,Tandare respectively the time constant and attenuation
constant, we haveTransfer Function =
Eo(s)
Ei(s)
=
1
[
1 +sT
1 +sT
]
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 9 / 30
Phase Lead Compensation...
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage. So taking Laplace transform of both side of
above equations,
Eo(s)
R2
=
1
R1
[Ei(s)Eo(s)] +Cs[Ei(s)Eo(s)]
Eo(s)
Ei(s)
=
1+sCR1
R1
R1+R2+sR1R2C
R2R1
Eo(s)
Ei(s)
=
R2
R1+R2
[
1 +sCR1
1 +
sR1R2C
R1+R2
]
On substituting the=
R1+R2
R2
andT=
R1R2
R1+R2
Where,Tandare respectively the time constant and attenuation
constant, we haveTransfer Function =
Eo(s)
Ei(s)
=
1
[
1 +sT
1 +sT
]
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 9 / 30
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage. So taking Laplace transform of both side of
above equations,
Eo(s)
R2
=
1
R1
[Ei(s)Eo(s)] +Cs[Ei(s)Eo(s)]
Eo(s)
Ei(s)
=
1+sCR1
R1
R1+R2+sR1R2C
R2R1
Eo(s)
Ei(s)
=
R2
R1+R2
[
1 +sCR1
1 +
sR1R2C
R1+R2
]
On substituting the=
R1+R2
R2
andT=
R1R2
R1+R2
Where,Tandare respectively the time constant and attenuation
constant, we haveTransfer Function =
Eo(s)
Ei(s)
=
1
[
1 +sT
1 +sT
]
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 9 / 30
Phase Lead Compensation...
The above network can be visualized as an amplier with a gain of
1
. Let
us draw the pole zero plot for the above transfer function.
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 10 / 30
The above network can be visualized as an amplier with a gain of
1
. Let
us draw the pole zero plot for the above transfer function.
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 10 / 30
Phase Lead Compensation...
The above network can be visualized as an amplier with a gain of
1
. Let
us draw the pole zero plot for the above transfer function.
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 10 / 30
The above network can be visualized as an amplier with a gain of
1
. Let
us draw the pole zero plot for the above transfer function.
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 10 / 30
Phase Lead Compensation...
The above network can be visualized as an amplier with a gain of
1
. Let
us draw the pole zero plot for the above transfer function.
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 10 / 30
The above network can be visualized as an amplier with a gain of
1
. Let
us draw the pole zero plot for the above transfer function.
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 10 / 30
Phase Lead Compensation...
Clearly we have
1
T
(which is a zero of the transfer function) is closer to
origin than the
1
T
- (which is the pole of the transfer function).
Thus we
can say in the lead compensator zero is more dominating than the pole
and because of this lead network introduces positive phase angle to the
system when connected in series.
Let us substitutes=j!in the above transfer function and also we have
<1. On nding the phase angle function for the transfer function we
have
Transfer Function =
Eo(j!)
Ei(j!)
=
1
[
1 +j!T
1 +j!T
]
(!) =tan
1
(!T)tan
1
(!T)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 11 / 30
Clearly we have
1
T
(which is a zero of the transfer function) is closer to
origin than the
1
T
- (which is the pole of the transfer function).
Thus we
can say in the lead compensator zero is more dominating than the pole
and because of this lead network introduces positive phase angle to the
system when connected in series.
Let us substitutes=j!in the above transfer function and also we have
<1. On nding the phase angle function for the transfer function we
have
Transfer Function =
Eo(j!)
Ei(j!)
=
1
[
1 +j!T
1 +j!T
]
(!) =tan
1
(!T)tan
1
(!T)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 11 / 30
Phase Lead Compensation...
Clearly we have
1
T
(which is a zero of the transfer function) is closer to
origin than the
1
T
- (which is the pole of the transfer function).
Thus we
can say in the lead compensator zero is more dominating than the pole
and because of this lead network introduces positive phase angle to the
system when connected in series.
Let us substitutes=j!in the above transfer function and also we have
<1. On nding the phase angle function for the transfer function we
have
Transfer Function =
Eo(j!)
Ei(j!)
=
1
[
1 +j!T
1 +j!T
]
(!) =tan
1
(!T)tan
1
(!T)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 11 / 30
Clearly we have
1
T
(which is a zero of the transfer function) is closer to
origin than the
1
T
- (which is the pole of the transfer function).
Thus we
can say in the lead compensator zero is more dominating than the pole
and because of this lead network introduces positive phase angle to the
system when connected in series.
Let us substitutes=j!in the above transfer function and also we have
<1. On nding the phase angle function for the transfer function we
have
Transfer Function =
Eo(j!)
Ei(j!)
=
1
[
1 +j!T
1 +j!T
]
(!) =tan
1
(!T)tan
1
(!T)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 11 / 30
Phase Lead Compensation...
Clearly we have
1
T
(which is a zero of the transfer function) is closer to
origin than the
1
T
- (which is the pole of the transfer function).
Thus we
can say in the lead compensator zero is more dominating than the pole
and because of this lead network introduces positive phase angle to the
system when connected in series.
Let us substitutes=j!in the above transfer function and also we have
<1. On nding the phase angle function for the transfer function we
have
Transfer Function =
Eo(j!)
Ei(j!)
=
1
[
1 +j!T
1 +j!T
]
(!) =tan
1
(!T)tan
1
(!T)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 11 / 30
Clearly we have
1
T
(which is a zero of the transfer function) is closer to
origin than the
1
T
- (which is the pole of the transfer function).
