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me352_hw1 - [3 Modify the equation of motion for the cruise...

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1 ME 352 System Dynamics and Control Homework #1 Due: Monday 28.02.2011 [1]. Write the equations of motion for the linear translational systems shown in Figure 1. Define the state variables as follows: (a) dt dy x y x dt dy x y x / , , / , 1 4 1 3 2 2 2 1 = = = = (b) dt dy x y x y x / , , 1 3 1 2 2 1 = = = (c) dt dy x y x y x / , , 2 3 2 2 1 1 = = = Write the state-variable equations with these state variables. Also, find the transfer functions ) ( / ) ( 1 s F s Y and ) ( / ) ( 2 s F s Y . Figure 1 [2]. For the car suspension system discussed in class (two mass car suspension system – quarter car model), (a) Plot the position of the car and the wheel after the car hits a “unit bump” (i.e., r is a unit step) using MATLAB. Assume that m 1 =10 kg, m 2 =350 kg, k w =500,000 N/m, k s =10,000 N/m. (b) Find the value of b (try with different values of b in your MATLAB simulation) that you would prefer if you were a passenger in the car. Comment on your results. Give MATLAB codes and graphs.
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Unformatted text preview: [3]. Modify the equation of motion for the cruise control model given by: b u v v m m + = & so that it has a control law; that is, let r u K(v v) =-where v r is the reference speed and K is a constant. This is a “proportional” control law where the difference between v r and the actual speed is used as a signal to speed the engine up or slow it down. Assume that m=1000 kg and b=50 N.s/m. Find the transfer function V(s)/V r (s) and the response v(t) for a unit step in v r using MATLAB/Simulink. Using trial and error, find a value of K that you think would result in a control system in which the actual speed converges as quickly as possible to the reference speed with no objectionable behavior. Give Simulink diagram and graphs....
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