Optimal tuning of PI controllers for first order plus dead time/long dead time models using dimensional analysis

For first order plus dead time models, an optimal method for tuning PI controllers is presented using dimensional analysis and numerical optimisation techniques. Considering a step change in setpoint, optimal equations for determining PI parameters are obtained through minimising the integral of absolute error (IAE). The optimisation process is constrained to guarantee a minimum Gain margin (G.M.) of 2 and a minimum Phase Margin (P.M.) of 60°. The proposed formulas can also be used for first order systems with long dead time. Simulation results show that the proposed method has a considerable superiority over conventional techniques. In addition, the closed loop system shows a robust performance in the face of model parameters uncertainties.