Thus we
can say in the lead compensator zero is more dominating than the pole
and because of this lead network introduces positive phase angle to the
system when connected in series.
Let us substitutes=j!in the above transfer function and also we have
<1. On nding the phase angle function for the transfer function we
have
Transfer Function =
Eo(j!)
Ei(j!)
=
1
[
1 +j!T
1 +j!T
]
(!) =tan
1
(!T)tan
1
(!T)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 11 / 30
Phase Lead Compensation...
Clearly we have
1
T
(which is a zero of the transfer function) is closer to
origin than the
1
T
- (which is the pole of the transfer function).
Thus we
can say in the lead compensator zero is more dominating than the pole
and because of this lead network introduces positive phase angle to the
system when connected in series.
Let us substitutes=j!in the above transfer function and also we have
<1. On nding the phase angle function for the transfer function we
have
Transfer Function =
Eo(j!)
Ei(j!)
=
1
[
1 +j!T
1 +j!T
]
(!) =tan
1
(!T)tan
1
(!T)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 11 / 30
Clearly we have
1
T
(which is a zero of the transfer function) is closer to
origin than the
1
T
- (which is the pole of the transfer function).
Thus we
can say in the lead compensator zero is more dominating than the pole
and because of this lead network introduces positive phase angle to the
system when connected in series.
Let us substitutes=j!in the above transfer function and also we have
<1. On nding the phase angle function for the transfer function we
have
Transfer Function =
Eo(j!)
Ei(j!)
=
1
[
1 +j!T
1 +j!T
]
(!) =tan
1
(!T)tan
1
(!T)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 11 / 30
Phase Lead Compensation...
Clearly we have
1
T
(which is a zero of the transfer function) is closer to
origin than the
1
T
- (which is the pole of the transfer function).
Thus we
can say in the lead compensator zero is more dominating than the pole
and because of this lead network introduces positive phase angle to the
system when connected in series.
Let us substitutes=j!in the above transfer function and also we have
<1. On nding the phase angle function for the transfer function we
have
Transfer Function =
Eo(j!)
Ei(j!)
=
1
[
1 +j!T
1 +j!T
]
(!) =tan
1
(!T)tan
1
(!T)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 11 / 30
Clearly we have
1
T
(which is a zero of the transfer function) is closer to
origin than the
1
T
- (which is the pole of the transfer function).
Thus we
can say in the lead compensator zero is more dominating than the pole
and because of this lead network introduces positive phase angle to the
system when connected in series.
Let us substitutes=j!in the above transfer function and also we have
<1. On nding the phase angle function for the transfer function we
have
Transfer Function =
Eo(j!)
Ei(j!)
=
1
[
1 +j!T
1 +j!T
]
(!) =tan
1
(!T)tan
1
(!T)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 11 / 30
Eect of Phase Lead Compensation
1
The slope of the magnitude plot reduces at the gain crossover
frequency so that relative stability improves and error decrease due to
error is directly proportional to the slope.
2
Phase margin increases.
3
Response become faster.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 12 / 30
1
The slope of the magnitude plot reduces at the gain crossover
frequency so that relative stability improves and error decrease due to
error is directly proportional to the slope.
2
Phase margin increases.
3
Response become faster.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 12 / 30
Eect of Phase Lead Compensation
1
The slope of the magnitude plot reduces at the gain crossover
frequency so that relative stability improves and error decrease due to
error is directly proportional to the slope.
2
Phase margin increases.
3
Response become faster.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 12 / 30
1
The slope of the magnitude plot reduces at the gain crossover
frequency so that relative stability improves and error decrease due to
error is directly proportional to the slope.
2
Phase margin increases.
3
Response become faster.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 12 / 30
Eect of Phase Lead Compensation
1
The slope of the magnitude plot reduces at the gain crossover
frequency so that relative stability improves and error decrease due to
error is directly proportional to the slope.
2
Phase margin increases.
3
Response become faster.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 12 / 30
1
The slope of the magnitude plot reduces at the gain crossover
frequency so that relative stability improves and error decrease due to
error is directly proportional to the slope.
2
Phase margin increases.
3
Response become faster.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 12 / 30
Advantages of Phase Lead Compensation
1
Due to the presence of phase lead network the speed of the system
increases because it shifts gain crossover frequency to a higher value.
2
Due to the presence of phase lead compensation maximum overshoot
of the system decreases.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 13 / 30
1
Due to the presence of phase lead network the speed of the system
increases because it shifts gain crossover frequency to a higher value.
2
Due to the presence of phase lead compensation maximum overshoot
of the system decreases.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 13 / 30
Advantages of Phase Lead Compensation
1
Due to the presence of phase lead network the speed of the system
increases because it shifts gain crossover frequency to a higher value.
2
Due to the presence of phase lead compensation maximum overshoot
of the system decreases.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 13 / 30
1
Due to the presence of phase lead network the speed of the system
increases because it shifts gain crossover frequency to a higher value.
2
Due to the presence of phase lead compensation maximum overshoot
of the system decreases.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 13 / 30
Disadvantages of Phase Lead Compensation
1
Steady state error is not improved.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 14 / 30
1
Steady state error is not improved.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 14 / 30
Phase Lag Compensation A system which has one zero and one dominating pole ( the pole which is
closer to origin that all other poles is known as dominating pole) is known
as lag network.
If we want to add a dominating pole for compensation in
control system then, we have to select a lag compensation network. The
basic requirement of the phase lag network is that all poles and zeros of
the transfer function of the network must lie in (-)ve real axis interlacing
each other with a pole located or on the nearest to the origin.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 15 / 30
closer to origin that all other poles is known as dominating pole) is known
as lag network.
