An inverted pendulum control system has transfer function P(s) = 1/s^2 - 100 1. Discuss the selection of the sampling time for this system (Recall the constraints on closed-loop bandwidth imposed by right half-plane poles and zeros) 2. Considering a sampling time of 0.01s, estimate approximately maximum crossover frequency that can be achieved with a strictly causal DT PID for a Phase Margin of 40deg 3. Discuss how the estimate of the maximum crossover frequency would change if we get a better sensor and we are able to sample twice as fast. 4. Use sampling Ts = 0.01s, crossover wc = 15rad/s, PM = 40 to design a strictly causal DT PID controller. 5. What happens if in #3 we choose wc = 5rad/s? (For simplicity, work with a CT controller to satisfy the PM equation: does the controller yield a stable closed-loop system?)