Hopf bifurcation control of hydro-turbine governing system with sloping ceiling tailrace tunnel using nonlinear state feedback

Highlights: • Nonlinear mathematical model of a hydro-turbine governing system with sloping ceiling tailrace tunnel is presented. • A novel control strategy using nonlinear state feedback with polynomial functions is proposed. • Hopf bifurcation control of a hydro-turbine governing system using the proposed control strategy is described. • Application and functional mechanism of the proposed control strategy are analyzed. - Abstract: Aiming at improving the regulation quality of a hydro-turbine governing system with sloping ceiling tailrace tunnel, Hopf bifurcation control using nonlinear state feedback is studied. Firstly, the nonlinear mathematical model of a hydro-turbine governing system with sloping ceiling tailrace tunnel is presented. Then, a novel control strategy using nonlinear state feedback with polynomial functions is proposed, and Hopf bifurcation control of a hydro-turbine governing system using the proposed control strategy is described. Finally, the application and functional mechanism of the proposed control strategy are analyzed by comparison with the PID strategy. The results indicate that: The proposed nonlinear state feedback control strategy is able to make the frequency of a hydro-turbine unit return to the initial value (i.e. rated frequency), and the regulation quality and the response speed are obviously better than those under the PID strategy. The effect of the linear term of nonlinear state feedback control strategy is to modify the system's linear stability, in order to eliminate or delay an existing bifurcation. Altering the nonlinear term can change the stability of bifurcation solutions, for example, converting a Hopf bifurcation from subcritical to supercritical.