Model reference adaptive control

This is employed when the process is not well-known. The Model Reference Adaptive Controller contains a reference model to which the command signal or set point change is applied as well as to the process itself (Fig. 7.98)<4 ). The output of the reference model is postulated as the desired controlled process output and this is compared with the actual process output. The difference (or error) e , between the two outputs is used to adjust the controller parameters so as to minimise the relevant integral criterion. For example, if the ISE criterion is employed then the quantity... 

Fio. 7.98. Block diagram of model reference adaptive control system... 

The architecture of the self-tuning regulator is shown in Fig. 7.99. It is similar to that of the Model Reference Adaptive Controller in that it also consists basically of two loops. The inner loop contains the process and a normal linear feedback controller. The outer loop is used to adjust the parameters of the feedback controller and comprises a recursive parameter estimator and an adjustment mechanism. 

Coughanowr, D. R. Process Systems Analysis and Control, 2nd edn. (McGraw-Hill, New York, 1991). Kuo, B. C. Discrete Data Control Systems (Prentice-Hall, Englewood Cliffs, New Jersey, 1970). Landau, Y. D. Adaptive Control—The Model Reference Approach (Marcel Dekker, New York, 1979). Popovic, D. and Bhatkar, V. P. Distributed Computer Control for Industrial Automation (Marcel Dekker, New York, 1990). 

Landau, Y. D. Adaptive Control—The Model Reference Approach (Marcel Dekker, New York, 1979). 

Model reference adaptive control is based on a Lyapunov stability approach, while the hyperstability method uses Popov stability analysis. All of the above methods have been tested on experimental systems, both SISO and MIMO (53), (54), (55). The selftuning regulator is now available as a commercial software package, although this method is not satisfactory for variable time delays, an important industrial problem. 

Oliver, W. K. Seborg, D. E. and Fisher, D.G., "Model Reference Adaptive Control Based on Lyapunov s Direct Method," Chem. Engr. Comm., 1973, 1, 125. 

Figure 21. Model reference adaptive control scheme. 

If the process is not known well, we need to evaluate the objective function on-line (while the process is operating) using the values of the controlled output. Then the adaptation mechanism will change the controller parameters in such a way as to optimize (maximize or minimize) the value of the objective function (criterion). In the following two examples we examine the logic of two special self-adaptive control systems model reference adaptive control (MRAC) and self-tuning regulators (STRs). 

Example 22.3 Model-Reference Adaptive Control (MRAC)... 

We notice that the model-reference adaptive control is composed of two loops. The inner loop is an ordinary feedback control loop. The outer loop includes the adaptation mechanism and also looks like a feedback loop. The model output plays the role of the set point while the process... 

The model-reference adaptive control was originally proposed by Whitaker et al. in 1958 and was developed for servo problems ... 

Design of Model-Reference Adaptive Control Systems for Aircraft, by H. P. Whitaker, J.Yamron, and A. Kezer, Report R-164, Instrumentation Laboratory, MIT, Cambridge, Mass. (1958). 

Discuss the logic of model-reference adaptive control and self-tuning regulators. Find the similarities and differences between the two configurations. 

Show qualitatively that the structure of a self-tuning regulator can be derived from that of a model-reference adaptive control if the parameter estimation is done by updating the reference model. 

Neural networks have also been used in model reference adaptive control (MRAC) structures (Figure 12.4) [Naranedra and Parthasarathy, 1990 Narendra, 1992]. This approach builds upon established techniques for adaptive linear control and incorporates neural networks to address the problem of controlling nonlinear systems. The MRAC approach is directed at adapting the controlled system such... 

The process of filtering the obtained conversion data with the aid of a polyma-ization model, the so-called Kalman filtering [1] or the model reference adaptive control [2], makes it possible to control the process accurately and to obtain the desired microstructuie (see Qiapter 7). 

Conventional Model-Reference Adaptive Control Techniques... 

For many years, there have basically been two distinct methods for finding the solution of the adaptive control problem [2]. These are direct and indirect control methods. When the controller parameters 6 k) are directly adjusted to reduce some norm of the output error between the reference model and the plant, this is called direct control or implicit identification. In indirect control, also referred to as explicit identification, the parameters of the plant are estimated as the elements of a vector p k) at each instant fc, and the parameter vector 0 k) of the controller is chosen assuming that p(fc) represents the true value of the plant parameter vector p. Figures 4.3 and 4.4 respectively show the direct and indirect model-reference adaptive control structures for a linear time invariant (LTI) plant. It is important to note that in both cases efforts have to be made to probe the system to determine its behaviour because control action is being taken based on the most recent in-... 

Fig. 4.3. Direct model-reference adaptive control structure...

The first controller implemented on the structure was the direct MRAC shown in Fig. 4.5. This gives a basis for comparison between direct and indirect control. Figure 4.6a shows a plot of the open-loop response envelope, the desired response envelope, and the closed-loop response achieved. As can be seen, the closed-loop system adapts to the reference-model response until the deadband is reached (after approximately 11s), at which point adaptation is turned off. The deadband is inherent to the Nitinol wire actuators. 

After successful implementation of conventional model-reference adaptive controllers on smart structures, the next logical step was to investigate the possibility of using a neural network for adaptive control implementations. The linear and nonlinear mapping properties of neural networks have been extensively utilized in the design of multilayered feed-forward neural networks for the implementation of adaptive control algorithms [10]. 

A neural network-based model reference adaptive control scheme for nonlinear plants is presented in this section. 

The schematic diagram of the model reference adaptive control system is shown in Fig. 4.12. 

In this study, adaptive control algorithms have been utilized for designing active controllers for smart structure test articles. Adaptive control schemes require only a limited a priori knowledge about the system in order to be controlled. The availability of limited control force and inherent deadband and saturation effects of shape memory actuators are incorporated in the selection of the reference model. The vibration suppression properties of smart structures were successfully demonstrated by implementing the conventional model reference adaptive controllers on the smart structure test articles. The controller parameters converged to steady state values within 8 s for both direct and indirect MRACs. 

Various neural network-based adaptive control techniques were discussed in this study. A major problem in implementing neural network-based MRACs is the translation of the output error between the plant and the reference model so as to train the neural controller. A technique called iterative inversion, which inverts the neural identification model of the plant for calculating neural controller gains, has been used. Due to the real-time computer hardware limitations, the performance of neural network-based adaptive control systems is verified using simulation studies only. These results show that neural-network based MRACs can be designed and implemented on smart structures. 

Hoskins, D.A. Neural Network Based Model-Reference Adaptive Control. Ph. D. Dissertation, University of Washington, UMI Dissertation Services, Ann Arbor, MI (1990)... 

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