Novel iterative formulation of Correlation-Based Tuning

This paper gives a simple iterative formulation of Correlation-based Tuning (CbT). A reference model sets the performance specifications of the control system, and the control objective is to minimize the output error, i.e., the difference between the controlled output and the reference model output. With this regard an optimization problem is defined, and the objective function is expressed as the squared sum of the cross-correlation function between the output error and the reference input. The minimization of this objective function specific to CbT is carried out by a Robbins-Monro procedure that ensures the iterative tuning of controller parameters. A novel iterative CbT algorithm is proposed on the basis of the iterative estimation of the gradient of the objective function in terms of two experiments per iteration conducted on the real-world control system. The algorithm is tested in the tuning of a PI controller dedicated to the speed control of a nonlinear servo system. Real-time experimental results are given.