If we want to add a dominating pole for compensation in
control system then, we have to select a lag compensation network. The
basic requirement of the phase lag network is that all poles and zeros of
the transfer function of the network must lie in (-)ve real axis interlacing
each other with a pole located or on the nearest to the origin.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 15 / 30
Phase Lag Compensation A system which has one zero and one dominating pole ( the pole which is
closer to origin that all other poles is known as dominating pole) is known
as lag network.
If we want to add a dominating pole for compensation in
control system then, we have to select a lag compensation network. The
basic requirement of the phase lag network is that all poles and zeros of
the transfer function of the network must lie in (-)ve real axis interlacing
each other with a pole located or on the nearest to the origin.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 15 / 30
closer to origin that all other poles is known as dominating pole) is known
as lag network.
If we want to add a dominating pole for compensation in
control system then, we have to select a lag compensation network. The
basic requirement of the phase lag network is that all poles and zeros of
the transfer function of the network must lie in (-)ve real axis interlacing
each other with a pole located or on the nearest to the origin.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 15 / 30
Phase Lag Compensation A system which has one zero and one dominating pole ( the pole which is
closer to origin that all other poles is known as dominating pole) is known
as lag network.
If we want to add a dominating pole for compensation in
control system then, we have to select a lag compensation network. The
basic requirement of the phase lag network is that all poles and zeros of
the transfer function of the network must lie in (-)ve real axis interlacing
each other with a pole located or on the nearest to the origin.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 15 / 30
closer to origin that all other poles is known as dominating pole) is known
as lag network.
If we want to add a dominating pole for compensation in
control system then, we have to select a lag compensation network. The
basic requirement of the phase lag network is that all poles and zeros of
the transfer function of the network must lie in (-)ve real axis interlacing
each other with a pole located or on the nearest to the origin.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 15 / 30
Phase Lag Compensation... The Lag Compensator is an electrical network which produces a sinusoidal
output having the phase lag when a sinusoidal input is applied. The lag
compensator circuit in the 's' domain is shown in gure.
Figure :
Here, the capacitor is in series with the resistorR2and the output is
measured across this combination.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 16 / 30
output having the phase lag when a sinusoidal input is applied. The lag
compensator circuit in the 's' domain is shown in gure.
Figure :
Here, the capacitor is in series with the resistorR2and the output is
measured across this combination.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 16 / 30
Phase Lag Compensation... The Lag Compensator is an electrical network which produces a sinusoidal
output having the phase lag when a sinusoidal input is applied. The lag
compensator circuit in the 's' domain is shown in gure.
Figure :
Here, the capacitor is in series with the resistorR2and the output is
measured across this combination.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 16 / 30
output having the phase lag when a sinusoidal input is applied. The lag
compensator circuit in the 's' domain is shown in gure.
Figure :
Here, the capacitor is in series with the resistorR2and the output is
measured across this combination.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 16 / 30
Phase Lag Compensation... The Lag Compensator is an electrical network which produces a sinusoidal
output having the phase lag when a sinusoidal input is applied. The lag
compensator circuit in the 's' domain is shown in gure.
Figure :
Here, the capacitor is in series with the resistorR2and the output is
measured across this combination.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 16 / 30
output having the phase lag when a sinusoidal input is applied. The lag
compensator circuit in the 's' domain is shown in gure.
Figure :
Here, the capacitor is in series with the resistorR2and the output is
measured across this combination.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 16 / 30
Phase Lag Compensation... The Lag Compensator is an electrical network which produces a sinusoidal
output having the phase lag when a sinusoidal input is applied. The lag
compensator circuit in the 's' domain is shown in gure.
Figure :
Here, the capacitor is in series with the resistorR2and the output is
measured across this combination.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 16 / 30
output having the phase lag when a sinusoidal input is applied. The lag
compensator circuit in the 's' domain is shown in gure.
Figure :
Here, the capacitor is in series with the resistorR2and the output is
measured across this combination.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 16 / 30
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Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 17 / 30
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 17 / 30
Phase Lag Compensation... The transfer function of this lag compensator is
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 18 / 30
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 18 / 30
Phase Lag Compensation... The transfer function of this lag compensator is
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 18 / 30
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 18 / 30
Phase Lag Compensation... The transfer function of this lag compensator is
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 18 / 30
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 18 / 30
Phase Lag Compensation...
We will have the output at the series combination of the resistor R2 and
the capacitor C. From the above circuit diagram, we getei=iR1+iR2+
1
C
Z
idt
eo=iR2+
1
C
Z
idt
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage.
Taking Laplace transform of above two equation we get,
Ei(s) =R1I(s) +R2I(s) +
1
Cs
I(s)
Eo(s) =R2I(s) +
1
Cs
I(s)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 19 / 30
We will have the output at the series combination of the resistor R2 and
the capacitor C. From the above circuit diagram, we getei=iR1+iR2+
1
C
Z
idt
eo=iR2+
1
C
Z
idt
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage.
Taking Laplace transform of above two equation we get,
Ei(s) =R1I(s) +R2I(s) +
1
Cs
I(s)
Eo(s) =R2I(s) +
1
Cs
I(s)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 19 / 30
Phase Lag Compensation...
We will have the output at the series combination of the resistor R2 and
the capacitor C. From the above circuit diagram, we getei=iR1+iR2+
1
C
Z
idt
eo=iR2+
1
C
Z
idt
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage.
