In Chapter 7, Figure P7.31 shows the block diagram of the speed control of an HEV rearranged

Question:

In Chapter 7, Figure P7.31 shows the block diagram of the speed control of an HEV rearranged as a unity feedback system (Preitl, 2007). Let the transfer function of the speed controller be

a. Assume first that the speed controller is configured as a proportional controller K_ISC = 0 and G_SC (s) = K_PSC . Calculate the forward path open loop poles. Now use MATLAB to plot the system’s root locus and find the gain, KPSC that yields a critically damped closed-loop response. Finally, plot the time-domain response, c(t), for a unit-step input using MATLAB. Note on the curve the rise time, T_r, and settling time, T_s.

b. Now add an integral gain, K_ISC, to the controller, such that K_ISC / K_PSC= 0.4. Use MATLAB to plot the root locus and find the proportional
gain, K_PSC, that could lead to a closed loop unit-step response with 10% overshoot. Plot c(t) using MATLAB and note on the curve the peak time, T_p, and settling time, T_s. Does the response obtained resemble a second-order under damped response?