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)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

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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Step 3: Determination of transfer function

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Step 4: Transformation to controllable canonical form

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Step 5: Determination of state-feedback gain matrix

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Step 6: Determination of state-feedback gain matrix

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