К выбору периода дискретизации нелинейных гибридных систем управления

Abstract

Hybrid systems are often used in various technical applications, such as robotics, aviation, space, energy, etc. The emergence of hybrid control systems is due to the use of computers to implement control laws, including nonlinear ones. Digital means cannot implement continuous control laws. However, the known methods of design, especially of nonlinear systems, lead precisely to continuous controls, which caused the need to discretize the continuous control with the largest possible period. Solving the problem of determining the maximum permissible sampling period of a nonlinear control system is a rather complex stage of its creation. In this article the problem of definition of the maximum allowed sample period of the nonlinear hybrid system control and its dependence on the module of the maximum eigenvalue of the functional matrix of quasilinear model of the continuous system is also considered. The nonlinear hybrid system is created by discretizing the control of the nonlinear continuous system. This continuous system is synthesized using the algebraic polynomial and matrix method of the nonlinear control systems design in which quasilinear models are used. It has been is established that the value of the maximum permissible sample period depends not only on the module of the maximum eigenvalue, but also on initial conditions and external influences. These dependences are complex and it is difficult to find them theoretically. Experimentally, based on the example of the specific nonlinear hybrid control system it is shown that eigenvalues smaller on the module lead to larger values of the maximum of the permissible sample period. The problem of choosing the sample period of control laws of the real hybrid control systems can be solved in the similar way based on a compromise between the system high-speed performance and the sample period.