基于LQ优化的磁悬浮输出反馈控制器设计

Output feedback controller design for magnetic levitation system via LQ optimization

磁悬浮球系统具有非线性的本质和明显的开环不稳定特点,其控制算法值得研究.虽然输出反馈PID控制方案因简单易行而被广泛应用,但其参数整定依赖经验导致控制精度不高且容易受到干扰而使控制失败.保持输出反馈的控制结构,提出将LQ二次优化方法用于控制参数优化的整定方案,优点在于使系统具有统一的最优解表达式,计算方便;将状态信息用于控制器设计,提高了输出反馈的控制性能,避免了状态采样的复杂计算.将所提方案与经典PID方案比较,仿真结果显示,具有LQ优化的输出反馈控制方案跟踪效果好且对外部干扰和内部参数摄动的敏感度有所降低.

Magnetic levitation is an open-loop unstable nonlinear system. Its control algorithm is worth being studied. Although the output feedback PID control scheme is widely used because of its simplicity,its control accuracy is poor due to the parameter tuning depends on design experience. With the output feedback structure,LQ quadratic optimization method was proposed to optimize its control parameters. The designed magnetic levitation control system has the following advantages. A uniform optimal solution was obtained which makes the calculation more convenient. The status information was used for the controller design,which improves the control performance of the output feedback. The proposed scheme avoided complex computations of state samples. Comparing the proposed scheme with the classical PID scheme,simulation results show that the proposed control scheme with LQ optimization has better tracking performance. The sensitivity to external disturbances and internal parameters perturbations is reduced.