2. Let a continuous-time system be described by 1 1 x = 0 1 -2 1 1 00 y=[200]x x+0 0 Let u(t) = pu, (t)-Kx(t). Find the feedforward gain p and the feedback gain matrix K so that the resulting system has eigenvalues at -2 and -1 ±j and will track asymptotically any step reference input.

2. Let a continuous-time system be described by 1 1 x = 0 1 -2 1 1 00 y=[200]x x+0 0 Let u(t) = pu, (t)-Kx(t). Find the feedforward gain p and the feedback gain matrix K so that the resulting system has eigenvalues at -2 and -1 ±j and will track asymptotically any step reference input.

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

2. Let a continuous-time system be described by
1 1
x = 0 1
-2
1
1
00
y=[200]x
x+0
0
Let u(t) = pu, (t)-Kx(t). Find the feedforward gain p and the feedback gain matrix K so that the
resulting system has eigenvalues at -2 and -1 ±j and will track asymptotically any step reference input.

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Open-loop transfer function Go) = KCs+4) sca+2)(st5) The open-loop pales are pele 0,-2,-5 and 'the open-loop zepir-4 The number of Sketch the roat-locas systemy the informatiere derived in Hi) and comment on the characteristics of thir 2ystem for different values Keg for small K and larger values of K. 1Oseful to koow that the equation g3 tQ.5s²+2&=+ 20= has the solutiOns X= -4, 23 +1.146
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