Predictive Control With Filtering Of Input And Output Variables

Abstract

The paper is focused on an implementation of a predictive controller with a colouring filter C in a disturbance model. The filter is often essential for practical applications of predictive control based on transfer function models. It is commonly considered as a design parameter because it has direct effects on closed loop performance. In this paper a computation of predictions for the case with the colouring polynomial is introduced. The computation is based on a particular model of the controlled system in the form of transfer function which is commonly used for description of a range of processes. Performance of closed loop system with and without the colouring polynomial in the disturbance model was compared. INTRODUCTION Model Predictive Control (MPC) or only Predictive Control (Camacho and Bordons 2004, Morari and Lee 1999, Mikles and Fikar 2008) is one of the control methods which have developed considerably over a few past years. Predictive control is essentially based on discrete or sampled models of processes. Computation of appropriate control algorithms is then realized especially in the discrete domain. The basic idea of the generalized predictive control (Clarke and Mohtadi 1987, Clarke and Mohtadi 1987) is to use a model of a controlled process to predict a number of future outputs of the process. A trajectory of future manipulated variables is given by solving an optimization problem incorporating a suitable cost function and constraints. Only the first element of the obtained control sequence is applied. The whole procedure is repeated in following sampling period. This principle is known as the receding horizon strategy. An implementation of a predictive controller based on a transfer function model with a colouring filter C in a disturbance model is described in this paper. The filter is often essential for practical applications of predictive control based on transfer function models. Surveys of practical applications of predictive control are presented in (Quinn and Bandgwell 1996, Quinn and Bandgwell 2000, Quinn and Bandgwell 2003). It is commonly considered as a design parameter because it has direct effects on closed loop performance. A computation of predictions for the case with the colouring polynomial is introduced. The computation is based on a particular model of the controlled system in the form of transfer function which is commonly used for description of a range of processes.The filtering of variables is the equivalent of the colouring polynomial in the noise model. It is practically very difficult to estimate the coefficients of the colouring polynomial. A model with the C-polynomial is then utilized as an example with filtering of input and output variables when the polynomial C is a tuning parameter. In the paper are derived prediction equations for an input output model in the form of transfer function both for the case with the C-filter and without the C-filter. Performance of closed loop system with and without the colouring polynomial in the disturbance model was compared. MODEL OF THE CONTROLLED SYSTEM A model of the second order which is widely used in practice and has proved to be effective for control of a range of various processes was applied. It can be expressed by following transfer function ( ) ( ) ( ) 2 2 1 1 2 2 1 1 1 1