Taking Laplace transform of above two equation we get,
Ei(s) =R1I(s) +R2I(s) +
1
Cs
I(s)
Eo(s) =R2I(s) +
1
Cs
I(s)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 19 / 30
We will have the output at the series combination of the resistor R2 and
the capacitor C. From the above circuit diagram, we getei=iR1+iR2+
1
C
Z
idt
eo=iR2+
1
C
Z
idt
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage.
Taking Laplace transform of above two equation we get,
Ei(s) =R1I(s) +R2I(s) +
1
Cs
I(s)
Eo(s) =R2I(s) +
1
Cs
I(s)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 19 / 30
Phase Lag Compensation...
We will have the output at the series combination of the resistor R2 and
the capacitor C. From the above circuit diagram, we getei=iR1+iR2+
1
C
Z
idt
eo=iR2+
1
C
Z
idt
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage.
Taking Laplace transform of above two equation we get,
Ei(s) =R1I(s) +R2I(s) +
1
Cs
I(s)
Eo(s) =R2I(s) +
1
Cs
I(s)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 19 / 30
We will have the output at the series combination of the resistor R2 and
the capacitor C. From the above circuit diagram, we getei=iR1+iR2+
1
C
Z
idt
eo=iR2+
1
C
Z
idt
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage.
Taking Laplace transform of above two equation we get,
Ei(s) =R1I(s) +R2I(s) +
1
Cs
I(s)
Eo(s) =R2I(s) +
1
Cs
I(s)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 19 / 30
Phase Lag Compensation...
We will have the output at the series combination of the resistor R2 and
the capacitor C. From the above circuit diagram, we getei=iR1+iR2+
1
C
Z
idt
eo=iR2+
1
C
Z
idt
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage.
Taking Laplace transform of above two equation we get,
Ei(s) =R1I(s) +R2I(s) +
1
Cs
I(s)
Eo(s) =R2I(s) +
1
Cs
I(s)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 19 / 30
We will have the output at the series combination of the resistor R2 and
the capacitor C. From the above circuit diagram, we getei=iR1+iR2+
1
C
Z
idt
eo=iR2+
1
C
Z
idt
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage.
Taking Laplace transform of above two equation we get,
Ei(s) =R1I(s) +R2I(s) +
1
Cs
I(s)
Eo(s) =R2I(s) +
1
Cs
I(s)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 19 / 30
Phase Lag Compensation...
We will have the output at the series combination of the resistor R2 and
the capacitor C. From the above circuit diagram, we getei=iR1+iR2+
1
C
Z
idt
eo=iR2+
1
C
Z
idt
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage.
Taking Laplace transform of above two equation we get,
Ei(s) =R1I(s) +R2I(s) +
1
Cs
I(s)
Eo(s) =R2I(s) +
1
Cs
I(s)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 19 / 30
We will have the output at the series combination of the resistor R2 and
the capacitor C. From the above circuit diagram, we getei=iR1+iR2+
1
C
Z
idt
eo=iR2+
1
C
Z
idt
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage.
Taking Laplace transform of above two equation we get,
Ei(s) =R1I(s) +R2I(s) +
1
Cs
I(s)
Eo(s) =R2I(s) +
1
Cs
I(s)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 19 / 30
Phase Lag Compensation...
We will have the output at the series combination of the resistor R2 and
the capacitor C. From the above circuit diagram, we getei=iR1+iR2+
1
C
Z
idt
eo=iR2+
1
C
Z
idt
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage.
Taking Laplace transform of above two equation we get,
Ei(s) =R1I(s) +R2I(s) +
1
Cs
I(s)
Eo(s) =R2I(s) +
1
Cs
I(s)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 19 / 30
We will have the output at the series combination of the resistor R2 and
the capacitor C. From the above circuit diagram, we getei=iR1+iR2+
1
C
Z
idt
eo=iR2+
1
C
Z
idt
Now let us determine the transfer function for the given network and the
transfer function can be determined by nding the ratio of the output
voltage to the input voltage.
Taking Laplace transform of above two equation we get,
Ei(s) =R1I(s) +R2I(s) +
1
Cs
I(s)
Eo(s) =R2I(s) +
1
Cs
I(s)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 19 / 30
Phase Lag Compensation...
Transfer Function =
Eo(s)
Ei(s)
=
R2+
1
Cs
R1+R2+
1
Cs
G(s) =
1 +R2Cs
1 + (R1+R2)Cs
On substituting theT=R2Cand=
R1+R2
R1
, Where,Tandare
respectively the time constant and DC gain
Transfer Function =G(s) =
1 +Ts
1 +Ts
The above network provides a high frequency gain of
1
. Let us draw the
pole zero plot for the above transfer function.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 20 / 30
Transfer Function =
Eo(s)
Ei(s)
=
R2+
1
Cs
R1+R2+
1
Cs
G(s) =
1 +R2Cs
1 + (R1+R2)Cs
On substituting theT=R2Cand=
R1+R2
R1
, Where,Tandare
respectively the time constant and DC gain
Transfer Function =G(s) =
1 +Ts
1 +Ts
The above network provides a high frequency gain of
1
. Let us draw the
pole zero plot for the above transfer function.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 20 / 30
Phase Lag Compensation...
