- Section B Answer One Question The Motion Of A Vehicle Steering System Can Be Approximated By A Normalised Linear Model W 1 (139.08 KiB) Viewed 28 times
Section B Answer one question The motion of a vehicle steering system can be approximated by a normalised linear model written as Q4. + น [p] = Co__1632] + 1]u y= [1 01 [] (c) Q=[ ] = X1 and X2 represent the lateral position and the heading angle of the centre of mass of the vehicle, u is the steering angle of the front wheel, a (0 < a < 1) is a constant parameter. (a) Comment on the performance of the open-loop system. 2 marks (b) Design a state feedback controller that stabilises the system and tracks a given reference r of the position of the vehicle. The expected closed-loop characteristic polynomial is p(s) = 52 + 2/Wns + wh 8 marks Taking a = 0.5, design the linear quadratic regulator (LQR) to minimise the cost function J = {S"[x" (t)Qx(t) + Ru?(t)]dt, R= 1 The optimal solution is obtained to be u=-[1 1.3028]x. i) Under this LQR control, what are the damping ratio and the natural frequency of the closed-loop system? 4 marks ii) Discuss what factors affect the minimum cost function. 2 marks (d) The two design methods in (a) and (b) are commonly used in state feedback control. Discuss the following for both design methods. i) What are the conditions to apply the pole-placement design in (a) and the LQR design in (b)? 2 marks ii) Discuss how to achieve fast-response dynamics of the closed-loop system with the two design methods, respectively. 2 marks