基于一阶PPF的垂尾振动分数阶控制

Traditional Positive Position Feedback (PPF) and first-order PPF controllers are inadequate in control effectiveness and robustness, and is thus difficult to be applied to the structures with perturbation effect. A novel Fractional Order (FOPPF¹) controller is proposed based on the fractional calculus theory and the first-order PPF to increase the designable space of the controller. Considering the frequency domain characteristic and global vibration amplitude of random response, an optimization design of the objective function for the FOPPF¹ controller is constructed. A scale model of the vertical tail with Macro Fiber Composite (MFC) piezoelectric patches is manufactured, and the corresponding FOPPF¹ controller is designed based on the proposed method. The phase frequency property of this controller in the target frequency band is changed gently, and the phase compensation can be effectively realized. Furthermore, the poles in the closed-loop system are insensitive to parameter perturbation; therefore, the proposed FOPPF¹ controller has good robustness. The free vibration and narrow-band random vibration control experiments are performed to validate the proposed control method. The free vibration response test results show that the equivalent damping coefficient of the FOPPF¹ controller for the nominal model is improved by about 50% of that of the first-order PPF controller. When a certain amount of offline or online perturbation is introduced into the first-order natural frequency of the vertical tail, results of the narrow-band random vibration control experiment show that the robustness, control efficiency and energy consumption ratio of the proposed FOPPF¹ controller is significantly better than those of the classical first-order PPF. Therefore, the proposed controller has great potential for application in vibration control of the vertical tail.