Transfer Function =
Eo(s)
Ei(s)
=
R2+
1
Cs
R1+R2+
1
Cs
G(s) =
1 +R2Cs
1 + (R1+R2)Cs
On substituting theT=R2Cand=
R1+R2
R1
, Where,Tandare
respectively the time constant and DC gain
Transfer Function =G(s) =
1 +Ts
1 +Ts
The above network provides a high frequency gain of
1
. Let us draw the
pole zero plot for the above transfer function.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 20 / 30
Transfer Function =
Eo(s)
Ei(s)
=
R2+
1
Cs
R1+R2+
1
Cs
G(s) =
1 +R2Cs
1 + (R1+R2)Cs
On substituting theT=R2Cand=
R1+R2
R1
, Where,Tandare
respectively the time constant and DC gain
Transfer Function =G(s) =
1 +Ts
1 +Ts
The above network provides a high frequency gain of
1
. Let us draw the
pole zero plot for the above transfer function.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 20 / 30
Phase Lag Compensation...
Transfer Function =
Eo(s)
Ei(s)
=
R2+
1
Cs
R1+R2+
1
Cs
G(s) =
1 +R2Cs
1 + (R1+R2)Cs
On substituting theT=R2Cand=
R1+R2
R1
, Where,Tandare
respectively the time constant and DC gain
Transfer Function =G(s) =
1 +Ts
1 +Ts
The above network provides a high frequency gain of
1
. Let us draw the
pole zero plot for the above transfer function.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 20 / 30
Transfer Function =
Eo(s)
Ei(s)
=
R2+
1
Cs
R1+R2+
1
Cs
G(s) =
1 +R2Cs
1 + (R1+R2)Cs
On substituting theT=R2Cand=
R1+R2
R1
, Where,Tandare
respectively the time constant and DC gain
Transfer Function =G(s) =
1 +Ts
1 +Ts
The above network provides a high frequency gain of
1
. Let us draw the
pole zero plot for the above transfer function.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 20 / 30
Phase Lag Compensation...
Transfer Function =
Eo(s)
Ei(s)
=
R2+
1
Cs
R1+R2+
1
Cs
G(s) =
1 +R2Cs
1 + (R1+R2)Cs
On substituting theT=R2Cand=
R1+R2
R1
, Where,Tandare
respectively the time constant and DC gain
Transfer Function =G(s) =
1 +Ts
1 +Ts
The above network provides a high frequency gain of
1
. Let us draw the
pole zero plot for the above transfer function.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 20 / 30
Transfer Function =
Eo(s)
Ei(s)
=
R2+
1
Cs
R1+R2+
1
Cs
G(s) =
1 +R2Cs
1 + (R1+R2)Cs
On substituting theT=R2Cand=
R1+R2
R1
, Where,Tandare
respectively the time constant and DC gain
Transfer Function =G(s) =
1 +Ts
1 +Ts
The above network provides a high frequency gain of
1
. Let us draw the
pole zero plot for the above transfer function.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 20 / 30
Phase Lag Compensation...
Transfer Function =
Eo(s)
Ei(s)
=
R2+
1
Cs
R1+R2+
1
Cs
G(s) =
1 +R2Cs
1 + (R1+R2)Cs
On substituting theT=R2Cand=
R1+R2
R1
, Where,Tandare
respectively the time constant and DC gain
Transfer Function =G(s) =
1 +Ts
1 +Ts
The above network provides a high frequency gain of
1
. Let us draw the
pole zero plot for the above transfer function.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 20 / 30
Transfer Function =
Eo(s)
Ei(s)
=
R2+
1
Cs
R1+R2+
1
Cs
G(s) =
1 +R2Cs
1 + (R1+R2)Cs
On substituting theT=R2Cand=
R1+R2
R1
, Where,Tandare
respectively the time constant and DC gain
Transfer Function =G(s) =
1 +Ts
1 +Ts
The above network provides a high frequency gain of
1
. Let us draw the
pole zero plot for the above transfer function.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 20 / 30
Phase Lag Compensation...
Transfer Function =
Eo(s)
Ei(s)
=
R2+
1
Cs
R1+R2+
1
Cs
G(s) =
1 +R2Cs
1 + (R1+R2)Cs
On substituting theT=R2Cand=
R1+R2
R1
, Where,Tandare
respectively the time constant and DC gain
Transfer Function =G(s) =
1 +Ts
1 +Ts
The above network provides a high frequency gain of
1
. Let us draw the
pole zero plot for the above transfer function.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 20 / 30
Transfer Function =
Eo(s)
Ei(s)
=
R2+
1
Cs
R1+R2+
1
Cs
G(s) =
1 +R2Cs
1 + (R1+R2)Cs
On substituting theT=R2Cand=
R1+R2
R1
, Where,Tandare
respectively the time constant and DC gain
Transfer Function =G(s) =
1 +Ts
1 +Ts
The above network provides a high frequency gain of
1
. Let us draw the
pole zero plot for the above transfer function.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 20 / 30
Phase Lag Compensation...
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 21 / 30
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 21 / 30
Phase Lag Compensation...
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 21 / 30
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 21 / 30
Phase Lag Compensation...
Clearly we have
1
T
(which is a zero of the transfer function) is far to
origin than the
1
T
(which is the pole of the transfer function). Thus we
can say in the lag compensator pole is more dominating than the zero and
because of this lag network introduces negative phase angle to the system
when connected in series.
Let us substitutes=j!in the above transfer function and also we have
<1. On nding the phase angle function for the transfer function we
have
(!) = tan
1
(!T)tan
1
(!T)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 22 / 30
Clearly we have
1
T
(which is a zero of the transfer function) is far to
origin than the
1
T
(which is the pole of the transfer function). Thus we
can say in the lag compensator pole is more dominating than the zero and
because of this lag network introduces negative phase angle to the system
when connected in series.
Let us substitutes=j!in the above transfer function and also we have
<1. On nding the phase angle function for the transfer function we
have
(!) = tan
1
(!T)tan
1
(!T)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 22 / 30
Phase Lag Compensation...
