Use of Dynamic Matrix Control in Simulation of Heat System

This paper demonstrates the use of Model Predictive Control (MPC) to system control. Dynamic Matrix Control (DMC) method was chosen and its functionality was verified by a simulation of system control based on a real laboratory model. A control algorithm and the simulation were realized in MATLAB/SIMULINK program environment. Results have proven capabilities of DMC method to control stable oscillatory and nonminimum phase systems. Additionally, real model parameters were tested with a demonstration of a possibility of tuning by a ratio of weighting values form objective function. INTRODUCTION Considering the scientific area of process control, it targets at present tendency of satisfying demands of the maximal productivity of the highest quality products at the lowest cost possible. With the power of the modern computing technology an approach of finding optimal results in reasonable time was made possible. Advanced methods popular in industries with slow and large dimensional systems are predictive control methods (Qin & Badgwell, 2003). These techniques commonly contain an internal model for system behavior predictions. Gained information is further used to calculate a sequence of control inputs by minimizing a sum of squares between the desired and predicted trajectories. Therefore an optimal output is received in reference to the minimal error, eventually to the change of control inputs. Development in this area started in 1980s with the publication of DMC method (Cutler & Ramaker, 1980). Original purpose of DMC was focused on multivariable constrained control problems, mainly occurring in chemical and oil industry. The influence of DMC caused its widespread use in world’s major industrial companies (Morari & Lee, 1999). Over the time there was a vast development of the DMC algorithm, its modifications and possibilities of application. (Garcia & Morshedi, 1986) provided a utilization of a quadratic algorithm for an efficient handling of constraints, tuning and robustness. (Shridhar & Cooper, 1997) suggested a tuning strategy of DMC parameters for SISO systems, followed by an approach in case of MIMO systems (Shridhar & Cooper, 1998). (Dougherty & Cooper, 2003) described an approach to tune the parameters of the basic DMC algorithm for the case of integrating processes. In occurrence of nonlinear processes (Dougherty & Cooper, 2003) suggested a new adaptive control strategy using the output of multiple linear DMC controllers to maintain the performance over a wide range of operational levels. The purpose of this paper is to give an insight on abilities of DMC options for the control of stable processes, primarily in the area of tuning its performance by changing the weight ratio of the optimization process between the output error and a demand of action value. The paper is organized in the following way. General principles of MPC are presented first, followed by the description of specific properties of the DMC method. Basic functionality and characteristics are introduced. The final section presents the implementation of the simulation into the MATLAB/SIMULINK program environment and its results. MODEL PREDICTIVE CONTROL Predictive control is an approach to control a process trough optimization. The main principle is in the prediction of future process outputs based on the inner model of the process. The goal of the control algorithm is to find such a vector of input values that the output of the model is optimal along the defined time area called horizon. To ensure robustness and stability an approach using feedback called the receding horizon strategy is often applied. From the vector of input values only the first value is used as an increment ∆u(k) added to the previous input giving the current input value u(k). In the next step the entire procedure is repeated with new process output values. The area of the optimization is defined by values of horizons representing the amount of sampling periods from the current time into the future. Values of horizons N1 and N2 limit the area, where the divergence between the desired and the output value is minimized. The horizon Nu limits the distance of steps where the action value is minimized. Proceedings 28th European Conference on Modelling and Simulation ©ECMS Flaminio Squazzoni, Fabio Baronio, Claudia Archetti, Marco Castellani (Editors) ISBN: 978-0-9564944-8-1 / ISBN: 978-0-9564944-9-8 (CD) Figure 1: Receding horizon strategy Calculation of the optimal output consists of a free response prediction describing the system behavior in the case of a constant input and the forced response with a reaction on a suggested series of inputs. Based on the superposition principle, the sum of these responses results in the future output prediction. Several methods of MPC are used in practice; the main differences are in the description of the controlled process and in the objective function. The Figure 2 shows a layout of the predictive control and a data transfer. Figure 2: Basic structure of model predictive control The optimization process is based on the minimization of values involved in control. Their mutual relations are formed by an objective function. The general expression of an objective function is     , ) 1 ( ) ( ) ( ) ( ˆ ) ( 1 2 2 2 1             u N