基于模型预测控制的直线倒立摆的MATLAB和ADAMS仿真研究

Simulation Research of Linear Inverted Pendulum Using MATLAB and ADAMS Based on Model Predictive Control

单级直线倒立摆是一个经典的、复杂的、欠驱动控制系统。模型预测控制作为一种在线优化控制方法善于处理复杂的控制问题。应用拉格朗日动力学方程建立倒立摆的动力学模型,在竖直向上平衡位置处进行线性化,得到近似线性连续状态空间方程,再将其离散化,推导出线性模型预测控制公式。在MATLAB中编写控制程序,仿真结果验证了初始非平衡状态和受到外力干扰两种情况下控制效果均较好,系统可以在较短的时间内达到稳定。为了进一步验证,运用联合仿真的方法,应用ADAMS建立简化的倒立摆的虚拟样机,在Simulink环境中建立模型预测控制程序,得到一致的控制效果。两种仿真结果综合表明,合理选择控制参数,模型预测控制方法能够较快地使欠驱动倒立摆系统稳定,实现不错的控制效果。

Single linear inverted pendulum is a classical,complex and under-actuated control system.Model predictive control,as an online optimization control method,is good at dealing with complex control problems.The Lagrange dynamic equation was applied to establish the dynamic model of the inverted pendulum,and the linear continuous state space equation was obtained by linearization at the vertical equilibrium position.Then the equation was discretized,and the linear model predictive control formula was derived according to the principle of the model predictive control.The control program is written in MATLAB,and the simulation results verify that the control effect is good under the initial non-equilibrium state and the external force interference,and the system can achieve stability in a short time.In order to verify further,a simplified virtual prototype was established by using ADAMS,and a model predictive control program was established in Simulink environment,and a consistent control effect was obtained.Both simulation results show that the model predictive control method can stabilize the underactuated inverted pendulum system quickly and achieve good control effect by selecting reasonable control parameters.