D-分割技术确定磁轴承的PID参数鲁棒稳定域

Robust stability regions of PID parameters for magnetic bearing based on D-partition technique

给出仅依靠频率响应确定磁轴承的PID控制参数鲁棒稳定域的方法。根据小增益定理得到闭环系统的鲁棒稳定性条件,由此推导出加性不确定性的内部稳定H∞指标,再由边界穿越定理和D-分割技术,推导了满足H∞指标的PID控制器的鲁棒参数稳定域边界的解析表达式。在稳定域中任选PID参数,可以使得系统稳定并满足鲁棒性能约束条件。该方法降低了PID控制器参数稳定域设计的难度,对磁轴承时滞系统PID参数调节具有良好的鲁棒性。仿真和实验证明了本文方法的有效性。

A method was introduced for finding all proportional integral derivation （PID） controllers that satisfy a robust performance constraint for a given transfer function of magnetic beating with time-delay by using the frequency response. The H-infinity index of additive weight uncertainty on the basis of robust- ness stability condition of closed loop system was first got by small gain theorem. Then, Based on the boundary crossing theorem, the parameter boundaries with the expected decay ratio index of PID control- ler were derived. The system can be stabilized and robustly meet the performance requirements by choo- sing PID controllers parameter in the stability region. The proposed method avoids the complexity of sta- bility regions of PID parameters, and the closed-loop system has strong robustness for magnetic bearing with time-delay system. The simulation and experiment results demonstrate the validity of this method.