Lagrangian-based state transition algorithm for tuning multivariable decentralised controller

Abstract

Tuning PID controllers for multivariable process to optimise process performance is computationally intensive as it requires solution of constrained nonlinear optimisation problem. In this backdrop, evolutionary computing methods have emerged as alternatives to conventional optimisation tools. This investigation proposes the use of LBSTA to exploit its numerical stability and performance to tune multivariable decentralised PID controller considering the physical constraints posed by MIMO process. Simulations on Wood and Berry binary distillation column benchmark problem are used to illustrate the PID tuning rule aimed at reducing IAE subject to physical constraints. Three cases of simulations are performed. Further, the simulations used 20 independent trials by STA with Lagrangian constraints. Constraints imposed on control signal considering physical limitations of the actuator makes the algorithm suitable for industrial applications. Our results show that the LBSTA is not only optimal than unconstrained PBPSO algorithm-based tuning, but also achieves the optimal performance considering the physical limitations.