Clearly we have
1
T
(which is a zero of the transfer function) is far to
origin than the
1
T
(which is the pole of the transfer function). Thus we
can say in the lag compensator pole is more dominating than the zero and
because of this lag network introduces negative phase angle to the system
when connected in series.
Let us substitutes=j!in the above transfer function and also we have
<1. On nding the phase angle function for the transfer function we
have
(!) = tan
1
(!T)tan
1
(!T)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 22 / 30
Clearly we have
1
T
(which is a zero of the transfer function) is far to
origin than the
1
T
(which is the pole of the transfer function). Thus we
can say in the lag compensator pole is more dominating than the zero and
because of this lag network introduces negative phase angle to the system
when connected in series.
Let us substitutes=j!in the above transfer function and also we have
<1. On nding the phase angle function for the transfer function we
have
(!) = tan
1
(!T)tan
1
(!T)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 22 / 30
Phase Lag Compensation...
Clearly we have
1
T
(which is a zero of the transfer function) is far to
origin than the
1
T
(which is the pole of the transfer function). Thus we
can say in the lag compensator pole is more dominating than the zero and
because of this lag network introduces negative phase angle to the system
when connected in series.
Let us substitutes=j!in the above transfer function and also we have
<1. On nding the phase angle function for the transfer function we
have
(!) = tan
1
(!T)tan
1
(!T)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 22 / 30
Clearly we have
1
T
(which is a zero of the transfer function) is far to
origin than the
1
T
(which is the pole of the transfer function). Thus we
can say in the lag compensator pole is more dominating than the zero and
because of this lag network introduces negative phase angle to the system
when connected in series.
Let us substitutes=j!in the above transfer function and also we have
<1. On nding the phase angle function for the transfer function we
have
(!) = tan
1
(!T)tan
1
(!T)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 22 / 30
Phase Lag Compensation...
Clearly we have
1
T
(which is a zero of the transfer function) is far to
origin than the
1
T
(which is the pole of the transfer function). Thus we
can say in the lag compensator pole is more dominating than the zero and
because of this lag network introduces negative phase angle to the system
when connected in series.
Let us substitutes=j!in the above transfer function and also we have
<1. On nding the phase angle function for the transfer function we
have
(!) = tan
1
(!T)tan
1
(!T)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 22 / 30
Clearly we have
1
T
(which is a zero of the transfer function) is far to
origin than the
1
T
(which is the pole of the transfer function). Thus we
can say in the lag compensator pole is more dominating than the zero and
because of this lag network introduces negative phase angle to the system
when connected in series.
Let us substitutes=j!in the above transfer function and also we have
<1. On nding the phase angle function for the transfer function we
have
(!) = tan
1
(!T)tan
1
(!T)
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 22 / 30
Eect of Phase Lag Compensation
1
Gain crossover frequency increases.
2
Bandwidth decreases.
3
Phase margin will be increase.
4
Response will be slower before due to decreasing bandwidth, the rise
time and the settling time become larger.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 23 / 30
1
Gain crossover frequency increases.
2
Bandwidth decreases.
3
Phase margin will be increase.
4
Response will be slower before due to decreasing bandwidth, the rise
time and the settling time become larger.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 23 / 30
Eect of Phase Lag Compensation
1
Gain crossover frequency increases.
2
Bandwidth decreases.
3
Phase margin will be increase.
4
Response will be slower before due to decreasing bandwidth, the rise
time and the settling time become larger.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 23 / 30
1
Gain crossover frequency increases.
2
Bandwidth decreases.
3
Phase margin will be increase.
4
Response will be slower before due to decreasing bandwidth, the rise
time and the settling time become larger.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 23 / 30
Eect of Phase Lag Compensation
1
Gain crossover frequency increases.
2
Bandwidth decreases.
3
Phase margin will be increase.
4
Response will be slower before due to decreasing bandwidth, the rise
time and the settling time become larger.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 23 / 30
1
Gain crossover frequency increases.
2
Bandwidth decreases.
3
Phase margin will be increase.
4
Response will be slower before due to decreasing bandwidth, the rise
time and the settling time become larger.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 23 / 30
Eect of Phase Lag Compensation
1
Gain crossover frequency increases.
2
Bandwidth decreases.
3
Phase margin will be increase.
4
Response will be slower before due to decreasing bandwidth, the rise
time and the settling time become larger.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 23 / 30
1
Gain crossover frequency increases.
2
Bandwidth decreases.
3
Phase margin will be increase.
4
Response will be slower before due to decreasing bandwidth, the rise
time and the settling time become larger.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 23 / 30
Advantages of Phase Lag Compensation
1
Phase lag network allows low frequencies and high frequencies are
attenuated.
2
Due to the presence of phase lag compensation the steady state
accuracy increases.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 24 / 30
1
Phase lag network allows low frequencies and high frequencies are
attenuated.
2
Due to the presence of phase lag compensation the steady state
accuracy increases.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 24 / 30
Advantages of Phase Lag Compensation
1
Phase lag network allows low frequencies and high frequencies are
attenuated.
2
Due to the presence of phase lag compensation the steady state
accuracy increases.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 24 / 30
1
Phase lag network allows low frequencies and high frequencies are
attenuated.
2
Due to the presence of phase lag compensation the steady state
accuracy increases.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 24 / 30
Disadvantages of Phase Lag Compensation
1
Due to the presence of phase lag compensation the speed of the
system decreases.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 25 / 30
1
Due to the presence of phase lag compensation the speed of the
system decreases.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 25 / 30
Phase Lag Lead Compensation With single lag or lead compensation may not satised design
specications.
