Robust Analysis and Design of Decentralized Control Systems

Dan Chen

Ph.D. Candidate  

Department of Chemical Engineering

University of California, Santa Barbara, CA, 93106

danchen@engineering.ucsb.edu

Abstract

Decentralized or multiloop control configurations are widely used for multivariable control problems in the process industries, despite the popularity of model-based, multivariable control techniques such as Model Predictive Control. One reason is that a decentralized control system has a simpler structure and can be implemented using conventional DCS software. Thus it is simpler to implement and maintain. Although there are a number of design methods available for decentralized control systems, they tend to ignore the effect of model uncertainty. In particular, design methods are not available for robust, multiloop PI/PID control systems. The objective of this research is to develop robust analysis and design methods for decentralized control systems by utilizing the model structure and statistical uncertainty information that is readily available from system identification.

A frequency domain method, Nyquist array analysis, is extended to accommodate statistical uncertainty bounds obtained from system identification techniques. Two types of uncertainty bounds on the system frequency response are derived: an uncertainty bound for each element of the system frequency response and an uncertainty bound for each column of the system frequency response. Gershgorin’s theorem is extended to include model uncertainty. Robust diagonal dominance and robust Gershgorin bands are defined for uncertain system models. Based on these results, new robust stability theorems are developed for systems with model uncertainty.

The proposed robust Nyquist stability analysis provides a simple but effective way to analyze the robust stability for decentralized control systems. The robust stability analysis and statistical uncertainty information provide a framework for developing design and tuning methods for robust multiloop PI/PID control systems.

1.

Chen, D. and D. E. Seborg, “Robust Design and Tuning for Decentralized PI Control Systems”, paper presented at the AIChE Annual Meeting, Los Angeles, CA, 2000.

2.

Chen, D. and D. E. Seborg, “Robust Nyquist Array Analysis Based on Uncertainty Descriptions from System Identification”, Automatica, accepted for publication.