Figure 7. Heat exchanger network case study topology. Figure 2. Representation of the lumped model: a) single cell detailed; b) a countercurrent heat exchanger. Tables 1 and 2 describe the geometric charac- teristics of each heat exchanger in the network and Matlab offers an interactive environment through Simulink, which was used in this work. A useful tool in Simulink to solve state equations are the S-functions, which enable the interaction with Simulink equation solvers. It can be defined as a computer language description of a Simulink block that, in this work, is written in Matlab. In Eqs. (1)-(9), “is the heat transfer coefficient, Vis the cell volume, C, is the heat capacity, p is the density, mis the mass flow rate and A; and A; are the shell and tube areas for each cell, respectively. In this work, the HEN model was implemented considering N= 10 in all the heat exchangers. Figure 3. Block diagram of the simulation steps using Simulink. ia Se SO es eee a ee eae process. The system of differential equations is solved using the Runge-Kutta method throughout the ode45 solver in Simulink. Neural network model predictive controller Two typical steps are involved when using neural networks for control: system identification and control design. First, the neural network is developed (or trained) to represent the plant. Then, for model predictive control, the control design is performed by using the plant model and an optimization algorithm computes the control signals that optimizes future plant performance at each time step. Figure 4. Schematic diagram of an artificial neural network learning process. Figure 5. Training, validation and test performances at each epoch for the neural network model. Figure 6. Training results for neural network predictive control and the associated errors. Figure 7. Validating results for neural network predictive control and the associated errors Table 3. Parameters of the ANN and MPC application of a neural-based predictive controller in a heat exchanger network plant. A lumped parameter model was implemented to generate the training data for the neural network. Comparison with the well- known PID controller showed that the overall perform- ance can be improved when a NNPC is applied as the control system for plants with complex dynamics. The controller system requires a well-trained network and adequate parameters for the predictive controller; however, an important advantage of this approach is that the output and input constraints can be directly included in the controller optimization problem. The case study showed that overshoot and settling time can be improved with a more sophisticated controller and the performance can be even more significant in bigger heat exchanger networks. Also, this simulation can be extended for real plants by using measured values of plant operation in the neural network train- ing and validation procedures and, then, the strategy can be applied as an industrial decision-making tool related to the operation of heat exchanger networks. Figure 8. Step response comparison for NNMPC and PID controller. Improvements in control performance regarding set point tracking are presented in this work by the The authors would like to acknowledge the fin- ancial support from the National Council for Scientific and Technological Development - CNPq (Brazil) and
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