轮式倒立摆的数学建模及状态反馈控制

轮式倒立摆是检验各种控制理论的理想模型，首先采取牛顿力学分析的方法，依次得出轮式倒立摆中直流电机、车体和摆杆动力学方程，从而基于小角度线性化方法得出轮式倒立摆的近似线性模型；然后基于Matlab进行轮式倒立摆的状态反馈控制，设计出其控制律，验证其可行性，但是轮式倒立摆的数学模型通常是经线性化处理后得出，为了提高仿真准确性，再基于虚拟样机技术，对轮式倒立摆进行Madab与ADAMS的联合仿真，仿真结果显示系统响应曲线在规定时间内迅速收敛至O附近．此结果不仅验证了联合仿真中状态反馈控制的正确性，而且表明联合仿真是控制理论研究中值得推广的方法。

Mathematical Modeling and State Feedback Control for Wheeled Inverted Pendulum

To control wheeled inverted pendulum is a good way to test all kinds of theories of control. Firstly, on the basis of Newtonian mechanics and dynamic characteristics, the dynamical equation of DC motor, cart and pendulum is studied. Then the approximate linear model of wheeled inverted pendulum is concluded, which is based on the the way of linearization of small Angle. Secondly, state feedback control based on Matlab is used to control wheeled inverted pendulum, and the control law is designed, and its feasibility is verified. Because the mathematical model of the wheeled inverted pendulum is linearized, the collaborative simulation of Matlab and ADAMS is also used to control wheeled inverted pendulum in order to improve the accuracy, which is based on virtual prototype technology. At last the results of simulation demonstrate the correctness of State feedback control of wheeled inverted pendulum, and it also indicates the way is worth advo- cating in the study of control theory.