Robust H-inf phase control for flexible system with weak damping

The characteristic of a fiexible system with weak damping is that the amplitude characteristics show a large change, and the situation on the Nyquist chart is extremely complicated. Due to the existence of weak damping, the perturbation range of the fiexible modal parameters allowed by the system is greatly compressed, and the robust stability is reduced, which brings challenges to the control design. To deal with this problem, the traditional H-inf loop shaping method often leads to the controller instability and poor robustness. In order to improve the stability margin of the system, increase the robustness and stability, and solve the problem of the instability of H-infcontrollers, this paper proposes a robust comprehensive design method based on phase control. In this method, by using the closed-loop pole configuration corresponding to the fiexible mode at low frequency, the phase control is realized. Through the phase control, the apex of the Nyquist curve of the weakly damped mode of the system is limited to the Right half plane. The H- inf weighting function relaxes the pole configuration requirements, reduces the conservativeness of strict positive real, and combines the phase control with the H-inf optimization solution to obtain a robust and self-stable H-inf controller. A specific design example is given. The simulation results show that this control method has extremely high robustness. This design example can provide a certain degree of robust design for other weakly damp.