Research On The Finite-time Stability Of Time-delay Hydraulic Turbine Governing System

The hydraulic turbine governing system(HTGS)is a complex non-linear system,which is composed of multiple subsystems.It contains two parts: the hydraulic turbine control system and the controlled system.The stability of the HTGS is related to the stable operation of the hydropower station.At present,the most widely used control method for hydropower stations is PID control,which has a relatively simple structure,easy operation,easy realization,and high reliability.As a traditional linear control method,PID control is difficult to accurately control the HTGS with nonlinear characteristics.Due to the limitation of PID parameter setting,its adaptability to working condition conversion is weak.However,the operating conditions of the HTGS are frequently changed,so it is necessary to explore new and more superior control methods for the system.In addition,due to the time delay in the transmission and reception of electrical signals,the inertia of the water flow in the pressure diversion pipe,and the time delay in the action of mechanical components.Time delay is widespread in the HTGS,and the precise control of the system has become more difficult.However,this issue is rarely considered in the modeling process of the HTGS.Therefore,considering the influence of time delay in the modeling process of the HTGS,and discussing the application of the finite time and fixed time control method,it has good theoretical research value.In summary,the main content of this article is as follows:(1)Finite-time control of HTGS with mechanical time delay.Considering the mechanical time delay in the hydraulic servo system,through modular modeling,a mathematical model of a Francis turbine governing system with mechanical time delay is established.With the help of the frequency distribution model and the Lyapunov stability theorem,the stability of the sliding surface and the HTGS is proved.Based on the finite time stability theory,with the help of sliding mode control method,the finite time control problem of the system is solved.(2)Mittag-Leffler stability of HTGS with mechanical time delay.In order to simplify the process of system stability verification,the Mittag-Leffler stability theorem is introduced,and with the help of linear matrix inequality and sliding mode control method,the finite time control problem of the system is solved.By optimizing the control strategy of the governor,the stability of the entire HTGS is realized.The research results may provide a certain theoretical reference for the stability control of the hydropower station in actual operation.(3)The fixed-time control of the hydraulic time delay HTGS.Due to the inertia phenomenon of the water flow in the pressure pipeline,the hydraulic time delay is widely present in the pressure pipeline.so a mathematical model of a Francis turbine regulating system with water pressure time delay is established.With the help of the fixed-time stability lemma and the introduction of the hyperbolic tangent function to suppress the chattering phenomenon in sliding mode control,a new type of sliding mode surface and controller is designed to solve the fixed-time control problem of the HTGS.And the problem of finite time control is sensitive to the initial value is also solved.