Performance measures, performance limits and optimal PI control for the IPDT plant

This paper considers PI controller tuning for the Integral Plus Dead Time (IPDT) plant subject to constraints on tolerable deviations from ideal shapes and guaranteeing minimal combined IAE (Integral of Absolute Error) measure composed of weighted IAE values of the setpoint and disturbance step responses. As the ideal responses at the plant output, monotonic (MO) transients are chosen. This implies one-pulse (1P) responses consisting of two monotonic intervals at the plant input. Optimal nominal tunings for the most important situations regarding the servo/regulation trade-off are determined by the newly developed Matlab/Simulink tool based on the performance portrait (PP) method. Generated results confirm Pareto-like limits of performance achievable under PI control and are used in classifying traditional tuning approaches into the setpoint and disturbance oriented ones. Principles of robust PP based tuning are briefly illustrated and conditions of invariance of the closed loop performance against the dead time uncertainty are formulated and checked by simulation.

► Performance achievable under PI control is outlined by performance portrait method.
► Cost function is composed of IAE values of the setpoint and disturbance responses.
► Shape related constraints on the plant input and output are applied.
► Numerical aspects are considered.
► Proposed tunings are compared with the best known traditional tuning approaches.