Fuzzy Gain Scheduling of the Fractional-Order PID Controller for a Continuous Stirred-Tank Reactor Process

Abstract

In most chemical industries, continuous stirred-tank reactors (CSTRs) are essential for the production of chemicals. The CSTR process is highly nonlinear and has both stable and unstable equilibrium points. Control system engineers face a difficult issue when designing a single controller for temperature control in both stable and unstable areas. Due to these problems, implementing the conventional proportional-integral-derivative (PID) controller may lead to instability in controlled variables. Therefore, in this paper, the entire operating region is divided into three regions. The fractional-order PID controller as a local controller is designed in each operating region to control the temperature, and its parameters are tuned with a genetic algorithm by minimizing the integral of absolute error and control input change with a weighting factor. Then, a fuzzy gain scheduling scheme based on the Tagaki-Sugno fuzzy model is used to properly interpolate the outputs of the local controllers. A set of simulations are carried out to demonstrate the effectiveness of the proposed controller, and its performance is compared with that of an adaptive nonlinear controller and fuzzy gain scheduling of the PID controller.