Technical Briefs

A Simple Switching Control for Linear Systems to Assure Nonovershooting Step Responses

[+] Author and Article Information
Bo Zhu

 Institute of Astronautics and Aeronautics, University of Electronic Science and Technology of China, Chengdu 611731, China; Department of Automatic Control, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

Kai-Yuan Cai

 Department of Automatic Control, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

J. Dyn. Sys., Meas., Control 134(3), 034503 (Apr 06, 2012) (7 pages) doi:10.1115/1.4005494 History: Received May 14, 2009; Revised October 28, 2011; Published April 06, 2012; Online April 06, 2012

In the paper, we show that for a class of linear plants, although the common linear control can be used to stabilize them, the step responses of the resulting closed-loop systems must have overshoot; however, a simple switching between them may avoid the overshoot. This indicates that switching control may overcome the performance limitation of linear feedback control in the overshoot-avoidance respect. A simple switching control scheme with such a quality is exploited and the conditions for its existence are presented. In the scheme, two common controllers are needed and they are only required to guarantee no overshoot on the time intervals [0, ts ) and [ts , ), respectively, where ts denotes the switching time. For actual implementation, a state-dependent version of the switching control law is developed. Two examples are presented to show its effectiveness.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

Unity-feedback control configuration

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Figure 2

The proposed switching control scheme

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Figure 3

State-dependent switching control law

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Figure 4

Simulation results of the second-order systems

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Figure 5

Simulation results of the third-order systems with a = 1

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Figure 6

Simulation results of the third-order systems with a = 2



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