Optimization of PID Controller Based on Maximization of the Proportional Gain Under Constraints on Robustness and Sensitivity to Measurement Noise

This technical note presents a new, simple and effective, four-parameters proportional–integral–derivative (PID) optimization method. The set of adjustable parameters is defined by the proportional gaink, integral gainkᵢ, damping ratio of the controller zeros (DRCZ), and desired value of the sensitivity to measurement noiseMₙ. GivenMₙand desired value of the maximum sensitivityMₛ, for both maximization ofkand maximization ofkᵢ, only three nonlinear algebraic equations need to be solved for a few values of DRCZ. Contrary to the method based on maximization ofkᵢ, in the method based on maximization ofkthe improvement of performance is obtained by decreasing DRCZ from 1 to the value corresponding to the minimum of the integrated absolute error (IAE). Moreover, this is achieved without deteriorating robustness to the model uncertainties, for a large class of stable processes. Compared to the recently proposed PID optimization methods, for the sameMₛandMₙ, lower values of IAE andMₚare obtained by using the method presented here.