ISA-PID controller tuning: A combined min-max / ISE approach

This communication addresses the problem of tuning a PID controller on the basis of a Model Reference Specification and posterior inclusion of Robustness considerations. The tuning is based upon a First Order Plus Time Delay (FOPTD) model and aims to achieve a step response specification. The industrial ISA-PID formulation is chosen. First of all the expression for the structure of optimal controllers as providers of an approximation of such a reference model is got. A tuning rule is derived where the four parameters of the ISA-PID are determined by means of two new parameters: one parameter, TM, is related to the desired closed-loop time constant and the other one, z, that characterizes the approximation problem by means of the corresponding weighting function. As it is usual designs where a weighting function is used to set up the synthesis problem there should be some guide on how to select such weight. In this communication it is shown how this can be done by taking into account an ISE criterion. The introduction of ISE-like criterions for both parameters generates the optimal controller as a PI controller and the PID controller arises when detuning is introduced in order to increase the robustness.