Consider a vehicle, which has a weight m = 1000 kg. Assuming the average friction coefficient b= 100, design a position control system such that the vehicle can move 100 m in 10.0 s with an overshoot less than 10%. Let y denote the displacement of the vehicle, then the dynamics of the vehicle can be described by the following equation mÿ(t) + by(t) = u(t) where m=1000, and b=100. Assume that the sampling period is 0.1s. Design a two-degree-of-freedom controller such that the transfer function from the command signal u(k) to the output y(k) follows the reference model.The two-degree-of-freedom controller consists of two parts, the feed-forward controller and the feedback controller, in the form of u(k) = uƒƒ(k) + Uƒb(k) where uƒƒ(k) is the feed-forward control signal and uƒ(k) is the feedback control signal. a) From the performance specification, determine the desired damping ratio and the natural frequency, and then the reference model in the continuous-time. Convert the reference model from the continuous-time to discrete time, which is the reference model Hm(z) to be used in the design of two-degree-of-freedom controller. b) Define the state variable x(t) = (y(t), y(t))T, find out the state-space model of the sampled system. c) Determine L in the state feedback controller Uƒb (k) = − Lx (k) d) Determine the transfer function for the feed-forward controller, Hƒƒ(z),such that Uƒƒ(z) = Hƒƒ(z)Uc(z) e) Assume that only the displacement, y, is measurable, is it still possible to use the two-degree-of-freedom controller to meet the performance specification? Justify your answer.

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consider a vehicle which has a weight m 1000 kg assuming the average f

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Consider a vehicle, which has a weight m = 1000 kg. Assuming the average friction coefficient b= 100, design a position control system such that the vehicle can move 100 m in 10.0 s with an overshoot less than 10%. Let y denote the displacement of the vehicle, then the dynamics of the vehicle can be described by the f