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摘要：倒立摆系统是一个经典的开环不稳定控制系统，在很多控制领域有重要的现实意义。本课题以二级倒立摆系统为研究对象，先简单介绍了倒立摆的结构和它的研究意义以及国内外研究现状，然后分析了倒立摆的性能并详细推导了它的数学模型。24296
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本课题主要研究二级倒立摆的线性二次最优控制，先通过MATLAB仿真任选加权阵Q、R的LQR最优控制，选定三组有代表性的Q、R值得到三组仿真波形，找出最合适的Q、R值用在LQR算法的倒立摆实时控制上，并取得了良好的控制效果。
课题也对二级倒立摆的模糊控制给出了仿真，通过MATLAB及SIMULINK仿真工具搭出SIMULINK仿真框图，仿真结果表明，模糊控制不仅能满足非线性系统的控制要求，而且能明显改善控制指标，整个系统具有更好的动态特性。
毕业论文关键词： 二级倒立摆；最优控制；模糊控制；MATLAB仿真
The design of control system of Linear 2-Stage Inverted Pendulum
Abstract：Inverted pendulum system is a classical opening loop unstable control system, so it has great practical significance in the field of control. This topic takes double inverted pendulum system as the research target, first this paper briefly introduces the structure of inverted pendulum and its research significance as well as domestic and foreign research status, then analyses the performance of inverted pendulum and deduces its mathematical model in detail.
This paper mainly studies linear quadratic optimal control of the double inverted pendulum, first through MATLAB simulation, it can choose any LQR optimal control from weighted array Q, R, then selects three groups of representative Q, R value, next gets three sets of simulation waveform, to find out the most suitable Q, R value and applies the value to LQR algorithm for real-time control of inverted pendulum, finally it has been successful.
This topic also simulates double inverted pendulum fuzzy control, Through MATLAB and SIMULINK simulation tool to build the SIMULINK simulation diagram, Simulation results show that fuzzy control can not only meet the requirements of the control of nonlinear systems, but also can obviously improve the control index, entire system can has a better dynamic characteristic.
The conclusion summarizes the significance, purpose and tasks of this topic.
Key Words： Double inverted pendulum; Optimal control; Fuzzy control;MATLAB simulation
目 录
1 绪论 1
1.1 倒立摆系统简介 1
1.2 倒立摆系统的研究意义和目的 2
1.3 国内外研究情况简介 2
1.4 课题的主要工作 4
2 倒立摆系统建模和性能分析 5
2.1 倒立摆系统特性分析 5
2.2 倒立摆系统的数学建模 5
2.2.1 倒立摆系统建模假设 5
2.2.2 符号说明 6
2.2.3 拉格朗日运动方程 6
2.2.4 推导建立数学模型 7
2.3 倒立摆系统的性能分析 12
2.3.1 稳定性分析 12
2.3.2 能控性能观性分析 12
3 二级倒立摆的LQR控制系统设计与仿真 14
3.1 线性二次型最优调节器原理 14
3.2 加权阵Q、R的选择 15
3.3 二级倒立摆的LQR控制系统框图 16
3.4 任选加权阵的LQR最优控制仿真 16
3.5 二级倒立摆的LQR实时控制 19
3.6 LQR控制器的特点与局限性 22
4 二级倒立摆的模糊控制系统设计与仿真 24
4.1 模糊控制的基本理论 24
4.1.1 模糊控制概述 24