Design and tuning of fuzzy PID controllers for multivariable process systems

Multivariable processes are often found in many industries such as chemical, refinery, and aerospace. The complex and nonlinear nature of multi-input and multi-output (MIMO) systems makes multivariable control a challenging task. Multivariable control become difficult in the presence of loop interactions where different control loops in the multivariable system exhibits coupled behavior in the control variables. When the multivariable system is broken into several single-input-single-output (SISO) control systems, the individual control loops can be characterized by equal number of SISO control problems. However, when interactions exists, an individual control loop will be affected by more than one control variable in the multivariable system. Therefore design of MIMO control systems is often a challenging research area in the area of multivariable control. -- There are many multivariable control techniques which have been developed to address the above issues, including advanced multivariable control techniques such as model predictive control. Among them, proportional integral derivative (PID) control has been the most common in industries. Application of fuzzy logic for control problems have been shown to improve overall performance significantly. Although there are many applications related to SISO based fuzzy PID systems, the application and design of fuzzy PID systems for multivariable systems are less common. The adaptive and nonlinear nature of fuzzy control allows fuzzy PID systems to handle nonlinear systems more efficiently than using linear PID controllers. -- The objective of this thesis is to develop a technique to design and tune PID type fuzzy controllers for multivariable process systems. In this work, the standard additive model (SAM) based fuzzy system is selected to design the rule base. The SAM inference system follows a special volume and centroid of membership based technique for defuzzification. A nonlinearity study has been performed to show the advantages of using a SAM based inference system against traditional min-max-gravity based inference systems. The SAM system is implemented on two fuzzy PID (FPID) systems. FPID type I is designed using Mamdani's style FPID system and constitute coupled rules to define the overall FPID output. FPID type II is designed using a rule decoupled system, in which each PID action is described using a separate rule base. -- FPID tuning is performed using the two-level tuning principle where the overall tuning is decomposed into two tuning levels, low-level and high-level. 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. -- The stability analysis using Nyquist array and Gershgorin band proves the robustness of the proposed method. The stability criterion is performed to define the hard limits for nonlinear tuning variables in the SAM system. The proposed FPID tuning technique guarantees the stability of the MIMO control system. -- The applicability of the proposed methods in this research is demonstrated through several control simulations and real-time experiments. The results show FPID systems able to handle such a complex system more robustly than using linear systems and also the experiments validated the design method proposed in this thesis.