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IMA Journal of Mathematical Control and Information Advance Access originally published online on November 17, 2007
IMA Journal of Mathematical Control and Information 2008 25(3):305-322; doi:10.1093/imamci/dnm030
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© The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Digital design of combined PI and state feedback controller for non-linear stochastic systems

Han-Qin Zhou

Control Systems Engineering, Jacobs Engineering Group, Inc., Houston, TX 77072, USA

Leang-San Shieh{dagger} and Ce Richard Liu

Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77204, USA

Qing-Guo Wang

Department of Electrical and Computer Engineering, National University of Singapore, Singapore 119260

{dagger} Email: lshieh{at}uh.edu

Received on April 27, 2006; Accepted on September 14, 2007

In this paper, a combined Proportional-Integral (PI) and state feedback linear discrete control scheme is proposed for non-linear stochastic systems. The state-dependent optimal linear model of the original non-linear plant is first constructed from system state feedback at each sampling period, then the discrete linear quadratic regulator approach with pole placement is applied to issue and update controller settings. If the system is under stochastic process noise, the innovation form of Kalman gain can be employed for optimal states estimation without requiring prior knowledge of noise properties. Stability conditions for sampled-data non-linear systems are addressed in discrete-time analysis. The effectiveness of the proposed method will be demonstrated by the simulation examples of both single-input single-output and multi-input multi-output non-linear processes.

Keywords: multivariable system; non-linear process; linear model; PI controller; stochastic disturbance.


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