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摘要：作为支承技术的一种，磁悬浮技术由于不存在直接的机械接触，与其他技术相比具有无摩擦、无需润滑、功耗低、清洁无污染等优点。经过几十年的发展，磁悬浮技术作为一种高新技术日趋成熟，其在交通、航天和工业等领域有着广泛的应用前景。
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本课题论文以实验室磁悬浮系统为设计的被控对象，以二次型泛函指标为控制系统的性能指标，利用线性二次型最优控制理论实现磁悬浮系统的平稳控制。课题首先建立了磁悬浮系统的动力学方程、电压平衡方程，得到了磁悬浮被控对象的数学模型，同时验证系统的能控性和能观性，分析与设计二次最优控制中加权矩阵Q和R的问题，通过找出磁浮系统的动态响应与Q和R阵遵循的基本规律，进行连续二次最优控制策略的算法研究与设计，得到最优控制器对应的反馈增益矩阵。然后利用MATLAB仿真软件编制磁悬浮系统的线性二次最优控制器算法，对整个控制系统进行仿真实验，通过改变Q和R的数值，分别得到取不同数值的仿真波形，分析它们的性能指标并进行比较，得出在不同情形下响应速度指标和稳定性能。最后利用SIMULINK进行磁悬浮系统的二次最优控制仿真，仿真结果表明磁间隙将回到在期望的平衡点，取得较好的控制效果。
关键词：线性二次型；磁悬浮；最优控制；MATLAB软件
Quadratic optimal control for Magnetic Levitation Ball System
Abstract:As a supporting technology, the magnetic levitation technology because there is no direct mechanical contact, compared with other technologies, with no friction, no lubrication, low power consumption, clean pollution-free advantages. After decades of development, the magnetic levitation technology as a high-tech matures, has a broad application prospects in the field of transportation, aerospace and industrial.
This topic using linear quadratic optimal control theory with quadratic functionals indicators as the performance of control system, with maglev system in the laboratory as the designed controlled object to achieve smooth control of maglev system. First this topic established maglev system dynamics equations and the voltage balance equation to achieve the mathematical model of the controlled object maglev.Also verify that the system controllability and observability, analysis and design of quadratic optimal control weighting matrices the problems Q and R. The relationship between parameters of matrix Q and R in linear quadratic regulator(LQR) algorithm and control system feedback matrix K are studied by finding the basic rules of maglev system dynamic response and the Q and R matrix. Then using MATLAB simulation software to write the linear quadratic optimal controller algorithm of maglev system,and make simulation experiment under MATLAB/SIMULINK environment.By changing the value of Q and R, the different value obtained simulation waveforms, analyze their performance and compare them in different circumstances response speed indicators and stable performance. Finally, for magnetic levitation system SIMULINK quadratic optimal control simulation, simulation results show that the magnetic gap will be back at the desired equilibrium point and achieve better control effect.
KeyWords: Linear Quadratic;Magnetic Levitation Ball System; Optimal Control; MATLAB
目 录
1 绪论1
1.1 本课题的意义1
1.2 磁悬浮技术的原理••2
1.2.1磁悬浮应用方式分类2
1.2.1磁悬浮控制方式分类2
1.3 磁悬浮技术的发展概况及展望•3
1.4 本课题的工作及主要内容••4
2 连续系统二次最优控制理论基础6
2.1 最优控制简介6
2.2 线性二次最优控制原理•6
2.3 二次最优控制的MATLAB应用7
2.3.1 MATLAB编程••8