回旋式倒立摆的H∞控制

倒立摆系统具有多变量、非线性、强耦合和不确定的特点，常被用来验证控制算法的优劣性。H∞在干扰抑制和鲁棒性上均有较为突出的表现。在对倒立摆控制研究情况和 H∞控制理论发展情况进行简单介绍后，围绕一阶回旋式倒立摆的H∞控制进行研究。首先，基于拉格朗日方程对一阶倒立摆进行动力学分析，并近似地得到平衡点附近的线性方程；对倒立摆系统进行分析，得到倒立摆系统是能观能控系统、但平衡点不稳定的结论。其次，简单介绍基于里卡蒂方程的 H∞控制器求解方法，并证明该控制器能够保证系统的稳定性。最后，仿真确定加权矩阵各元素和 H∞性能指标的大小对系统性能的影响和对电机扭矩的要求，并最终确定一组相对合适的参数进行控制器设计。

H∞ Control of a Rotary Inverted Pendulum

Inverted pendulum system has the characteristics of multivariability,nonlinearity,strong coupling,and uncertainty,and the system is commonly used to verify the advantages and disadvantages of control algorithms.H∞ has outstanding performance in interference suppression and robustness.After a brief introduction of the research on the control of the inverted pendulum and the development of the H∞ control theory,the H∞ control of the first-order cyclotron inverted pendulum is studied.Firstly,the dynamics of the first-order inverted pendulum is analyzed based on the Lagrange equation,and the linear equation near the balance point is approximately obtained.By analyzing the inverted pendulum system,it is concluded that the inverted pendulum system is an observable and controllable system,but the equilibrium point is unstable.Then,a brief introduction is given to the solution method of the H∞ controller based on the Riccati equation,and it is proven that the controller can ensure the stability of the system.Finally,the impact of the elements of the weighting matrix and the size of the H∞ performance index on system performance and the requirements for engine torque are determined through simulation,and a set of relatively suitable parameters are ultimately determined for controller design.