Consider the system i = Ax + Bu, y = Cx with-12A = | 1-1B= | 2,C= [1 0 0]13Design a controller K such that the control input u = -Kâ places the poles of A – BK at {-2, -1±j}. â is the estimated value of x obtained using thebelow observer design specifications: (I) ââ is the state of a full-order observer whose poles are located at {-5, -4, –3}.11) Let K = [kı k2 k3] be the controller gain. k3 =

Given x·=Ax+Buy=CxA=1-1210-1113B=121C=100poles of A-BK are at {-2,-1±j}

Answered: Consider the system i = Ax + Bu, y = Cx…

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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Control Systems
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The question is in the attached file.
A discrete-time PID controller is introduced in the control system at figure 1 to improve the steady state and the transient performances. a) What's the transfer function D(z) of the controller? (Rectangular approximation). b) Find the integral gain Ki for the velocity error Ev to be equal to 0.05. c) Find Kp and Ka (proportional and derivative gains) to cancel all poles of G(z) Y(s) 3(s+4) (s+1)(s+3) R(z)- D(z) B(s) T=0.05sec Figure 1
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Y(s) U(s) s? + 2Ems + m² For the generic second order plant (s) = ,the PID controller U(s) E(s) + Kas is used in cascade to form a unity feedback closed loop C(s) = -= Kp + control system, whose reference input is R(s). a) Find the error between the reference input and the plant output, E(s) = R(s) – Y(s). b) If Kp = 250 , K, = m² and K-1. find the transfer function of the unity feedback closed loop system.
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EENG226-Signals and Systems Please solve it very quickly ??

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