Foundations of Generic Optimization pp 283-312 | Cite as

# Two-Level Tuning of Fuzzy PID Controllers for Multivariable Process Systems

## Abstract

This paper presents a novel design and tuning technique of fuzzy PID (FPID) controllers for multivariable process systems. The inference mechanism of the FPID system follows the Standard Additive Model (SAM)-based fuzzy rule structure. The proposed design method can be used for any *n×n* dimensional multiinput– multi-output (MIMO) process system and guarantees closed-loop stability. In general the design of FPID for MIMO systems is challenging, mainly due to the existence of loop interactions. To address this issue a static decoupler is implemented which has the capacity to remove steady-state loop interactions. The each control loop is assigned with a FPID system. Two types of FPID configurations are considered. The first FPID system follows the Mamdani-type rule structure, where error and error rates are directly used in the input space to derive fuzzy rules. The second FPID configuration consists decoupled fuzzy rules where three decoupled rule bases are assigned to follow individual PID actions. The tuning is achieved while using the two-level tuning principle as described in [1]. The low-level tuning is dedicated to devise linear gain parameters in the FPID system where as the high-level tuning is dedicated to adjust the fuzzy rule base parameters. The low-level tuning method adopts a novel linear tuning scheme for general decoupled PID controllers and the high-level tuning adopts a heuristic-based method to change the nonlinearity in the fuzzy output. For robust implementation, a stability analysis is performed using Nyquist array and Gershgorin band. The stability properties provides the hard limits allowed for fuzzy rule parameters and also guarantees to operate within a given gain phase margin limits. The performance and the design criterion is finally evaluated using several control simulations.

## Keywords

Multivariable control Fuzzy PID control Standard additive model Linear PID tuning Nonlinear fuzzy tuning Stability## Preview

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