GMV-PID Controller Design with Gradient Method for the Energy Weighting Factor in Nonlinear Plants

Since the PID tuning formula of Ziegler-Nichols step test, perhaps the best known, the process control literature is still showing lots of PID control schemes to improve the closed-loop stability. In this paper, using the relationship between the PID and generalized minimum variance (GMV) controller and adjusting online the control weighting factor by an adaptive learning algorithm of first-order (gradient method), a new control design is investigated. Besides, the control algorithm is gathering the direct estimation technique, with the covariance resetting procedure based on the weighted prediction error, to deal with nonlinear plants. Numerical and practical experiments are shown to evaluate the behavior of the proposed GMV-PID control design.