Design And Simulation Of Self-Tuning Predictive Control Of Time-Delay Processes

Abstract

Majority industrial processes such as thermal, chemical biological, metallurgical, plastic etc., have time-delays. Therefore, the problem of the identification and optimal control of such systems is of great importance. These time-delay processes can be effectively handled by the Model-based Predictive Control method. The paper deals with design of an algorithm for self-tuning predictive control of such processes. The self-tuning principle is one of possible approaches to control of nonlinear systems or systems with uncertainties. Three types of processes were chosen for simulation verification of the designed self-tuning predictive controller. The program system MATLAB/SIMULINK was used for testing and verification of this predictive controller. INTRODUCTION Time delay is very often encountered in various technical systems, such as electric, pneumatic and hydraulic networks, chemical processes, long transmission lines, robotics, etc. The existence of pure time lag, regardless if it is present in the control or/and the state, may cause undesirable system transient response, or even instability. Consequently, the problem of controllability, observability, robustness, optimization, adaptive control, pole placement and particularly stability and robustness stabilization for this class of systems, has been one of the main interests for many scientists and researchers during the last five decades. For control engineering, such processes can often be approximated by the FOTD (First-Order-Time-Delay) model. Time-delay in a process increases the difficulty of controlling it. However the approximation of higherorder process by lower-order model with time-delay provides simplification of the control algorithms. When high performance of the control process is desired or the relative time-delay is very large, the predictive control strategy is one of possible approaches. 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. First versions of Smith Predictors were designed in the continuous-time modifications, see e.g (Normey-Rico and Camacho 2007). Because most of modern controllers are implemented on digital platforms, the discrete versions of the time-delay controllers are more suitable for time-delay compensation in industrial practice. Most of authors designed the digital timedelay compensators with fixed parameters. However, the time-delay compensators are more sensitive to process parameter variations and therefore require an auto-tuning or adaptive (self-tuning) approach in many practical applications. Two adaptive modifications of the digital Smith Predictors are designed in (Hang et al. 1989; Bobal et al. 2011) and implemented into MATLAB/SIMULINK Toolbox (Bobal et al. 2012a; Bobal et al. 2012b). Model predictive control (MPC) is becoming increasable popular method in industrial process control where time-delays are component parts of the system. However, an accurate appropriate model of the process is required to ensure the benefits of MPC. Furthermore, perturbations of a time-delay and parameters of an external linear model may induce complex behaviours (oscillations and instabilities) of the closed-loop system. Problems with time-variant model parameters can be solved using adaptive (selftuning) approach. MODEL PREDICTIVE CONTROL Model Predictive Control, also known as Receding Horizon Control (RHC), attracts considerable research attention because of its unparalleled advantages. These include (Lu 2008): • Applicability to a broad class of systems and industrial applications. • Computational feasibility. Proceedings 27th European Conference on Modelling and Simulation ©ECMS Webjorn Rekdalsbakken, Robin T. Bye, Houxiang Zhang (Editors) ISBN: 978-0-9564944-6-7 / ISBN: 978-0-9564944-7-4 (CD) • Systematic approach to obtain a closed-loop control and guaranteed stability. • Ability to handle hard constraints on the control as well as the system states. • Good tracking performance. • Robustness with respect to system modeling uncertainty as well as external disturbances. The MPC strategy performs the optimization of a performance index with respect to some future control sequence, using predictions of the output signal based on a process model, coping with amplitude constraints on inputs, outputs and states. For a quick comparison of MPC and traditional control scheme, such as PID control, Fig. 1 shows the difference between the MPC and PID control schemes in which “anticipating the future” is desirable while a PID controller only has capacity of reacting to the past behaviours. The MPC algorithm is very similar to the control strategy used in driving a car (Lu 2008). Figure 1: Difference between the MPC and PID control k+1 k-1 k y(t) ˆ ( ) y t w (t) past future u(t) time N1