Extending the Symmetrical Optimum criterion to the design of PID type-p control loops

An extension of the Symmetrical Optimum criterion for the design of PID type-p closed- loop control systems is proposed. Type-p control loops are characterized by the presence of p integrators in the open-loop transfer function. For designing a PID type-p control loop there should exist an PIpD, or PI(p−1)D, or PID and so on, if the controlled process is of type-0 or type-1 or type-(p − 1) respectively. A type-II control loop achieves zero steady state position and velocity error, a type-III control loop achieves zero steady state position, velocity and acceleration error and therefore a type-p control loop is expected to track both faster reference signals and eliminate higher order errors at steady state. For deriving the proposed control law, a transfer function containing dominant time constants and the plant's unmodelled dynamics has been considered in the frequency domain. The final control law consists of analytical expressions that involve both dominant dynamics and model uncertainty of the controlled process. For justifying the potential of the proposed theory, simulation results for representative processes met in many industry applications are presented.

► In this paper the design of PID type-p control loop is proposed.
► Type-p control loops eliminate higher order errors and therefore are capable of tracking faster reference signals.
► The control law is offered for controlling type-0, I (integrating process), II etc. process.
► Simulation results from PID type-III control loops are presented.
► Analytical expressions regarding the PID controller's parameters are presented, up to type-V control loops.