Singularly perturbation method for multivariable proportional-integral-derivative controller tuning

Abstract

Efficient control of industrial processes is of great importance. The industrial control performance has to meet the desired optimum operation. However, the tuning process becomes a challenging matter especially for Multiple-Input Multiple- Output (MIMO) system with two-time scale characteristic. This motivates the use of singularly perturbation method in the design of Multivariable Proportional-Integral- Derivative (MPID) controller tuning. The singularly perturbation methods based on Naidu and Jian Niu were considered and tested. It is observed that singularly perturbation system by method of Naidu gives a good approximation at low, middle and high frequencies. Two MIMO systems with two-time scale characteristic that are wastewater treatment plant, and Newell and Lee evaporator were used as test beds. Traditionally, the MPID controller tuning namely Davison, Penttinen-Koivo, Maciejowski and Combined are based on full order static matrix inverse model. In this work, the singularly perturbed MPID controller tuning methods are proposed based on the dynamic matric inverse to improve the tuning of MIMO system. Furthermore, Particle Swarm Optimization has been applied in the tuning of the parameters for an optimum control performance. Comparing the closed loop performance and process interaction of traditional MPID and the proposed singularly perturbed MPID controller methods, the latter methods are able to improve transient responses, provide low steady state error, and reduce the process interaction.