Predictive Control Of Time-Delay Processes

Abstract

In technical practice often occur higher order processes when a design of an optimal controller leads to complicated control algorithms. One of possibilities of control of such processes is their approximation by lower-order model with time-delay (dead time). One of the possible approaches to control of dead-time processes is application of predictive control methods. The paper deals with design of an algorithm for predictive control of high-order processes which are approximated by second-order model of the process with time-delay. INTRODUCTION Some technological processes in industry are characterized by high-order dynamic behaviour or large time constants and time-delays. Time-delay in a process increases the difficulty of controlling it. However using the approximation of higher-order process by lower-order model with time-delay provides simplification of the control algorithms. Let us consider a continuous-time dynamical linear SISO (single input ( ) u t – single output ( ) y t ) system with time-delay d T . The transfer function of a pure transportation lag is d T s e where s is a complex variable. Overall transfer function with time-delay is in the form ( ) ( ) d T s d G s G s e = (1) where ( ) G s is the transfer function without time-delay. Processes with time-delay are difficult to control using standard feedback controllers. One of the possible approaches to control processes with time delay is predictive control. The predictive control strategy includes a model of the process in the structure of the controller. The first time-delay compensation algorithm was proposed by (Smith 1957). This control algorithm known as the Smith Predictor (SP) contained a dynamic model of the time-delay process and it can be considered as the first model predictive algorithm. Model Based Predictive Control (MBPC) or only Predictive Control 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 namely in the discrete domain. The term Model Predictive Control designates a class of control methods which have common particular attributes (Camacho and Bordons 2004, Mikles and Fikar 2008). • Mathematical model of a systems control is used for prediction of future control of a systems output. • The input reference trajectory in the future is known. • A computation of the future control sequence includes minimization of an appropriate objective function (usually quadratic one) with the future trajectories of control increments and control errors. • Only the first element of the control sequence is applied and the whole procedure of the objective function minimization is repeated in the next sampling period. The principle of MBPC is shown in Fig. 1, where ( ) t u is the manipulated variable, ( ) t y is the process output and ( ) t w is the reference signal, N1, N2 and Nu are called minimum, maximum and control horizon. This principle is possible to define as follows: k+1 k-1 k y(t) ˆ ( ) y t w (t) past future u(t) time N1