简易旋转倒立摆及控制装置的设计

目的]设计并制作一套简易旋转倒立摆及其控制装置.方法]采用9S12XE单片机作为简易旋转倒立摆及控制装置的监测和控制系统的核心,采用L298驱动直流电机作为动力.通过编码器及最优控制策略LQR在平衡点附近给出系统的线性化模型,对系统的稳定性、能控性进行调试.结果]应用Lagrange方程对试验采用的单级旋转倒立摆系统进行建模,获得了旋臂长度（r）、水平和竖直方向的角位移（Q）、摆杆质心与铰链距离（L）4者的最佳平衡点与动态方程;优化LQR控制器获得最优状态反馈增益矩阵;进行计算机编程,应用9s12XE单片机控制,并执行试验;结果表明旋转臂的转动频率趋近于摆杆的转周期则摆杆能到达正负155度以上,能很快地完成设计要求的基本动作,并且能迅速进入PID控制器调控范围,完成坚立状态.结论]经误差分析表明该装置的稳定性良好,误差范围可控制在正负15度之内;调试结果证明,已实现了倒立摆的平衡控制.

Design of Simple Rotary Inverted Pendulum and Control Device

Objective ] To design a simple rotary inverted pendulum and control device. Method ] The system uses 9SI2XE micro-controller as a core monitoring and controlling system of simple rotary inverted pendulum and control device, using L298 drive DC motors. By the encoder and LQR optimal control strategy given linearized model of the system in the vicinity of the equilibrium point, the system＇ s stability, controllability are debugged to achieve a balanced inverted pendulum control. Result ] Using Lagrange equation, the adopted rotary inverted pendulum was modeled, the optimal balance point and dynamic equation of the length of the rotary arm（ r）, angular displacement of level and vertical direction （Q）, the pendulum mass and hinge distance L ] were obtained; LQR was optimized to obtain the best state; 9512XE single chip microcomputer control was applied to carry out the test. The results showed that pendulum rod can up to above negative 155 angel when the rotation cycle fre- quency approaches the pendulum rod rotating arm and rapidly complete the basic design requirements. Conclusion ] Through error analysis, it was found that the device has good stability, error range could be controlled within positive and negative 15 angle; the results proved the balance control of inverted pendulum.