基于SimMechanics的单级倒立摆建模和仿真

Modeling and Simulation of Single Inverted Pendulum Based on Sim Mechanics

倒立摆本身是一个多变量、强耦合、非线性和不稳定系统,通过倒立摆可以检验各种控制策略的可行性,是一个理想的研究控制理论平台。利用Sim Mechanics环境下对单级倒立摆系统的控制问题进行仿真研究。建立单级倒立摆的数学模型,基于数学模型建立了Sim Mechanics仿真模型,并进行起摆控制。起摆后切换成PID、极点配置和状态反馈(LQR)方法对倒立摆进行稳摆控制,并整定了各方案的控制器参数。除PID没有控制小车位移,其他两种方法对小车和摆杆角度进行了控制。仿真参数在快速性和超调量等指标中折中优化选取,仿真效果良好,为下一步实验奠定了理论基础。

The inverted pendulum is a system which has multiple variables, strong coupling, nonlinearity, and instability. The in- verted pendulum can check the feasibility of various control strategies, so it is an ideal research platform of control theory. In this paper, the single inverted pendulum was simulated based on SimMechanics. First the mathematical model and SimMechanics model of the single in- verted pendulum were established and the pendulum was swung up. Using PID, pole placement and state feedback （LQR）method, the inverted pendulum was controlled stable with feedback, and the controller parameters were adjusted. Except PID, the cart displacement, and pendulum degree were controlled with the other control strategies. The controller parameters were selected among the indices such as rapidity and overshoot, which showed good simulation results and has provided theoretical foundation for the following experiments.