Choose as state variables: x,(1) = u,(1) and x, (t) = i(1). Obtain the following state space model C R, +R, x, y= Ou and calculate the system matrices for L = 0.5, R = 1, R2 = 1and C = 1. From the state space model obtain the transfer function of the system. By using controllability gramian, check if the system representation R(A, B,C) is controllable Design a state feedback u(t)=-Kx(1), which will place the closed-loop poles on desired locations: 14 = -1 and 1f = -2. By using observability matrix, check if the system representation R(A,B,C) is observable. Design a reduced-order state observer with desired poles 2 =-2.

Choose as state variables: x,(1) = u,(1) and x, (t) = i(1). Obtain the following state space model C R, +R, x, y= Ou and calculate the system matrices for L = 0.5, R = 1, R2 = 1and C = 1. From the state space model obtain the transfer function of the system. By using controllability gramian, check if the system representation R(A, B,C) is controllable Design a state feedback u(t)=-Kx(1), which will place the closed-loop poles on desired locations: 14 = -1 and 1f = -2. By using observability matrix, check if the system representation R(A,B,C) is observable. Design a reduced-order state observer with desired poles 2 =-2.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Concept explainers

Rectangular Coordinate System

In a rectangular coordinate system, each point based on the pair of coordinates is specified uniquely in the plane. From two fixed perpendicular lines, these coordinates are at a distance in the rectangular coordinate system. Each line is known as the reference axis and axes as plural. The point where they meet is called the origin (0,0).

Question

Consider the following electrical system:
R L
C= uc
u
R
The equations describing the system dynamics are the following:
u(1) = 1 di(e)
dt
2+(R, + R, i() + u,(1)
cdu, 0 - i(1)
Choose as state variables: x,(1) = u,(1) and x,(t) = i(t).
Obtain the following state space model
R, +R,
+ Ou
and calculate the system matrices for L = 0.5, R, = 1, R2 = land C = 1.
From the state space model obtain the transfer function of the system.
By using controllability gramian, check if the system representation R(A, B,C) is
controllable
Design a state feedback u(t) =-Kx(1), which will place the closed-loop poles on
desired locations: 14 = -1 and 14 = -2.
By using observability matrix, check if the system representation R(A,B,C) is
observable.
Design a reduced-order state observer with desired poles 24 = -2.
2.

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