Design of PID Controllers for Unstable Systems Using Multiple Dominant Poleplacement Method

Abstract

Design of PID controllers for Unstable First Order Plus Time Delay (UFOPTD) systems and Unstable Second Order Plus Time Delay (USOPTD) systems using Multiple Dominant Poleplacement (MDP) method is proposed in this paper. The MDP method is extended to design PID controllers with a lead/lag filter for UFOPTD and USOPTD systems. The MDP method assumes the existence of the stable real dominant closed loop pole with a multiplicity of 5. In this method, PID filter time constant is used as a tuning parameter so that the PID parameters can be derived analytically. The proposed method is applied to various transfer function models and a nonlinear model of isothermal CSTR. Comparison of the servo and regulatory performances of the proposed controller with recently reported methods for nominal model parameters is made to demonstrate the efficacy of the present method. The performance comparison is made in terms of Integral Absolute Error (IAE). The proposed multiple dominant pole placement method performs better than the recently reported methods. Simple PID tuning rules in terms of model parameters are given for unstable FOPTD systems.

Keywords:

• Unstable FOPTD system
• Unstable SOPTD system
• PID controller
• Multiple dominant pole placement method
• Time delay
• Isothermal CSTR
• Jacketed CSTR