Controls Theory Assignment MEC 308

1. Sketch the general shape of the root locus for each of the open-loop pole zero plots shown in Figure P8.2.

2. Sketch the root locus for the unity feedback system shown in Figure P8.3 for the following transfer functions:

3. Design a PI controller to drive the step response error to zero for the unity feedback system shown in Figure P9.1, where

The system operates with a damping ratio of 0.5. Compare the specifications of the uncompensated and compensated systems.

4. Find analytical expressions for the magnitude and phase response for each G(s) below.

5. Sketch the Nyquist diagram for each of the systems in Figure P10.1.

6. Using the Nyquist criterion, find the range of K for stability for each of the systems in Figure P10.4.

7. Design the value of gain, K, for a gain margin of 10 dB in the unity feedback system of Figure P11.1 if

8. Given the unity feedback system of Figure P11.1, use frequency response methods to determine the value of gain, K, to yield a step response with a 20% overshoot if

9. The unity feedback system of Figure P11.1 with

is operating with 20% overshoot.a. Find the settling time.b. Find Kp.c. Find the phase margin and the phase-margin frequency.

d. Using frequency response techniques, design a compensator that will yield a threefold improvement in Kp and a twofold reduction in settling time while keeping the overshoot at 20%.

10. For the unity feedback system shown in Figure P7.1, where

find the steady-state errors for the following test inputs:

11. Figure P7.2 shows the ramp input r(t) and the output c(t) of a system. Assuming the output’s steady state can be approximated by a ramp, find

12. For the unity feedback system shown in Figure P7.1, where

find the steady-state error if the input is

13. For the unity feedback system shown in Figure P7.1, where

14. For the open-loop pole-zero plot shown in Figure P8.4, sketch the root locus and find the break-in point.

15. The unity feedback system shown in Figure P9.1 with

a. What is the value of the appropriate static error constant?b. Find the transfer function of a lag network so that the appropriate static error constant equals 4 without appreciably changing the dominant poles of the uncompensated system.

16. Name two different frequency response characteristics that can be used to determine a system’s transient response?

17. What kind of compensation improves both steady-state error and transient response?

18. How can you tell from the root locus that the natural frequency does not change over a region of gain?

19. What major advantage does compensator design by frequency response have over root locus design?

20. Briefly describe the design procedure for a controller?