digital control theory

ELE4DCT – Digital Control Theory Assignment 2 This assignment is due by 2:00pm, Monday 19 October 2015. You must show all working clearly and neatly. Late submissions will not be assessed. (Total: 25 marks) Question 1. For the sampled-data system in Figure 1, express the output C(z) as a function of the input and the transfer functions shown. (5 marks) H(s) G(s) R(s) C(s) T E2(s) E1(s) T Figure 1 Question 2. A discrete-time system is described by the signal-flow graph in Figure 2. The state variables are labeled as ( ) 1 x k and ( ) 2 x k in Figure 1. (a) Write the state-space equation of the system. (5 marks) (b) Derive the pulse transfer function ( ) ( ) U z Y z of the system in Figure 1. (5 marks) u(k) -0.4 -0.8 y(k) 1 2 1 z 1 -1 z -1 x2(k) x1(k) Figure 2 Question 3. A discrete-time system is given by ( ) 0 1 ( ) 1 0 0.5 0 (k 1) k u k              x   x y(k)  [0.5 0.5]x(k) (a) Design a full-state feedback controller of the form u(k)  Kx(k) to place the two closed-loop poles at 0.5, z1  z2  0.8 . (5 marks) (b) With the full-state feedback controller designed in (a), write the closed-loop state equation. (5 marks)

Is this the question you were looking for? If so, place your order here to get started!