Consider a simplified cruise control system for an automobil

Consider a simplified cruise control system for an automobile as shown in Figure 1. Given: K=9, G_1(s)=1/s, G_s(s)=1/(s+3), H(s)=1 Design a lead compensator G_c^lead(s) and a PD compensator G_c^pd(s) such that the two dominant closed-loop poles of the compensated system will have zeta=0.6 and omega_n=4. With the desired zeta and omega_n, determine the closed-loop poles location and the time-domain specification such as the rise time t_r, the peak time t_p, the percentage maximum overshoot %M_P, and the setting time t_s due a unit step input. Show your calculations in the report What are the transfer functions of the lead and PD compensators G_c(s) and their respective G_d(s)? Use MATLAB to obtain the squareroot locus of the compressed system and obtian the open-loop gain of G_d(s). Identify and verify all the closed-loop pole location. Attached your squareroot-locus plot(in table form and graphical form to show the closed-loop pole location). Use MATLAB to show the unit step response of the compensated system and verify whether the design objectives have been met or not.

Solution

lead compensator = a(1+ Ts)/ 1+ Ts