BITS, PILANI - K. K. BIRLA GOA CAMPUSSemester I, 2014-15

Control Systems (EEE/INSTR F242)

This is a sample problem on analysis and design using MATLAB. Students may chooseappropriate transfer function G(s) for practice. The actual problem statement in theexamination may vary from the sample problem given here.

Instructions:

1. Transient analysis is with reference to step response.

2. Rise time is defined as time taken for the step response to increase from 10% to90 % of the steady state value.

3. Peak overshoot is mentioned in per cent.

4. Settling time is to be found out for 2% tolerance.

Problem statement: A unity gain negative feedback control system is given with

the plant transfer function G(s) = k(s+z1)(s+p1)(s+p2)(s+p3)(s+p4)

= k(s+z1)s4+as3+bs2+cs+d

and a series

compensator Gc(s).

Part A:

Analyse the open loop system, G(s), and answer the following questions:

1. Open loop stable/unstable/marginally stable

2. Order =

3. Type =

4. Actual settling time Ts (s) =

5. Actual rise time Tr (s) =

6. Actual steady state error ess, (%) =

7. Gain margin (dB) =

8. Phase margin (degrees) =

Part B:Analyse the closed-loop uncompensated (that is, with Gc(s) = 1) system and answerthe following questions: (You may use sisotool)

1. Maximum value of K for stability =

Determine k1 such that the uncompensated closed-loop system (that is, withGc(s) = k1), operates at 25 % peak overshoot in its step response

2. k1 =

For this operating condition, answer the following questions

1

3. Actual settling time Ts (s) =

4. Actual rise time Tr (s) =

5. Actual steady state error ess =

6. Actual peak overshoot (%) =

7. Actual peak time (s) =

8. Gain margin (dB) =

9. Phase margin (degrees) =

Part C:

For the uncompensated system given in the problem statement, it is required toachieve the settling time Ts = 2 s with the percent overshoot Mp = 15%. Design a P-Dcontroller (Gc(s) = Kp + sKd):

1. Kp =

2. Kd =

From the step response plot and Bode plot determine

3. Actual settling time Ts (s) =

4. Actual rise time Tr (s) =

5. Actual steady state error ess (%) =

6. Actual peak overshoot (%) =

7. Actual peak time (s) =

8. Gain margin (dB) =

9. Phase margin (degrees) =

2