Divergent instability control of aeroelastic system driven by aerodynamic forces under disturbance based on discrete sliding mode control algorithms

Abstract

Divergent instability control of 2D pretwisted blade section of wind turbine driven by aerodynamic forces under disturbance is investigated. Realization of divergent instability control is based on two types of discrete sliding mode control algorithms. The structure is modeled as 2D pretwisted blade section integrated with structural damping, which is driven by aerodynamic model with perturbed disturbance. Discrete sliding mode control algorithm suitable for disturbance control is investigated to control divergent flap/lead-lag vibrations of blade section. To increase convergence performance and reduce the chattering phenomenon, discrete sliding mode control based on disturbance observer is applied. Convergence of disturbance observer is analyzed, and stability of closed-loop system is discussed. The simulation results show that not only the convergence accuracy can be improved by sliding mode control based on disturbance observer controller, but also the displacement chattering and the control input chattering can be effectively eliminated. Compared with conventional discrete sliding mode control, it has more advantages in the control of divergent instability. To facilitate the real-time realization and automation and at the same time to ensure accuracy, a design of quadratic feedback to build the performance control matrix in sliding mode control based on disturbance observer is developed in present study.

Aeroelastic vibration analysis of wind turbine blade with Gurney flap

“…In this section, based on the structural characteristics of the blade, we develop the equivalent model to obtain the frequency characteristics of the main body of the blade, instead of the previous method of directly giving the natural frequency value. 3,4,[33][34][35] This processing method is because the structural form of the blade has a major impact on the natural frequency, and it is closer to the actual situation.…”

“…The inner values of Green's function matrix mentioned above can be obtained directly from the equations above. The matrix representation of the first derivative of Green's function is the expression after the derivation of n. After introducing the relations listed in equations (34) and (35) and the above matrix and coefficients, the equations ( 36) and (37) can be obtained.…”

“…The fourth-order and five stages Runge Kutta method algorithm is used to solve the two kinds of blades vibration equations, and the aerodynamic damping matrix is taken into account. 35 When the wind speed is 8 m/s and 10 m/s, the vibration of the blades can be observed. In order to investigate the torsional vibration behavior in detail, we magnify the part of the time from 2 s3.3s, then we can observe the comparison results as shown in Figure 5.…”