Answered: The block diagram below shows a…

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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The block diagram below shows a feedback controller for a skyscraper elevator’s vertical position.

(a) Determine the closed-loop transfer function of the system, HCL(s) = Y(s)/R(s).
(b) Assume that all initial conditions are zero. From HCL(s) in part (a), derive the equation of motion of the system.
(c) Define the state variables of the system as phase variables and substitute them into the equation of motion in part (b).
(d) Define the control input vector as u(t) = r(t). Rewrite the equation of motion in part (b) instate-space form, xdot = Ax+Bu.
(e) Define 2 outputs: the elevator position and the elevator velocity. Write the output equation in state-space form, y = Cx + Du.

R(s)
Desired
vertical
position
Controller
K + 1
Elevator dynamics
1
s(s² + 3s + 3)
Y(s)
Vertical
position

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