Evolutionary design of marginally robust multivariable PID controller.

Two Margin-based design methods for tuning of decentralized PI controllers for multivariable systems are presented. The first method is predefined marginally robust controller (PMR) which is based on solving a constrained optimization problem to satisfy the desired values of the multivariable phase and gain margins that are set based on the designer's knowledge of the working condition of the plant. The second method is self-setting marginally robust (SMR) that is an automatic controller design procedure. This method, by solving a many-objective optimization problem (MaOP), sets controller coefficients and finds optimum gain and phase margins. It offers a trade-off between tracking, interaction, and robustness. Evolutionary algorithm is applied to solve the problems and disk margin to define the multivariable stability margins. Proposed methods by combining the simplicity of margin-based design and effectiveness of optimization problems offer a practical solution in tuning the industrial multivariable controllers. Simulation results show that these methods are simple, practical, and at the same time, comparable with other robust multivariable controllers.