Nonlinear and Adaptive Control

Krstic, M., Kanellakopoulos, L, Kokotovic, P. V. (1995). Nonlinear and adaptive control design. New York, NY Wiley. 

M. Krstic, I. Kanellapoulos and P. Kokotovic, Nonlinear and Adaptive Control Design. Wiley, New York, 1995. 

Having successfully implemented conventional MRAC techniques, the next logical step was to try to incorporate the MRAC techniques into a neural network-based adaptive control system. The ability of multilayered neural networks to approximate linear as well as nonlinear functions is well documented and has foimd extensive application in the area of system identification and adaptive control. The noise-rejection properties of neural networks makes them particularly useful in smart structure applications. Adaptive control schemes require only limited a priori knowledge about the system to be controlled. The methodology also involves identification of the plant model, followed by adaptation of the controller parameters based on a continuously updated plant model. These properties of adaptive control methods makes neural networks ideally suited for both identification and control aspects [7-11]. 

Adaptive Control. An adaptive control strategy is one in which the controller characteristics, ie, the algorithm or the control parameters within it, are automatically adjusted for changes in the dynamic characteristics of the process itself (34). The incentives for an adaptive control strategy generally arise from two factors common in many process plants (/) the process and portions thereof are really nonlinear and (2) the process state, environment, and equipment s performance all vary over time. Because of these factors, the process gain and process time constants vary with process conditions, eg, flow rates and temperatures, and over time. Often such variations do not cause an unacceptable problem. In some instances, however, these variations do cause deterioration in control performance, and the controllers need to be retuned for the different conditions. 

The subject of adaptive control is one of current interest. New algorithms are presently under development, but these need to be field-tested before industrial acceptance can be expected. It is clear, however, that digital computers will be required for implementation of self-adaptive controllers due to their complexity. An adaptive controller is inherently nonlinear and therefore more complicated than the conventional PID controller. 

It may be useful to point out a few topics that go beyond a first course in control. With certain processes, we cannot take data continuously, but rather in certain selected slow intervals (c.f. titration in freshmen chemistry). These are called sampled-data systems. With computers, the analysis evolves into a new area of its own—discrete-time or digital control systems. Here, differential equations and Laplace transform do not work anymore. The mathematical techniques to handle discrete-time systems are difference equations and z-transform. Furthermore, there are multivariable and state space control, which we will encounter a brief introduction. Beyond the introductory level are optimal control, nonlinear control, adaptive control, stochastic control, and fuzzy logic control. Do not lose the perspective that control is an immense field. Classical control appears insignificant, but we have to start some where and onward we crawl. 

Adaptive controllers can be usefully applied because most processes are nonlinear (Section 7.16) and common controller design criteria (Section 7.12) are based on linear models. Due to process non-linearities, the controller parameters required to give the desired response of the controlled variable change as the process steady state alters. Furthermore, the characteristics of many processes vary with time, e.g. due to catalyst decay, fouling of heat exchangers, etc. This leads to a deterioration in the performance of controllers designed upon a linear basis. 

In order to tackle the problem of uncertainties in the available model, nonlinear robust and adaptive strategies have been developed, while, in the absence of full state measurements, output-feedback control schemes can be adopted, where the unmeasurable state variables can be estimated by resorting to state observers. The development of model-based nonlinear strategies has been fostered by the development of efficient experimental identification methods for nonlinear models and by significantly improved capabilities of computer-control hardware and software. 

B. Guo, A. Jiang, X. Hua, and A. Jutan. Nonlinear adaptive control for multivariable chemical processes. Chemical Engineering Science, 56 6781-6791, 2001. 

In the fifth chapter, a general overview of temperature control for batch reactors is presented the focus is on model-based control approaches, with a special emphasis on adaptive control techniques. Finally, the sixth chapter provides the reader with an overview of the fundamental problems of fault diagnosis for dynamical systems, with a special emphasis on model-based techniques (i.e., based on the so-called analytical redundancy approach) for nonlinear systems then, a model-based approach to fault diagnosis for chemical batch reactors is derived in detail, where both sensors and actuators failures are taken into account. 

The nonlinear and nonstationary nature of a typical chemical process leads to a change in its dynamic characteristics during operation. To cope with this situation, a controller should be able to adjust its parameters in an optimum manner. Thus we are naturally led to the adaptive control systems which were discussed in Chapter 22. 

Consider the neutralization of an acidic effluent industrial waste with a caustic solution. The titration curve of the waste being neutralized is nonlinear and changes with time due to unmeasured disturbances. Develop a qualitative self-adaptive control scheme and describe the functions of its components. (You can consult Ref. 3.)... 

No degree of sophistication in the control system (from adaptive control, to expert systems, to Kalman filters, to nonlinear model predictive control) will work if you do not know how your process works. Many people have tried to use complex controllers to overcome ignorance about the process fundamentals, and they have failed Learn how the process works before you start designing its control system. 

These openloop-adaptive controllers are really just another form of nonlinear control. They have been quite successfully used in many industrial processes, particularly in batch processes where operating conditions can vary widely and in processes where different grades of products are made in the same equipment. 

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... 

Dones, I., Manenti, F., Preisig, HA., and Buzzi-Ferraris, G. (2010) Nonlinear model predictive control a self-adaptive approach. Ind. Eng. Chem. Res., 49, 4782-4791. 

Fuzzy models have been employed in robotics to establish the inverse dynamic model for a robot manipulator in its joint space (Qiao and Zhu 2000) or to avoid complex analytical formulation of isotropic target impedance and xmcertainty of parameters related to the robot and environment model through a new fuzzy impedance control law (Petrovic and Milacic 1998). Furthermore, fuzzy inference has been introduced into variable structure adaptive control for the nonlinear robot manipulator systems giving robusmess against system xmcertainties and external disturbances (Zhao and Zhu 1995). 

Secondly, conjugated polymers were studied as biomimetic artificial muscles. A scalable physics based electro-chemo-mechanical model was developed to connect an input voltage to bending of the material. The reduced version of the model was used to design a robust adaptive controller. Also, a nonlinear mechanical model was investigated. Furthermore, a torsional actuator was developed by depositing PPy on a tube substrate with helically wound platinum fibers. A set of experiments were conducted to confirm the torsional and other actuation modes as well as the model. 

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