Consider the plant transfer function to be put in the unity feedback loop of Fig. 5.60

Chapter 5, Problem 5.33

(choose chapter or problem)

Consider the plant transfer function to be put in the unity feedback loop of Fig. 5.60. This is the transfer function relating the input force u(t) and the position y(t) of mass M in the noncollocated sensor and actuator problem. In this problem we will use rootlocus techniques to design a controller D(s) so that the closed-loop step response has a rise time of less than 0.1 sec and an overshoot of less than 10%. You may use MATLAB for any of the following questions: (a) Approximate G(s) by assuming that m 0, and let M = 1, K = 1, b = 0.1, and D(s) = K. Can K be chosen to satisfy the performance specifications? Why or why not? (b) Repeat part (a) assuming that D (s) = K(s + Z), and show that K and Z can be chosen to meet the specifications. (c) Repeat part (b), but with a practical controller given by the transfer function Pick p so that the values for K and Z computed in part (b) remain more or less valid. (d) Now suppose that the small mass m is not negligible, but is given by m = M/10. Check to see if the controller you designed in part (c) still meets the given specifications. If not, adjust the controller parameters so that the specifications are met.