Figure 4 5.2 Conventional PID control of the heat exchangers
Related Figures (6)
The neural network-based (NN) predictive controller uses a neural network model of the controlled plant tc predict future plant performance (Figure 1). The plant can be nonlinear as well as influenced by various uncertainties. The NN predictive controller calculates the predicted control input that will optimize the plant performance over a specified future time horizon (Soloway and Haley, 1996). Figure 1: The scheme of neural-network-based predictive control The predictions are used by a numerical optimization procedure to determine the control signal that minimize: the performance criterion (1) over the specified horizon: 2. Neural network-based model predictive control primary controlled output. The output of the primary controller is used to adjust the set point of a secondar controller, which generates a control signal to the controlled process. The process output yi is fed back to th primary controller, and a signal from an intermediate stage of the process y2 is fed back to the secondar controller. The main advantage of the cascade control is that the better control performance is assured for a types of load disturbances. The primary controller is usually tuned as a controller with an integral action, as it i responsible for achieving the control objective. The secondary controller must compensate the load disturbanc as fast as possible and using the P controller with a high gain for fast action is usually sufficient. The secondar controller is tuned at first and the primary controller is tuned with working inner loop. As the behaviour of th controlled process is often nonlinear and asymmetric and as the dynamics of the inner loop has to be taken int account for the primary controller tuning, the primary controller tuning is not so straight forward. So, the neur network model of the controlled process can be used to improve the primary controller tuning. 4. Control system with an auxiliary control input Figure 3: Scheme of a control system with an auxiliary control input 5. Simulations and results Table 1: Parameters of the conventionally tuned PID controllers 5.3 NNPC of the heat exchangers The transfer function parameters were identified as follows: the order n = 2, the gain K = - 30 Ks m*%, the time constant T = 183 s, and the time delay D= 6s. The PID controller parameters are presented in Table 1. Table 2: Values of IAE, ISE, and V In Eq(5), e(f) is the error between the reference value r(t) and the actual process output y(t). The numerical results are compared in Table 2. According to IAE and ISE, the control performance was bette when the control structures with NNPC were used, see Table 2. Conventional PID control led to the worst values of IAE and ISE as well as to maximum overshoots and undershoots in control responses. The maximum tota volume of cooling water was consumed in simple NNPC. According to the IAE, ISE and V, the best contro structure is the NNPC-based control system with and auxiliary control input. The second best is the NNPC based cascade control. The NNPC-based control system (CS) with the main NN predictive controller and with the auxiliary conventional P controller was also designed and used in simulation experiments for the temperature control in the HEN. The main manipulated variable was the flow rate of the hot stream and the auxiliary manipulated variable was the flow rate of the cold stream. The input to the both controllers is the same control error (Figure 3). The control setup of the main NN predictive controller was as follows. The neural network had 4 delayed process inputs, 3 delayed process outputs and one hidden layer with 6 neurons. 1500 training samples were used. The parameter values in the performance criterion Eq(1) used for the NNPC design were: the prediction and control horizons Ni = 1, Ne = 5, Nu= 2, the weighting parameter A = 0.01. The minimum control input gimin = 1.6667x10% m%s", the maximum control input gimax = 0.0086 ms". The auxiliary controller was the P controller with the gain 0.95 Kt st m3, NNPC-based cascade control of 5 HEs in series and control using NNPC-based CS with an auxiliary control input were compared with control using simple NNPC and two conventional PID controllers. The simulation results are presented in Figure 5. The results were compared also using the total consumption of cooling water V consumed during control, the integral quality criteria IAE (integrated absolute error) and ISE (integrated squared error) defined e. g. in (Ogunnaike and Ray, 1994) as follows
