Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Consider a linear system of the form dx dt where u is a scalar and d is a disturbance that enters the system through

image

Consider a linear system of the form dx dt where u is a scalar and d is a disturbance that enters the system through a disturbance vector FER". In this problem, we will explore how integral feedback compensates for a constant disturbance by giving zero steady- state output error even when d 0. = Ar + Bu + Fd, y = Cx, (a) First, apply basic state feedback u = - Kafr to the system. With an appropriate choice of Ksf, the closed loop system will stabilize and approach a steady state equilibrium, xe,sf. Je, sf- Solve for this equilibrium point to show that, for a nonzero disturbance d, this system will have a nonzero steady state error. (b) Next, we will set up the system to do integral control: Augment the state space description of this system to include a state z that inte- grates the output of the system. In other words, let the augmented system be: 40-40 + Bu + Fd, and find A, B, and F. You are welcome to write these as block matrices. d dt (c) Apply integral control (with r = 0, since our aim is to reject dis- turbances): u = -Kic-kiz to the augmented system from part b. With an appropriate choice of gains Kic and k, the system will again stabilize and approach a stable equilibrium point Te,ic, Zeic Ye,ic. Solve for this equilibrium point. Under what conditions on F does this controller enable the system to reach zero steady-state error on the state, Te,ic = 0?

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Applied Regression Analysis And Other Multivariable Methods

Authors: David G. Kleinbaum, Lawrence L. Kupper, Azhar Nizam, Eli S. Rosenberg

5th Edition

1285051084, 978-1285963754, 128596375X, 978-1285051086

More Books

Students also viewed these Mechanical Engineering questions

Question

* What is the importance of soil testing in civil engineering?

Answered: 1 week ago

Question

Explain the concept of shear force and bending moment in beams.

Answered: 1 week ago