The linear quadratic regulator cannot track reference without static error, and the output voltage total harmonic distortion (THD) is too high when proportional-resonant (PR) controller carries nonlinear load. Therefore, this paper presents an optimal multi-resonant servo control for the design of medium frequency power supply. This method can stabilize the closed-loop system stability and realize asymptotic tracking. Moreover, it has rapid dynamic response and strong harmonic suppression. A model of the medium frequency power system is established, and multi-resonant servo control is theoretic analyzed. Through the method of increasing the dimension of system matrix, the optimal tracking problem is transformed into the optimal adjustment problem. The LQR function of Matlab software is used to obtain the status feedback gain matrix. The simulations and experiments on the prototype show that the designed controller can bring good steady-state performance and dynamic performance to the closed-loop system, where the steady state voltage is between 114.8V and 115.2V and the dynamic recovery time is within 10ms. It is capable of strong anti-interference in the nonlinear load, and the output voltage harmonic is much lower than that by the PR control and robust control methods.%针对标准线性二次型调节器(LQR)不能无静差跟踪参考以及比例谐振(PR)控制器带非线性负载时输出电压总谐波畸变率过高的问题,提出一种多谐振最优伺服控制算法并应用到中频电源设计中.该方法能够实现闭环系统稳定和渐进跟踪,同时还具有动态响应快、抑制谐波能力强的优点.建立中频电源系统模型,并对最优控制和多谐振伺服控制进行理论分析,通过系统矩阵维数增广的方法将最优跟踪问题转化为最优调节问题,利用Matlab软件的lqr函数求解出状态反馈增益矩阵.通过仿真软件和实验样机对整个系统进行了仿真和实验验证,结果表明:所设计的控制器使闭环系统具有良好的稳态性能和动态性能,稳态电压稳定在114.8~115.2V,动态响应恢复时间在10ms以内,对非线性负载具有较强的谐波抑制能力,输出电压总谐波远少于PR控制和鲁棒控制等方法.
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