Nonlinear dynamic analysis for a Francis hydro-turbine governing system and its control

In this paper, we introduce a novel model of a hydro-turbine system with the effect of surge tank based on state-space equations to study the nonlinear dynamical behaviors of the hydro-turbine system. The critical points of Hopf bifurcation and the relationship of the stability satisfying with the adjustment coefficients are obtained from direct algebraic criterion. Furthermore, the bifurcation diagrams and Lyapunov exponents are presented and analyzed. The dynamical behaviors of the points with representative characteristics are identified and studied in detail. Both theoretical analysis and numerical simulations show that chaotic oscillations, which cannot stabilize the system, may occur with the changes of adjustment coefficients. To control the undesirable chaotic behaviors in this system, fuzzy sliding mode governor based on the sliding mode control (SMC) and the fuzzy logic are designed, and considering the bounded disturbance. Finally, series of numerical simulations are presented to verify the effectiveness of the proposed governor, which prove that the hydro-turbine governing system can maintain a better operation station under the designed governor.