control systems 7llllllllllllllllllllllll.pdf

lllll

1. Control 2 - P. Zanchetta -University of Nottingham, UK
D/Aconverterdelay
D/A
u(t)u*(t)
T
u*(t)
u(t)
t
T/2

2. Control 2 - P. Zanchetta -University of Nottingham, UK
Methodsfordesigningdigitalcontrollers
Emulation(
s
>15
n
)
GetplantTFG(s)
Design the controller in s-
domainusingrootlocus
Discretize the controller to get
G
c
(z)using orz-transf.
Implementdifferenceeq.inp
Discretedesign(4
n
<
s
<15
n
)
GetplantTFG(s)
Discretize the plant TF to get
G(z)using orz-transf.
Design the controller in the z
domainusingz-planerootlocus
Implementdifferenceeq.inp
1Tz
1z2
s



1Tz
1z2
s




3. Control 2 - P. Zanchetta -University of Nottingham, UK
z-Transform
 




0k
k
z)k(f)z(F)k(f
f(t)
0 T 2T 3T 4T t
f(k)
0 T 2T 3T 4T t
T
  )z(Fz)1k(fZ
1


4. Control 2 - P. Zanchetta -University of Nottingham, UK
ztransformsofCommonsignals
f(k)
0 T 2T 3T 4T t
T
f(k)
0 T 2T 3T 4T t
T
1
Unit step function Ramp function

5. Control 2 - P. Zanchetta -University of Nottingham, UK
ztransformsofCommonsignals
f(k)
0 T 2T 3T 4T t
T
1
Exponential function
f(t)=exp(-t)
T
e

T2
e


6. Control 2 - P. Zanchetta -University of Nottingham, UK
ztransformsofCommonsignals
f(k)
0 T 2T 3T 4T t
T
Damped sinusoid
f(t)=exp(-t)sint

7. Control 2 - P. Zanchetta -University of Nottingham, UK
Basicdigitalcontrolsystem