Adaptive Predictive Control of Three - Tank - System

Abstract

This paper is focused in application of a self - tuning predictive controller for real - time control of a three - tank - system laboratory model. The objective laboratory model is a two input - two output (TITO) nonlinear system. It is based on experience with authentic industrial control applications. The controller integrates a predictive control synthesis based on a multivariable state - space model of the controlled system and an on - line identification of an ARX model corresponding to the state - space model. The model parameters are recursively estimated using the recursive least squares method with the directional forgetting. The control algorithm is based on the Generalised Predictive Control (GPC) method. The optimization was realized by minimization of a quadratic objective function. Results of real-time experiments are also included. approaches, the control actions are taken based on past errors. MPC uses also future values of the reference signals. The aim of this contribution is implementation of an adaptive predictive controller for control of the three - tank - system laboratory model. The design of the controller is based on a state - space model. An initial state - space model was constructed according to first principles and physical rules. The parameters of the system were not recognizable. Moreover, the laboratory model is a nonlinear system with variable parameters and its description by a linear model is valid only in a neighbourhood of a steady state. Self-tuning controllers (11), (12) are a possible approach to the control of this kind of system. However, the state - space description is not quite suitable for a recursive identification of the parameters of the process which is performed during control with self - tuning controllers. The state space model was then converted to a model in the form of difference equations. This model is suitable for the recursive identification. So the proposed approach combines both types of models. The state - space model is used for the controllers design and the corresponding input/output model for the estimation of the unknown parameters. Of course it is possible to base the controllers design on the input/output model as well. But the main theoretical results of predictive control come from a state space formulation, which can be used easily both for SISO and MIMO systems. It also enables to solve tasks which are unsolvable when using an input/output model. For example control with state constraints. Reverse conversion of the difference equations to the original state - space model is not possible. It is explained in section 3. An alternative state - space model was than established and used for the controllers design. This model corresponds to the original model despite the fact that it has a different structure. So it is possible to assume that this model describes main properties of the controlled process as well as the original model. The Generalised Predictive Control (GPC) method (13), (14) was then applied for the controllers design. In the optimization part of the algorithm a quadratic cost function was used. The algorithm takes into account constraints of manipulated variables. The recursive least squares method with the directional forgetting is used in the identification part.