B-splines neural network assisted PID autotuning

Abstract

This paper describes an extension of previous work on the subject of neural network proportional, integral and derivative (PID) autotuning. Basically, neural networks are employed to supply the three PID parameters, according to the integral of time multiplied by the absolute error (ITAE) criterion, to a standard PID controller. These networks were previously trained o!-line, remaining "xed thereafter.In order to make this approach adaptive, one additional neural network is used here to model the relation between the PID parameters and the plant identi"cation measures to the ITAE value. This model will be afterwards employed in an on-line minimization routine which "nds the optimal PID parameters; these will be used to adapt, on-line, the neural networks responsible for the PID parameters.control, because as an analytical expression for its calculation is not known, the optimal PID values must be obtained from an optimization process, relying on simulations of the closed-loop system. As this is a time-consuming operation, involving the application of several perturbations to the plant, this is seldom employed in real time.The work described here arises from past research in this "eld. In this previous approach, ITAE optimum PID values, for several systems, are calculated previously, and are used to train o!-line three neural networks, to approximate the mappings between plant identi"cation measure(s) and the optimal PID parameters. The controller is started with values obtained from the neural networks tuner, based on an open-loop identi"cation. If the plant changes, the tuner provides the controller with approximate optimal PID values, obtained from the neural networks, based on closed-loop plant identi"cation. This scheme will be further detailed in Section 2.In order to improve the performance of the neural network tuner as a result of continuous on-line operation, a new scheme, involving neural networks and genetic algorithms will be presented and discussed in Section 3. Focussing our attention in this paper on the time-variant case, Section 4 introduces the neural networks used, B-spline neural networks. The training algorithm employed will be discussed in Section 5.Focusing now on the modules of the neural network tuner, Section 6 will describe the results obtained for the o!-line and on-line training of the neural networks responsible for the PID parameters. Section 7 will discuss the results obtained for the o!-line and on-line training of the neural network employed for the ITAE calculation.Conclusions and a summary of future work are presented in Section 8.