For an unstable uncompensated system, lead compensation
provides fast response but does not provide enough phase margin whereas
lag compensation stabilize the system but does not provide enough
bandwidth.
So we need multiple compensators in cascade.
Given below is the circuit diagram for the phase lag- lead compensation
network.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 26 / 30
specications.
For an unstable uncompensated system, lead compensation
provides fast response but does not provide enough phase margin whereas
lag compensation stabilize the system but does not provide enough
bandwidth.
So we need multiple compensators in cascade.
Given below is the circuit diagram for the phase lag- lead compensation
network.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 26 / 30
Phase Lag Lead Compensation With single lag or lead compensation may not satised design
specications.
For an unstable uncompensated system, lead compensation
provides fast response but does not provide enough phase margin whereas
lag compensation stabilize the system but does not provide enough
bandwidth.
So we need multiple compensators in cascade.
Given below is the circuit diagram for the phase lag- lead compensation
network.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 26 / 30
specications.
For an unstable uncompensated system, lead compensation
provides fast response but does not provide enough phase margin whereas
lag compensation stabilize the system but does not provide enough
bandwidth.
So we need multiple compensators in cascade.
Given below is the circuit diagram for the phase lag- lead compensation
network.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 26 / 30
Phase Lag Lead Compensation With single lag or lead compensation may not satised design
specications.
For an unstable uncompensated system, lead compensation
provides fast response but does not provide enough phase margin whereas
lag compensation stabilize the system but does not provide enough
bandwidth.
So we need multiple compensators in cascade.
Given below is the circuit diagram for the phase lag- lead compensation
network.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 26 / 30
specications.
For an unstable uncompensated system, lead compensation
provides fast response but does not provide enough phase margin whereas
lag compensation stabilize the system but does not provide enough
bandwidth.
So we need multiple compensators in cascade.
Given below is the circuit diagram for the phase lag- lead compensation
network.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 26 / 30
Phase Lag Lead Compensation With single lag or lead compensation may not satised design
specications.
For an unstable uncompensated system, lead compensation
provides fast response but does not provide enough phase margin whereas
lag compensation stabilize the system but does not provide enough
bandwidth.
So we need multiple compensators in cascade.
Given below is the circuit diagram for the phase lag- lead compensation
network.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 26 / 30
specications.
For an unstable uncompensated system, lead compensation
provides fast response but does not provide enough phase margin whereas
lag compensation stabilize the system but does not provide enough
bandwidth.
So we need multiple compensators in cascade.
Given below is the circuit diagram for the phase lag- lead compensation
network.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 26 / 30
Phase Lag Lead Compensation With single lag or lead compensation may not satised design
specications.
For an unstable uncompensated system, lead compensation
provides fast response but does not provide enough phase margin whereas
lag compensation stabilize the system but does not provide enough
bandwidth.
So we need multiple compensators in cascade.
Given below is the circuit diagram for the phase lag- lead compensation
network.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 26 / 30
specications.
For an unstable uncompensated system, lead compensation
provides fast response but does not provide enough phase margin whereas
lag compensation stabilize the system but does not provide enough
bandwidth.
So we need multiple compensators in cascade.
Given below is the circuit diagram for the phase lag- lead compensation
network.
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 26 / 30
Phase Lag Lead Compensation...
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 27 / 30
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 27 / 30
Phase Lag Lead Compensation...
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 27 / 30
Figure :
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 27 / 30
Phase Lag Lead Compensation...
This circuit looks like both the compensators are cascaded. So, the
transfer function of this circuit will be the product of transfer functions of
the lead and the lag compensators.
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s1+ 1
s1+ 1
1
s+
1
2
s+
1
2
!We know= 1.
)
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s+
1
1
s+
1
1
!
s+
1
2
s+
1
2
!Where,
1=R1C12=R2C2
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 28 / 30
This circuit looks like both the compensators are cascaded. So, the
transfer function of this circuit will be the product of transfer functions of
the lead and the lag compensators.
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s1+ 1
s1+ 1
1
s+
1
2
s+
1
2
!We know= 1.
)
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s+
1
1
s+
1
1
!
s+
1
2
s+
1
2
!Where,
1=R1C12=R2C2
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 28 / 30
Phase Lag Lead Compensation...
This circuit looks like both the compensators are cascaded. So, the
transfer function of this circuit will be the product of transfer functions of
the lead and the lag compensators.
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s1+ 1
s1+ 1
1
s+
1
2
s+
1
2
!We know= 1.
)
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s+
1
1
s+
1
1
!
s+
1
2
s+
1
2
!Where,
1=R1C12=R2C2
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 28 / 30
This circuit looks like both the compensators are cascaded. So, the
transfer function of this circuit will be the product of transfer functions of
the lead and the lag compensators.
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s1+ 1
s1+ 1
1
s+
1
2
s+
1
2
!We know= 1.
)
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s+
1
1
s+
1
1
!
s+
1
2
s+
1
2
!Where,
1=R1C12=R2C2
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 28 / 30
Phase Lag Lead Compensation...
This circuit looks like both the compensators are cascaded. So, the
transfer function of this circuit will be the product of transfer functions of
the lead and the lag compensators.
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s1+ 1
s1+ 1
1
s+
1
2
s+
1
2
!We know= 1.
)
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s+
1
1
s+
1
1
!
s+
1
2
s+
1
2
!Where,
1=R1C12=R2C2
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 28 / 30
This circuit looks like both the compensators are cascaded. So, the
transfer function of this circuit will be the product of transfer functions of
the lead and the lag compensators.
