Consider the system described in Problem 2.10-2. (a) Find the transfer function of this system. (b) Let

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Consider the system described in Problem 2.10-2.01 (+)-x(*)+-(*) 1) = 03 y(k)=[-2 1 ]x(*)


(a) Find the transfer function of this system.

(b) Let u(k) = 1, k ≥0 (a unit step function) and x(0) = 0 . Use the transfer function of part (a) to find the system response.

(c) Find the state transition matrix Φ(k) for this system.

(d) Use (2-90) to verify the step response calculated in part (b). This calculation results in the response expressed as a summation. Then check the values y(0), y(1) , and y(2).

(e) Verify the results of part (d) by the iterative solution of the state equations.

Equation 2-90y(k) = C(k)x(0) + C(k  1  j)Bu(j) + Du(k) - j=0

Problem 2.10-2

Consider the system described by1 (* + 1) = [ 0  ] (*) + [  (*) 3 y (k)=[-2 1] x(k)

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Digital Control System Analysis And Design

ISBN: 9780132938310

4th Edition

Authors: Charles Phillips, H. Nagle, Aranya Chakrabortty

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