Bode plot and control system root locus graph

controls systems

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 LEAD COMPENSATOR A compensator having the characteristics of a lead network is called a lead compensator. If a sinusoidal signal is applied to the lead network, then in steady state the output will have a phase lead with respect to the input. The lead compensation increases the bandwidth, which improves the speed of response and also reduces the amount of overshoot . Lead compensation appreciably improves the transient response, whereas there is a small change in steady state accuracy . Generally, lead compensation is provided to make an unstable system as a stable system. A lead compensator is basically a high pass filter and so it amplifies high frequency noise signals . If the pole introduced by the compensator is not cancelled by a zero in the system, then lead compensation increases the order of the system by one.

3. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 3 The general form of lead compensator transfer function

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

5. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 5 Bode plot of lead compensator

6. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 6 PROCEDURE FOR DESIGN OF LEAD COMPENSATOR USING BODE PLOT The following steps may be followed to design a lead compensator using bode plot and to be connected in series with transfer function of uncompensated system, G(s). Step 1: The open loop gain K of the given system is determined to satisfy the requirement of the error constant. Step-2: The bode plot is drawn for the uncompensated system using the value of K, determined from the previous step.

7. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 7 Step-3: The phase margin of the uncompensated system is determined from the bode plot. Step-4: Determine the amount of phase angle to be contributed by the lead network by using the formula given below ,

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9. ARASU ENGINEERING COLLEGE IC 8451&CONTROL SYSTEMS 9 Step-6: Determine the open loop transfer function of compensated system. Block diagram of lead compensator

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