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s1+ 1
s1+ 1
1
s+
1
2
s+
1
2
!We know= 1.
)
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s+
1
1
s+
1
1
!
s+
1
2
s+
1
2
!Where,
1=R1C12=R2C2
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 28 / 30
Phase Lag Lead Compensation...
This circuit looks like both the compensators are cascaded. So, the
transfer function of this circuit will be the product of transfer functions of
the lead and the lag compensators.
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s1+ 1
s1+ 1
1
s+
1
2
s+
1
2
!We know= 1.
)
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s+
1
1
s+
1
1
!
s+
1
2
s+
1
2
!Where,
1=R1C12=R2C2
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 28 / 30
This circuit looks like both the compensators are cascaded. So, the
transfer function of this circuit will be the product of transfer functions of
the lead and the lag compensators.
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s1+ 1
s1+ 1
1
s+
1
2
s+
1
2
!We know= 1.
)
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s+
1
1
s+
1
1
!
s+
1
2
s+
1
2
!Where,
1=R1C12=R2C2
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 28 / 30
Phase Lag Lead Compensation...
This circuit looks like both the compensators are cascaded. So, the
transfer function of this circuit will be the product of transfer functions of
the lead and the lag compensators.
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s1+ 1
s1+ 1
1
s+
1
2
s+
1
2
!We know= 1.
)
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s+
1
1
s+
1
1
!
s+
1
2
s+
1
2
!Where,
1=R1C12=R2C2
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 28 / 30
This circuit looks like both the compensators are cascaded. So, the
transfer function of this circuit will be the product of transfer functions of
the lead and the lag compensators.
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s1+ 1
s1+ 1
1
s+
1
2
s+
1
2
!We know= 1.
)
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s+
1
1
s+
1
1
!
s+
1
2
s+
1
2
!Where,
1=R1C12=R2C2
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 28 / 30
Phase Lag Lead Compensation...
This circuit looks like both the compensators are cascaded. So, the
transfer function of this circuit will be the product of transfer functions of
the lead and the lag compensators.
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s1+ 1
s1+ 1
1
s+
1
2
s+
1
2
!We know= 1.
)
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s+
1
1
s+
1
1
!
s+
1
2
s+
1
2
!Where,
1=R1C12=R2C2
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 28 / 30
This circuit looks like both the compensators are cascaded. So, the
transfer function of this circuit will be the product of transfer functions of
the lead and the lag compensators.
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s1+ 1
s1+ 1
1
s+
1
2
s+
1
2
!We know= 1.
)
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s+
1
1
s+
1
1
!
s+
1
2
s+
1
2
!Where,
1=R1C12=R2C2
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 28 / 30
Phase Lag Lead Compensation...
This circuit looks like both the compensators are cascaded. So, the
transfer function of this circuit will be the product of transfer functions of
the lead and the lag compensators.
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s1+ 1
s1+ 1
1
s+
1
2
s+
1
2
!We know= 1.
)
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s+
1
1
s+
1
1
!
s+
1
2
s+
1
2
!Where,
1=R1C12=R2C2
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 28 / 30
This circuit looks like both the compensators are cascaded. So, the
transfer function of this circuit will be the product of transfer functions of
the lead and the lag compensators.
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s1+ 1
s1+ 1
1
s+
1
2
s+
1
2
!We know= 1.
)
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s+
1
1
s+
1
1
!
s+
1
2
s+
1
2
!Where,
1=R1C12=R2C2
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 28 / 30
Phase Lag Lead Compensation...
This circuit looks like both the compensators are cascaded. So, the
transfer function of this circuit will be the product of transfer functions of
the lead and the lag compensators.
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s1+ 1
s1+ 1
1
s+
1
2
s+
1
2
!We know= 1.
)
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s+
1
1
s+
1
1
!
s+
1
2
s+
1
2
!Where,
1=R1C12=R2C2
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 28 / 30
This circuit looks like both the compensators are cascaded. So, the
transfer function of this circuit will be the product of transfer functions of
the lead and the lag compensators.
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s1+ 1
s1+ 1
1
s+
1
2
s+
1
2
!We know= 1.
)
Vo(s)
Vi(s)
=
Eo(s)
Ei(s)
=
s+
1
1
s+
1
1
!
s+
1
2
s+
1
2
!Where,
1=R1C12=R2C2
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 28 / 30
Comparison between lead and lag compensators
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Comparison between lead and lag compensators
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Comparison between lead and lag compensators
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Comparison between lead and lag compensators
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Comparison between lead and lag compensators
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Comparison between lead and lag compensators
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Comparison between lead and lag compensators
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Comparison between lead and lag compensators
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Comparison between lead and lag compensators
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Comparison between lead and lag compensators
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Comparison between lead and lag compensators
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Comparison between lead and lag compensators
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Comparison between lead and lag compensators
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Lead compensatorLag compensatorHigh passLow passApproximates derivative plus propor-
tional control
Approximates integral plus propor-
tional control
Contributes phase leadAttenuation at high frequenciesIncreases the gain crossover fre-
quency
Moves the gain-crossover frequency
lower
Increases bandwidthReduces bandwidth
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 29 / 30
Thank you
Please send your feedback at [email protected]
For download and more information
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 30 / 30
Please send your feedback at [email protected]
For download and more information
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 30 / 30
Thank you
Please send your feedback at [email protected]
For download and more information
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 30 / 30
Please send your feedback at [email protected]
For download and more information
Dr. Nilesh Bhaskarrao Bahadure (Ph.D.) Control System June 30, 2021 30 / 30
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