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 Consider that the dominant closed-loop poles of the uncompensated system are satisfactory with the transient response, but its static velocity error constant K_v is not satisfactory. It is desirable to have K_v^G_d=30 sec^-1. Design a lag compensator and a PI compensator to satisfy the design objectives. What are the transfer functions G_c(s) of your compensators? Use MATLAB to verify your dominant closed-loop poles location of the compensated system, determine its open-loop gain, and verify that the unit step response satisfies the design objectives. If the design objectives are not satisfied, explain why they are not satisfied. Attach your MATLAB results (not all the pages of your MATLAB output; carefully include the portion of results that reflect your MATLAB work).

Solution

C/R = G.Gc, A2/( 1+HA2)