Direct inverse control (Figure 4-1) utilises an inverse system model. The inverse model is cascaded with the process, so that the composed system results in an identity mapping between desired response (i.e. the network inputs) and the controlled system output. The network thus acts directly as the controller in such a configuration.
Process u d yp r yp z-1
Figure 4-1 - Direct Inverse Control.
Though direct inverse control is well-tested in simulation studies, few laboratory or pilot-scale experimental work has been reported. Real-time application typically involves first identifying the forward dynamics from open-loop perturbation experiments (e.g., step changes). This forward dynamic model may have the following general form as in equation 4-1:
(
+1, ... − −1, −1, −2... − −1)
= k k k n k k k n
k f y y y u u u
u (4-1)
where yk is the process variable and uk is the manipulated variable at time step k. The methodology for training direct inverse neural networks is illustrated in Figure 4-2.
Direct Inverse Neural Network Dynamic Process Training signal + - z-1 z-k y(k+1) z-1 z-k u(k)
Figure 4-2 - Framework for training direct inverse control neural network controllers.
Khalid & Omatu (1992) trained a neural network to learn the inverse dynamics for temperature control of a 8 [dm3] water bath. The water bath was equipped with a stirrer and the single final control element was a 600 [W] electric heater. The control objective required stepping the temperature set point with minimal error. The neurocontroller performed better than conventional PID control and had effective disturbance rejection capabilities. Dirion et al. (1995) also used back-propagation to learn the inverse temperature dynamics of a jacketed water bath. Two heat exchangers in the cooling circuit allowed for both heating and cooling of the water bath. Although a single open-loop experiment was sufficient to determine the forward model, Dirion et al. (1995) stressed the importance of covering a wide range of possible input space data (i.e., domain).
Savkovic-Stevanovic (1996) developed a conventional direct inverse neurocontroller for a pilot plant distillation process. The top product composition was the controlled variable with the reflux rate the single manipulated variable. Open loop training data were collected in the region of the desired set point. The inverse model included feed rate, pressure drop and bottoms flow rate as input nodes, thereby providing additional process information as feedforward control within the feedback neurocontrol structure. Savkovic-Stevanovic (1996) did not explain the selection criteria for the input layer's structure in terms of time delay inputs of the controlled variable nor the addition of other process variables as feedforward information. The control response proved to be oscillatory, possibly due to the identity mapping produced by direct inverse control.
Palancar et al. (1998) studied real-time direct inverse control for the neutralisation of aqueous solutions of acetic and propionic acids with NaOH in a laboratory scale CSTR. The controlled variable was the reactor's downstream pH with the NaOH flow rate as manipulated variable. A simplified fundamental model (i.e., the dynamics of pH sensor and the valve transients were not incorporated) was used to generate open- loop data for training a forward neural network model of the neutralisation process. An inverse model was trained based on the forward neural network. The back- propagation algorithm trained both the forward and inverse models. The forward neural network model was updated on-line and used in the control loop to adapt the inverse controller on-line. The control response was highly oscillatory and due to a lack of sufficient training data for typical operating conditions, the generalisation to disturbances was unsatisfactory.
Hussain and Kershenbaum (2000) considered the real-time control of a 100 [L] exothermic CSTR fitted with an external heat exchanger. Forward and inverse neural network models were used in an internal model control (IMC) strategy. Owing to safety and cost considerations, the heat generation and product composition were computed using a simulated process model in tandem with the actual process. Steam was sparged into the reactor to generate the calculated heat generation, making only the composition a purely calculated variable. The control system had the calculated concentration and the measured reactor temperature as the process inputs, with the temperature set point of the cooling jacket as the single manipulated variable. The IMC controller thus served as a master controller to a temperature PID slave controller that manipulated cooling water flow into the external heat exchanger. The training data for the forward model was generated in the open-loop by perturbing the jacket temperature set point. Open-loop data collection was necessitated by the absence of an appropriate method to compute process dynamics from closed loop data. A real exothermic CSTR could never be operated safely in the open-loop. Back- propagation was used to train both the forward and inverse neural network models. The controller proved sensitive to plant/model mismatch and the accuracy of the inverse model.
These real-time applications all involve using back-propagation as the learning rule and their complexity is limited to SISO control applications. The back-propagation algorithm has a sensitive dependence on chosen initial conditions and hence finding the global optimum is not assured (Ydstie, 1990). Critically, these real-time applications emphasise the performance impact of choosing the correct input space (i.e., vectors) based on past process variable measurements, but do not present a systematic or theoretical approach to selecting the input space. The input vector in each case was selected using trial-and-error evaluation. Though model validation techniques have been proposed as guidelines to assess the appropriate number of past inputs and outputs, the final selection was determined on a case-specific basis
(Hussain and Kershenbaum, 2000). The number of delayed inputs to the neural network was frequently estimated from the order of the system and dead time of the process. Model development was always based on open-loop response data, limiting the application of these techniques to open-loop stable processes.
Though these real-time applications typically involved conventional set point tracking, Nguyen and Widrow (1990) noted that neural networks may be trained to minimise cost functions instead of a performance error. This approach contrasts with direct inverse control in that the identity mapping is not sought as the objective function. The desired performance of the closed loop is specified by a reference model or cost function (Hunt et al. ,1992). Hunt et al. (1992) denote this variant of direct inverse control as model reference control (Figure 4-3). In general, this approach is more robust than direct inverse control that seeks perfect control (Seborg, 1989). Process u d yp Reference/ Performance Model Σ - + ec r ec yr
Figure 4-3 - Direct model reference control.