Problem 1: Common rules of thumb for controller discretization is to have "6 samples per rise time" in order to achieve a reasonable approximation of the CT controller, without wasting computing resources. Derive the effect on PM that this choice will have.
Problem 2: A motor position control system has transfer function
P(s) = 1/s2(s + 1)
Design a PID controller to approximately maximize its BW, keeping the PM above 40deg.
Problem 3: Consider the system with transfer function P(s) = 1/s which is to be controlled by a strictly causal DT-PI controller of the form C(z) = K(z-a)/z(z-1) so that the loop crossover frequency is 1 rad/s and the phase margin is 45o.
1. Discuss the selection of a suitable sampling time for the controller.
2. Use Ts = 0.3(sec) to design a DT-PI to meet the specifications by designing the controller in CT first, and then discretizing it.
3. Use Ts = 0.3(sec) and design the DT-PI to meet the specifications in DT entirely.