MAE 170 Problem set 3 handout problems Problem 1 This problem is to simulate the car PI cruise control system discussed in class. The dynamic model for the car is dmvff=−±)d, and the cruise controller is ()(pdifkvvk vv=−−−−∫dt. Using the state vector vxz⎧ ⎫=⎨ ⎬⎩⎭with and output vector 0(),(0)0,tdzvvdtz=∫vyf⎧⎫=⎨⎬, define the system in state space form, that is, define A,B,C,D. Hint: The system has two inputs: and dvdf. Problem 2 Assume that the system parameters are as stated below, and that the initial velocity of the car is 20 m/s, with a desired cruise velocity of 30 m/s. Using Matlab’s lsim function, simulate the response of this system. Assume that the disturbance force fd(t) is defined as fdvec, below. Turn in your code and a plot of both outputs as functions of time (0-25 s). m = 1000;kp = 500;ki = 200;%You define A,B,C,D Gss = ss(A,B,C,D);t = (0:.05:25)';one_vec = ones(size(t)); fdvec = 1000*one_vec + 500*sign(sin(t)) + 500*(rand(size(t))-.5); %You define the input u, hint: u=[vdvec fdvec].
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