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Figure 1: a) The heat exchanger scheme. b) The steady-state temperature profile for co-current flow A tubular heat exchanger is the simplest form of heat exchanger and consists of two coaxial tubes carrying the hot and cold fluids. The co-current tubular heat exchanger was considered in the research, where petroleum is heated by hot water passed through a copper tube (Vasi¢kaninova and BakoSova, 2015), (Figure 1). Among the input variables, the hot water flow rate, gs(f), was selected as the control input. The controlled variable was the outlet petroleum temperature, Tiouz. The mathematical model of the HE was derived under several simplifying assumptions. Coordinate z measures the distance of a modelled section from the inlet. The fluids move in a plug velocity profile and the petroleum, tube and water temperatures: 74(z,f, T2(z,) and T3(Z,f), are functions of the axial coordinate, z, and time, ¢ The petroleum, water and tube material densities, pi, as well as the specific heat capacities, Cpi, i= 1, 2, 3, are assumed to be constant. The simolified nonlinear dvnamic mathematical model of the co-current heat exchanaer is described bv three 2. Tubular heat exchanger

Figure 1 a) The heat exchanger scheme. b) The steady-state temperature profile for co-current flow A tubular heat exchanger is the simplest form of heat exchanger and consists of two coaxial tubes carrying the hot and cold fluids. The co-current tubular heat exchanger was considered in the research, where petroleum is heated by hot water passed through a copper tube (Vasi¢kaninova and BakoSova, 2015), (Figure 1). Among the input variables, the hot water flow rate, gs(f), was selected as the control input. The controlled variable was the outlet petroleum temperature, Tiouz. The mathematical model of the HE was derived under several simplifying assumptions. Coordinate z measures the distance of a modelled section from the inlet. The fluids move in a plug velocity profile and the petroleum, tube and water temperatures: 74(z,f, T2(z,) and T3(Z,f), are functions of the axial coordinate, z, and time, ¢ The petroleum, water and tube material densities, pi, as well as the specific heat capacities, Cpi, i= 1, 2, 3, are assumed to be constant. The simolified nonlinear dvnamic mathematical model of the co-current heat exchanaer is described bv three 2. Tubular heat exchanger

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v.2 Neural-network-based predictive control or the heat exchanger Model-based predictive control (MPC) is a strategy that is widely used in process industry. MPC uses the system model to predict the system's future outputs based on the current value of the system output and future value of inputs. Using this information, it calculates the optimal value of the future control inputs with respect to a predefined cost function. A typical block diagram for MPC is shown in Figure 2. The objective of the predictive control strategy is to estimate the future output of the plant and to minimize a cost function (6) based on the error between the predicted output of the processes and the reference trajectory
v.2 Neural-network-based predictive control or the heat exchanger Model-based predictive control (MPC) is a strategy that is widely used in process industry. MPC uses the system model to predict the system's future outputs based on the current value of the system output and future value of inputs. Using this information, it calculates the optimal value of the future control inputs with respect to a predefined cost function. A typical block diagram for MPC is shown in Figure 2. The objective of the predictive control strategy is to estimate the future output of the plant and to minimize a cost function (6) based on the error between the predicted output of the processes and the reference trajectory
Table 1: Closed-loop control performance criteria
Table 1: Closed-loop control performance criteria
Figure 3: a) Control trajectories ensured by NNPC (solid) and PID controller (dashed), reference (dash- dotted), tolerance (dotted). b) Control trajectories ensured by robust MPC (solid) and PID controller (dashed), reference (dash-dotted), and tolerance (dotted). Simulations of the advanced and the PID control were done using the model of the heat exchanger in Eq(1)- Eq(3) in MATLAB/Simulink R2014b using CPU i5 1.7 GHz and 6 GB RAM. The results of NNPC and PID control are compared in Figure 3a, where the trajectories of the petroleum temperature in the outlet stream are shown. The analytical quality criteria were also evaluated, see Table 1, where fset represents the mean value of the settling time, ISE and IAE are integral of squared error and integral of absolute error and Vota is the total consumption of hot medium. NNPC assured the minimum values of all criteria. In comparison to PID control, the settling time was reduced in about 70 %, the values of IAE and ISE decreased in 64 % and 66 %, respectively, the overall consumption of hot medium was reduced in approximately 32 %. The disadvantage of this strategy was a small offset and oscillating control response. The results of robust MPC with integral action are presented in Figure 3b. The control trajectory achieved using robust MPC is smooth and without offset. In comparison with PID control, the settling time was reduced in about 33 %, the values of IAE and ISE decreased in 56% and 49%, respectively, and the overall consumption of hot medium was reduced in approximately 5 %.
Figure 3: a) Control trajectories ensured by NNPC (solid) and PID controller (dashed), reference (dash- dotted), tolerance (dotted). b) Control trajectories ensured by robust MPC (solid) and PID controller (dashed), reference (dash-dotted), and tolerance (dotted). Simulations of the advanced and the PID control were done using the model of the heat exchanger in Eq(1)- Eq(3) in MATLAB/Simulink R2014b using CPU i5 1.7 GHz and 6 GB RAM. The results of NNPC and PID control are compared in Figure 3a, where the trajectories of the petroleum temperature in the outlet stream are shown. The analytical quality criteria were also evaluated, see Table 1, where fset represents the mean value of the settling time, ISE and IAE are integral of squared error and integral of absolute error and Vota is the total consumption of hot medium. NNPC assured the minimum values of all criteria. In comparison to PID control, the settling time was reduced in about 70 %, the values of IAE and ISE decreased in 64 % and 66 %, respectively, the overall consumption of hot medium was reduced in approximately 32 %. The disadvantage of this strategy was a small offset and oscillating control response. The results of robust MPC with integral action are presented in Figure 3b. The control trajectory achieved using robust MPC is smooth and without offset. In comparison with PID control, the settling time was reduced in about 33 %, the values of IAE and ISE decreased in 56% and 49%, respectively, and the overall consumption of hot medium was reduced in approximately 5 %.
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