Comparison of methods of nonlinear control systems design

The issue of designing nonlinear control systems is a complex problem. A lot of methods are known that allow us to find a suitable control for a given nonlinear object that provides asymptotic stability of the nonlinear system equilibrium and an acceptable quality of the transient process. Many of these methods are difficult to apply in practice. Thus, comparing some of the methods in terms of simplicity of use is of great interest. Two analytical methods for the synthesis of nonlinear control systems are considered. They are the algebraic polynomial-matrix method that uses a quasilinear model, and the feedback linearization method that uses the Brunovsky model in combination with special feedbacks. A comparative analysis of the algebraic polynomial-matrix method and the feedback linearization method is carried out. It is found out that the algebraic polynomial-matrix method (APM) is much simpler than the feedback linearization method (FLM). A numerical example of designing a system that is synthesized by these methods is considered. It is found out that the system synthesized by the APM method has a region of attraction of the equilibrium position twice as large as the region of attraction of the system synthesized by the FLM method. It is reasonable to use the algebraic polynomial-matrix method with the quasilinear models in case of synthesis of control systems of objects with differentiable nonlinearities.

Lyapunov Analysis of Two Imbalanced Power System Areas

The transient stability is the capability of the system to preserve synchronism while being affected by large disturbances. It is a nonlinear problem that requires a simultaneous solution for many differential equations. Therefore, a thorough analysis is needed to resolve it. In this paper, we present the transient stability for multimachine under different fault cases and to analyze using the Lyapunov function. It serves as an analytical tool to determine the necessary condition to be stable. The system is stable as long as it is contained in the region of attraction. Meanwhile, the swing equation and reduced admittance matrix are used to model the system in three conditions, pre-fault, during the fault, and post-fault. The numerical simulations are conducted to verify that the synchronism can be preserved despite under faults on the transmission lines by achieving the critical clearing time.