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针对旋转倒立摆自动起摆的控制问题,提出了基于BVP算法的自动起摆控制策略。该方法将倒立摆起摆控制问题转化成求解非线性方程的两点边值问题(Two-point BoundaryValue Problem BVP),构造了含参变量具有傅立叶级数形式的起摆力矩函数,将力矩函数代入倒立摆系统,利用Matlab工具箱中的bvp4c函数求解两点边值条件,获得起摆过程的起摆控制的时间序列。基于BVP算法的起摆控制的求解,本质上属于开环前馈控制。为了抑制参数摄动,进行了平衡点附近的稳摆控制设计。稳摆设计是针对系统模型不稳定性和非最小相位特性分别进行的。对起摆、稳摆及其切换过程进行了仿真和实验研究,验证了所提出的自动起摆控制策略的有效性。
Aiming at the control problem of the automatic swinging of the rotating inverted pendulum, a control strategy based on the BVP algorithm is proposed. The method transforms the pendulum control problem into the two-point boundary value problem (BVP) for solving the nonlinear equation, and constructs the peaking torque function with the parametric variables in Fourier series. The torque function is substituted into Inverted pendulum system, the bvp4c function in Matlab toolbox is used to solve two-point boundary conditions, and the time series of the pendulum control of the pendulum process is obtained. The solution of the pendulum control based on the BVP algorithm is essentially an open loop feedforward control. In order to suppress the parameter perturbation, the design of the pendulum control near the equilibrium point was carried out. Steady-state design is carried out separately for the system model instability and non-minimum phase characteristics. The pendulum, pendulum and its switching process are simulated and experimentally studied, and the validity of the proposed automatic pendulum control strategy is verified.