Unified complex coefficient PID controller tuning for complex coefficient system

Abstract

Generally, controllers are tuned to meet the desired time and frequency domain specifications for integer/fractional order real coefficient systems whose frequency response is symmetric about the origin of the complex frequency plane. These controllers are tuned through analytical/numerical approaches. On the contrary, the frequency responses of the complex coefficient systems are unsymmetrical, and hence tuning of controllers should consider both positive and negative frequencies. In this article, tuning of complex coefficient proportional integral derivative controller is proposed for such systems to meet the desired gain and phase margin specifications in positive and negative frequencies. For illustration, the simulation results are presented for stable, unstable, and non-minimal phase systems with the proposed tuning method.