磁悬浮系统的哈密顿建模和无源控制

Hamiltonian modeling and passive control of magnetic levitation system

针对磁悬浮系统非线性特点,采用端口受控哈密顿系统理论与无源性控制原理研究磁悬浮系统的建模和控制。将磁悬浮看作能量变换装置,从能量平衡角度推导出单自由度磁悬浮系统的端口受控哈密顿模型。在哈密顿结构基础上,引入结构互联和阻尼配置,给出闭环系统期望的哈密顿函数,设计了磁悬浮系统的无源控制器。设计中直接采用哈密顿函数作为存贮函数,保证了数学严密性,且使系统在满足无源性的条件下达到要求的性能,具有明确的物理意义。仿真结果表明,系统能够快速响应,并且对负载的变化具有很强的抗干扰性能。

In view of the nonlinear characteristic of Magnetic levitation system, applying port-controlled Hamihonian systems and passivity-based control theory, the modeling and control of Magnetic levitation system is presented. Magnetic levitation was viewed as an energy-transformation device. From the energy- balance relation, the Port Controlled Hamihonian model of single-degree-freedom Magnetic levitation sys- tem was established. Based on the Hamiltonian structure, the passive controller of Magnetic levitation system was designed using the method of interconnection and damping assignment. In the design, the Hamihonian function was used directly as the storage function, which can assure the precise mathematical form, and the system can achieve the required performance and can bring more definite physical meaning on the condition of satisfying passivity. The simulation results show that the system has rapid response, and strong disturbance attenuation to the variance of load.