Adaptive optimal control design for systems with complex dynamics based on soft computing methods

Thesis of Master's Degree in Precision Instrument Engineering and Industrial Automation in Oil Industries

Abstract

Nonlinear dynamic systems face many challenges that must be investigated. Among these problems, we can point out things like extreme nonlinearity, changing operating conditions, dynamic uncertainty, both structured and unstructured, and external disturbances. Despite the recent advances in the field of nonlinear control systems, the design of a suitable controller and its optimal performance are strongly dependent on the extraction of a very accurate mathematical model of the system. In industrial systems, due to the presence of high non-linearity, accurate modeling is very difficult. In other words, we face high uncertainty in the mathematical definition and modeling of a system. Although conventional nonlinear control methods such as adaptive and sliding controllers compensate for parameter uncertainty, they are quite vulnerable in the face of unstructured modeling uncertainty. Instead and on the other hand, controllers based on computing intelligence, thanks to their special feature of not depending on the mathematical model, do not have such a limitation. Despite recent advances, neural network-based controllers are still not capable of utilizing human expertise. Also, controllers based on fuzzy logic cannot use the lessons learned from the dynamic behavior of the system to improve their efficiency.

According to the above, it can be said that in this thesis, in fact, we want to present a new design of the combination of the best and latest control methods mentioned above with optimal and adaptive control methods. Our intended controllers increase their resistance to known and unknown uncertainties by examining and using the unknown dynamic behavior of systems. Conventional control structures show poor performance against this type of uncertainties. Our proposed controller is designed based on the principles and tools of soft computing, and therefore will not have such limitations. It should be noted that in the design of this type of controller, a lot of initiative should be spent and parameters should be set very carefully. Despite these advantages, many of these types of controllers suffer from the problem of instability in their applications. In this article, we will propose controllers that use optimal control and adaptive control techniques based on Lyapunov theory instead of conventional and innovative methods to solve this shortcoming. With these designs, the stability of our controllers will be guaranteed, unlike other smart ones.

Keywords: robotic arm, energy management, adaptive control, soft computing, PMSM.

Chapter 1- Introduction

Controller design methods for nonlinear systems can be divided into three categories. The first method includes the linearization of nonlinear systems around the working point [1]. In this case, classical control laws are used for approximate systems. Despite the simplicity of these rules, the control system is not guaranteed to work in general. The second method is to design the controller based on the dynamics of non-linear systems. In this method, the characteristics of non-linear systems are preserved, which makes the design very difficult due to the complex dynamics of these systems [2]. In addition, the above methods use accurate mathematical modeling, which is very efficient in theory, but in practice, due to various reasons, such as changes in operating conditions, dynamic uncertainties, both structured and unstructured, and external disturbances, they suffer performance loss. In fact, it is very difficult to obtain an accurate mathematical model for the processes of complex industrial systems. In addition, there are other factors that cannot be predicted, such as turbulence, temperature, changes in system parameters, etc. Therefore, the dynamics of the system cannot be expressed only on the basis of possibly accurate mathematical models. The third method implements non-linear controllers by intelligent computing tools such as artificial neural networks [1] (ANNs) and fuzzy logic systems [2] (FLSs) [3-8]. These techniques have given good results in many of their applications, and as a powerful tool, they have been able to create high resistance for systems that are not mathematically well-defined and exposed to uncertainty [9,10].The general approximation theory [3] is the main reason for increasing the use of such models and states that with these methods they are theoretically able to estimate any real function and attachments with desired accuracy. Different models of artificial neural networks and fuzzy logic are used to solve many complex problems and the results are generally favorable [11-14], and it can be recognized that these methods will be an alternative to conventional and classical control methods. As an example of the empowerment and application of artificial intelligence, we can refer to the design of controllers for spacecraft and satellites, an example of which is given in [15].

1-1- Research background

Continuing the review of the research background in the research topic, we will review the works done selectively and briefly:

Perhaps one of the oldest designs for unknown systems that have been successfully It is presented in the article given in [27]. This design was done by Gregory C. Chow in 1973 for linear systems with uncertain parameters and based on the theory of optimal control, and theoretically it has shown favorable results. The above design was only suitable for linear systems and was not very useful in the real world and in practice, but it laid the foundation for new and better designs.

After 1973 and in an effort to design for unknown non-linear systems, many articles, theses and books were published, and if we want to mention them all, it would take a lot of time. Here, according to the available facilities and resources, and in the order of the date of publication, we will state a few things as a brief indication and a general statement of the weaknesses and strengths.

At first, we can refer to the doctoral dissertation of Mr. Moon Ki Kim from the University of Illinois at Chicago [28], which at that time (1991) examined and researched a new strategy in the machine-building industry. His work was a new method in the design of control systems called Adaptive Fuzzy Controller (AFC) [4], which due to its age, the advantages and disadvantages of the work are clear to a large extent and do not need additional explanation.

Many similar works were carried out until 2006, which we avoid explaining about them and only provide a few examples as examples for those interested to check in the references [29-35].

Our main sources, which are actually criteria They are considered functional and comparative for us from 2007 onwards, especially the last 3 years, which we will briefly describe some of them by stating their advantages and disadvantages. have given Some of the research also had a more general aspect, which can help us in this thesis. In the following, we will briefly refer to a few cases and leave the supplementary and analytical explanations to the future and the main text of the thesis.

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There are other articles and theses that have references in this field, but the mentioned cases may be closer and more attainable in terms of their relationship with our research topic. But in the future, if we get another suitable source, we will not hesitate to apply and analyze it and use it to improve our work. 1-2- Outline of this thesis will be organized in the following framework: The first chapter includes the introduction and an example of the application of artificial intelligence in the design of the control system. Comparatively, we present Lyapunov theory as well as artificial neural networks and fuzzy logic systems as soft computing techniques.

In the fourth chapter, we examine the flexible robotic arm system considering friction and interference as follows. First, we model and compare the rigid and flexible systems, then we design the adaptive control for the rigid arm. After this step, we will perform the adaptive design to compensate the effect of friction and interference with the methods of adaptive friction compensation[6] and adaptive disturbance compensation[7]. In the next step, the fuzzy controller will be used to control the flexible robotic arm, and finally, by combining two adaptive and fuzzy methods, we will reach the final design in this section, and the results will be indicative of the design success.