Design of a Finite-Time Terminal Sliding Mode Controller for a Nonlinear Hydro-Turbine Governing System

Abstract

We focus on the finite-time control of a hydro-turbine governing system (HGS) in this paper. First, the nonlinear mathematical model of the hydro-turbine governing system is presented and is consistent with the actual project. Then, based on the finite-time stability theory and terminal sliding mode scheme, a new finite-time terminal sliding mode controller is designed for the hydro-turbine governing system and a detailed mathematical derivation is given. Only three vector controllers are required, which is less than the HGS equation dimensions and is easy to implement accordingly. Furthermore, numerical simulations for the proposed scheme and an existing sliding mode control are presented to verify the validity and advantage of improving transient performance. The approach proposed in this paper is simple and provides a reference for relevant hydropower systems.

Nonlinear finite‐time control of hydroelectric systems via a novel sliding mode method

“…In this case, L(t s ) and L(t x ) in Equations (A9) and (A18) are no longer zero and one just needs to substitute the bound of the neighbouring region into the corresponding Lyapunov function to calculate the finite and fixed settling time, respectively. In this case, the calculated time is smaller than the time in Equations ( 14) and (15).…”

“…(1) Designing the sliding surface (6) (2) Designing the equivalent controller (8) (3) Designing the switching controller (9) (4) Following Theorem 1 to calculate the control parameters 𝜖 > 0, 𝜁 > 0 and 𝜎 > 0 (5) Based on Equation ( 14) in Theorem 1 and Equation (15) in Theorem 2 to find the finite settling time T x , and its bound T x max Remark 1. The introduction of symbolic function in the sliding surface enhances the sliding surface converging into equilibrium.…”

“…Any controlling law designed based on a linearized representation is a compromise [13]. For this reason, state-of-the-art methods have been introduced to hydroelectric systems, for instance, sliding mode control [14][15][16][17], fuzzy control [18,19], predictive control [20,21], and so on.…”

Design and dynamic control of integrated synergetic controller for single penstock two-machine hydropower system

“…The hydroelectric power system is a highly complex nonlinear system that uses a turbine governor and generator exciter to control the active power and terminal voltage [6][7][8]. The current research on the safe and stable operation of power systems is mainly carried out in two aspects: (1) the establishment of the sophisticated nonlinear model of the system [9][10][11]；(2) the appropriate control forms and methods [12,13]. The hydraulic coupling of a single penstock multimachine system increases the system's complexity, and how to reduce the effects of hydraulic coupling and improve the stability of the unit and grid operation has attracted the attention of many scholars.…”