Human knows the objective process of objective world and transforming the world, which is always low-level to advanced, from simple to complex, in depth process. As in terms of control, the first control system is linear. For example, the watt steam regulator, the level of liquid level is adjusted. This is due to the restrictions on the ability to understand the objective level of natural phenomena and the ability to solve practical problems, because the physical description and mathematical solution to the linear system is more easy to implement, and has formed a complete linear theory and analysis. research method. However, for nonlinear systems, in addition to a small number of cases, there is no versatile general method, and each method can only be valid for a certain type of problem, and it is not universally applicable. So, you can say that our understanding and processing of nonlinear control systems is basically in the primary stage. In addition, from our accuracy requirements of the control system, the most engineering technical issues are used in linear system theory, and satisfactory results can be obtained within a certain range. Therefore, a nonlinear factor of a real system is often ignored by us, or is replaced by a variety of linear relationships. This is the rapid development of linear system theory, and the nonlinear system theory has not had the main causes of attention and development. However, with the continuous development of science and technology, people's analytical requirements for the actual production process are increasing, and the results of various more accurate analysis and scientific experiments show that any actual physical system is non-linear. The so-called linear is only a simplified or approximate to nonlinearity, or a special example of nonlinearity. For example, a simplest family is an ohm ordered. The ohmic theorem has a mathematical expression of u = IR. In this formula, the voltage U at both the resistor is proportional to the current I via its current I, which is a simple linear relationship. However, even for such a simple single-resistance system, its dynamic characteristics are strictly non-linear. Because when the current is passed through the resistance, heat is generated, the temperature is increased, and the resistance is changed with the temperature rise. Research on nonlinear control systems, and some significant progress has been made in the 1940s. The main analytical methods are: phase plane method, Li Yapovaff method and description function method. These methods have been widely used to solve the actual nonlinear system problem. However, these methods have certain limitations, and they cannot be a general method for analyzing nonlinear systems. For example, although all of the features of the system can obtain all the features of the system, such as stability, transition process, etc., but the system greater than the third-order cannot be applied. Li Yapinov law is limited to the absolute stability of the analysis system, and the characteristics of nonlinear components are required to meet certain conditions. Although many scholars at home and abroad have been studied in this year, some new methods, such as the Bobov criterion, generalized circular criteria, and input and output stability theory. However, in general, nonlinear control system theory is still in development stage, far from being improved, and many problems have to be resolved, and the field is very broad. Nonlinear control theory as a promising control theory, will become the main melody of the control theory of the 21st century, will provide more advanced control systems for our human society, so that the automation level has a greater flying over.
