Generalized Predictive Control Using Genetic Algorithms (GAGPC). An Application to Control of a Non-linear Process with Model Uncertainty

Predictive Control is one of the most powerful techniques in process control, but its application in non-linear processes is challenging. This is basically because the optimization method commonly used limits the kind of functions which can be minimized. The aim of this work is to show how the combination of Genetic Algorithms (GA) and Generalized Predictive Control (GPC), what we call GAGPC, can be applied to nonlinear process control. This paper also shows GAGPC performance when controlling non-linear processes with model uncertanties. Success in this area will open the door to using GAGPC for a better control of industrial processes. 1 Motivation and objectives One limitation that should be overcome in a control process problem is the existence of non-linearities. They appear in di erent forms in almost all industrial processes, { for example, actuator non-linearities such as: saturations, dead-zones, backlash { or non-linear processes. Another important problem is model imperfection, usually the mathematical model cannot exactly reproduce the process behaviour. Predictive control has demonstrated excellent performances in both theoretical studies and industrial applications ([2], [8], [3]). Even so, their application in the control of non-linear processes is complicated. This is basically because of the optimization method that has come to be used in these controllers. The proposed solution in this paper is based on the use of a very powerful optimizer: Genetic Algorithms ([4], [5]). The combination of Generalized Predictive Control GPC ([6], [7]), and Genetic Algorithms (GA) is what we call GAGPC. In [10], [1] and [9] GAGPC controllers and their application in the control of processes with non-linear actuators are described in more detail. This work ? Supported by the Spanish Government Commission CICYT project TAP96-1090C04-02. shows how this technique is applied to non-linear processes, even with modelling errors, and remarks on how to use it in real-time control. The work is divided in several parts that cover the following points: { A brief description of the Generalized Predictive Control using Genetic Algorithms (GAGPC). { GAGPC application to real-time control. { GAGPC in non-linear process control with model errors. 2 Generalized Predictive Control using Genetic Algorithms (GAGPC) The predictive control used is the Generalized Predictive Controller (GPC) with the following essential characteristics: { It requires a process model and a disturbance model to obtain output predictions ( gure 1). Fig. 1. Model to obtain predictions. In the original formulation of the GPC, the CARIMA model is used: y(t) = yu(t) + n(t) (1) y(t) = B(z ) A(z ) u(t 1) + T (z ) A(z ) d(t) (2) From which the output predictions in time 't + i', with the available information until time 't', are obtained, y(t + ijt). { The control action is obtained from minimization of the following cost index: