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A discrete-time system is described by the following equations -1 0 x(k+1)= 1 -2 0 1 0 x(k)+ 0 -3 y(k)=[110]x(k) u(k) a) Find the transfer function Y(z)/U(z). b) Transform the system equations into the controllable canonical form. c) Using the pole placement design technique, find the state feedback gain matrix K so that the compensated system has poles at (0.5, j0.5, -j0.5}

A discrete-time system is described by the following equations -1 0 x(k+1)= 1 -2 0 1 0 x(k)+ 0 -3 y(k)=[110]x(k) u(k) a) Find the transfer function Y(z)/U(z). b) Transform the system equations into the controllable canonical form. c) Using the pole placement design technique, find the state feedback gain matrix K so that the compensated system has poles at (0.5, j0.5, -j0.5}

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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A discrete-time system is described by the following equations 11 0 0 x(k)+ -1 0 x(k+1)= 1 -2 0 0 -3 y(k)=[110]x(k) u(k) a) Find the transfer function Y(z)/U(z). b) Transform the system equations into the controllable canonical form. c) Using the pole placement design technique, find the state feedback gain matrix K so that the compensated system has poles at {0.5, j0.5, -j0.5}
Transcribed Image Text:A discrete-time system is described by the following equations 11 0 0 x(k)+ -1 0 x(k+1)= 1 -2 0 0 -3 y(k)=[110]x(k) u(k) a) Find the transfer function Y(z)/U(z). b) Transform the system equations into the controllable canonical form. c) Using the pole placement design technique, find the state feedback gain matrix K so that the compensated system has poles at {0.5, j0.5, -j0.5}
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