Root Locus Design For all the following the problems, we assume the unity feedback system shown below;
- Consider a unity feedback system where G(s) — (s+6) (s+2)(s+3)(s+5) It is operating with dominant pole damping ratio of 0.707. a) Design a PD controller (finding K1 and K2) so that the settling time is reduced by a factor of 2. b) Compare the transient and steady state performance of the uncompensated and compensated systems. c) Use MATLAB to verify the design 2. Consider the unity feedback system with G(s) — (s4.3)(s4-5) a) Show that the system cannot satisfy the following transient performance requirements with gain alone. i) Settling time = 2/3 second. H) percent overshoot = 1.5% b) Design a phase lead compensator to satisfy the above transient performance c) Verify the design using MATLAB 3. Consider the unity feedback system with C(s) — s(s+3)(s+6) a) Design a PI controller (finding K1 and K2) to drive the ramp response error to zero b) Use MATLAB to simulate the ramp response. Show both the input ramp and the output response on the same plot. 4. For the unity feedback system where G(s) — (s+2)(s+3)(s+7) is operating with 10%
overshoot. a) What is the value of the appropriate error constant? b) Find the transfer function of a lag network so that the appropriate error constant equals 4 without appreciably changing the dominant poles of the uncompensated system. c) Use MATLAB to verify the design S. Given the unity feedback system with G(s) — (s • 2)(s I 4)(s I 6)(s I 8) a) Find the lead-lag compensator to satisfy the following specifications i) Settling time = 0.5 sec shorter than the uncompensated system ii) Damping ratio = 0.5 iii) Improve the steady state error by a factor of 30 (Assume compensator zero is at -S for phase lead compensation port.)
b) Verify using MATLAB