30 1. Consider a motor G(s) The input is the voltage in volts and the output is the angle in radians. A s(s+) controller K(s) = (1+) was used. No-sisotool is allowed for this problem. Any plots needed, should be n Reall plotted using the MATLAB command 'step'. Do hand calculations wherever needed. Include all MATLAB codes. a. What will be the closed loop poles for this system, assume H=1, F=1? Are the closed loop poles in the correct region for overshoot to be less than 5% and the settling time to be less than 2s? Remember the regions are calculated based on 1st/2nd order formulae: T, b. What is the actual overshoot in the response y(t) of the closed loop system for a unit step r(t)? This is the response generated using step() in MATLAB. Show this step response. Why is the actual overshoot different from the one predicted in part a? and M₂ = et cot Imagl |Reall c. Design a prefilter F(s) such that the (Ts and Mp of the) new step response of the CLTF becomes what you'd expect from the formulae. Show the new step response. d. Also plot the voltage given to motor as a function of time, without the prefilter and with the prefilter. Explain the differences in detail.

Fig: 1