Research Papers

Stable Controller Interpolation and Controller Switching for LPV Systems

[+] Author and Article Information
Bryan P. Rasmussen

 Texas A&M University, College Station, TX 77843-3123brasmussen@tamu.edu

Young Joon Chang

 Texas A&M University, College Station, TX 77843-3123

J. Dyn. Sys., Meas., Control 132(1), 011007 (Dec 09, 2009) (12 pages) doi:10.1115/1.4000075 History: Received December 10, 2008; Revised May 22, 2009; Published December 09, 2009; Online December 09, 2009

This paper examines the gain-scheduling problem with a particular focus on controller interpolation with guaranteed stability of the nonlinear closed-loop system. For linear parameter varying model representations, a method of interpolating between controllers utilizing the Youla parametrization is proposed. Quadratic stability despite fast scheduling is guaranteed by construction, while the characteristics of individual controllers designed a priori are recovered at critical design points. Methods for reducing the state dimension of the interpolated controller are also given. The capability of the proposed approach to guarantee stability despite arbitrarily fast transitions leads naturally to application to switched linear systems. The efficacy of the method is demonstrated in simulation using a multi-input, multi-output, nonminimum-phase system, while interpolating between two controllers of different sizes and structures.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Output blending of LCN and LQN

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Figure 2

General feedback control diagram

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Figure 3

Youla parameter-based feedback control diagram

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Figure 7

Disturbance rejection at design conditions

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Figure 8

Tracking during transition between design conditions

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Figure 9

Tracking during transition between design and off-design conditions

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Figure 4

Quadratic weighting function for a two-dimensional scheduling space

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Figure 5

Quadruple tank system and selected operating points

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Figure 6

Step response of PI and H∞ controlled systems at associated design points




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