Designing adaptive optimal control 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

Non-linear 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 performance.

According to the above content, it can be said that in this thesis, in fact, we want to present a new design combining 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 intelligent manufacturers.

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

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 provide high resistance to systems that are not mathematically well-defined and exposed to uncertainty.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 mention the design of controllers for spacecraft and satellites, an example of which is given in [15]. We discuss:

Perhaps one of the earliest successful designs for unknown systems is presented in the paper 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 reference and a general statement of the weaknesses and strengths.

At first, we can refer to the doctoral thesis 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 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 done until 2006, which we avoid explaining about them and only give a few examples as examples for interested people to check in the references [29-35].

Our main sources, which are actually performance and comparison criteria for us, are from 2007 onwards, especially the last 3 years, and we will briefly state a few of them by stating their advantages and disadvantages.

The first one is an article that was published in 2007 [47]. In this article, with the help of fuzzy rules and its combination with adaptive control, controllers are designed to track the output of the MIMO system with uncertain dynamics. The main idea of ??this work was to solve the problem of tracking these systems in block-triangular mode. The problem of not knowing the transformation function due to its non-linearity has been somewhat reduced with the help of fuzzy logic and a suitable approximation has been made. By using the backstep design method, the fuzzy adaptive controller can be implemented for nonlinear MIMO systems. In this design, tracking of the input from the output side is guaranteed in closed loop mode. Due to the use of fuzzy, this method has somewhat reduced the mathematical complexity of the problem, but nevertheless, it can be simplified by using the second type of fuzzy and neural networks. In addition, to ensure the stability of the system, we can use Lipanov's method and . . used.

The second case is an article that was published in the International Journal of Information & Mathematical Science in 2008[48]. In this article, it can be said that what we mentioned above about the previous article has been taken into consideration, and with the help of the second type of fuzzy, the simplification has reached the optimal level, and with the help of the Lyapunov technique, stability has been guaranteed. The simulation results also show the effect of the adaptive controller on the efficiency of the whole system. Perhaps the problem that can be considered in this design is that this controller does not work well in systems with a time delay. In the next case, the solution to this problem is also explained to some extent