class for root locus and bode plote diagram

control system

1. IC 8451&CONTROL SYSTEMS Department of Electrical and Electronics Engineering Approved by AICTE | Affiliated to Anna University | Accredited by NAAC | Accredited NBA | Recognized by UGC under 2(f) and 12(B) Chennai Main Road, Kumbakonam- 612 501. ARASU ENGINEERING COLLEGE 1

2. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 2 LAG COMPENSATOR A compensator having the characteristics of a lag network is called a lag compensator . If a sinusoidal signal is applied to a lag network, then in steady state the output will have a phase lag with respect to input. Lag compensation results in a large improvement in steady state performance but results in slower response due to reduced bandwidth . The attenuation due to the lag compensator will shift the gain crossover frequency to a lower frequency point where the phase margin is acceptable. Thus , the lag compensator will reduce the bandwidth of the system and will result in slower transient response. Lag compensator is essentially a low pass filter and so high frequency noise signals are attenuated. If the pole introduced by the compensator is not cancelled by a zero in the system , then lag compensator increases the order of the system by one.

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4. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 4 REALISATION OF LAG COMPENSATOR USING ELECTRICAL NETWORK

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7. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 7 PROCEDURE FOR THE DESIGN OF LAG COMPENSATOR USING BODE PLOT The following steps may be followed to design a lag compensator using bode plot and to be connected in series with transfer function of uncompensated system, G(s). Step-1: Choose the value of K in uncompensated system to meet the steady state error requirement. Step-2 : Sketch the bode plot of uncompensated system. Step -3 : Determine the phase margin of the uncompensated system from the bode plot. If the phase margin does not satisfy the requirement then lag compensation is required. Step-4 : Choose a suitable value for the phase margin of the compensated system.

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10. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 10 Step-8: Determine the open loop transfer function of compensated system.

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12. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 12 EXAMPLE A unity feedback system has an open loop transfer function, G(s ) = K/s(1+2s). Design a suitable lag compensator so that phase margin is 40 ◦ and the steady state error for ramp input is less than or equal to 0.2 .

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