Applications of a Model Based Predictive Control to Heat-Exchangers Radu Bălan * , Vistrian Mătieş * , Victor Hodor ** , Olimpiu Hancu * , Sergiu Stan *** * Technical University of Cluj-Napoca, Dept. of Mechatronics, Cluj-Napoca, Romania ** Technical University of Cluj-Napoca, Dept. of Thermodynamics, Cluj-Napoca, Romania ** Technical University of Cluj-Napoca, Dept. of Mechanics and Programming, Cluj-Napoca, Romania Abstract—Model based predictive control (MBPC) is an optimization-based approach that has been successfully applied to a wide variety of control problems. When MBPC is employed on nonlinear processes, the application of this typical linear controller is limited to relatively small operating regions. The accuracy of the model has significant effect on the performance of the closed loop system. Hence, the capabilities of MBPC will degrade as the operating level moves away from its original design level of operation. This paper presents an MPC algorithm which uses on-line simulation and rule-based control. The basic idea is the on- line simulation of the future behaviour of control system, by using a few control sequences and based on nonlinear analytical model equations. Finally, the simulations are used to obtain the ‘optimal’ control signal. These issues will be discussed and nonlinear modeling and control of a single- pass, concentric-tube, counter flow or parallel flow heat exchanger will be presented as an example. I. INTRODUCTION Model Based Predictive Control (MBPC) refers to a class of algorithms that utilize an explicit process model to compute the control signal by minimizing an objective function [1]. The performance objective typically penalizes predicted future errors and manipulated variable movement subject to various constraints. The ideas appearing in greater or lesser degree in all the predictive control family are basically: -explicit use of a model to predict the process output in the future; -on line optimization of a cost objective function over a future horizon; -receding strategy, so that at each instant, the horizon is displaced towards the future, which involves the application of the first control signal of the sequence calculated at each step. Performance of MBPC could become unacceptable due to a very inaccurate model, thus requiring a more accurate model. This task is an instance of closed-loop identification and adaptive control. Here it is important to remember that the model is only used as an instrument in creating the best combined performance of the controller and the actual system, so the model does not necessarily need to be a good open-loop model of the system. The performance measure should be able to capture as much of the closed loop behavior as possible. Let’s consider that it is possible to compute: - the predictions of output over a finite horizon (N); - the cost of an objective function, for each possible sequence:    ) ( ),.., 1 ( ), ( . N t u t u t u u    (1) and then to choose the first element of the optimal control sequence. For a first look, the advantages of the proposed algorithm [2] include the following: -the minimum of objective function is global; -it is not necessary to invert a matrix, so potential difficulties are avoided; -it can be applied to nonlinear processes if a nonlinear model is available; -the constraints (linear or nonlinear) can easily be implemented. The drawback of this scheme is a very long computational time, because there are possibly a lot of sequences. For example, if u(t) is applied to the process using a “p” bits numerical-analog converter (DAC), the number of sequences is 2 p * N .Therefore, the number of sequences must be reduced. In the next sections, these issues will be discussed and nonlinear modeling and control of a single-pass, concentric-tube, counter flow heat exchanger will be presented as an example. II. THE MODEL OF THE HEAT-EXCHANGER Heat exchangers are devices that facilitate heat transfer between two or more fluids at different temperatures. Usually, MBPC uses a linear model and an on-line least square algorithm (RLS) to determine the parameters. Heat exchangers are nonlinear processes. To apply the standard MBPC algorithms it is possible to use multiple model adaptive control approach (MMAC) which uses a bank of models to capture the possible input-output behavior of processes [3]. Other solutions are based on neural networks and fuzzy logic [4], [5]. In this paper it is used an example from [6]: a heat exchanger with hot fluid -engine oil at 80ºC, cold fluid - water at 20º C, by using a single-pass counter flow (or parallel flow for some experiments) concentric-tube. Other data and notations: length (L): 60m, heat transfer coefficients (k 1 =1000 W/(m 2 ºC), k 2 =80 W/(m 2 ºC)), the temperature profile of fluids and wall ( ) , ( 1 t z  , ) , ( 2 t z  , ) , ( t z w  ), specific heat (c 1 , c 2 , c w ), cross- sectional area for fluids flow and wall (S 1 , S 2 , S w ), density of fluids and wall (ρ 1 , ρ 2 , ρ w ), flow speed of fluids (v 1 , v 2 ), transfer area (S) (fig. 1). If physical properties (density, heat capacity, heat transfer coefficients and flow speed) are assumed 3URFHHGLQJV RI WKH WK 0HGLWHUUDQHDQ &RQIHUHQFH RQ &RQWURO  $XWRPDWLRQ -XO\     $WKHQV  *UHHFH 7