基于非线性状态依赖Riccati方程的直线倒立摆一致性控制

Consistent nonlinear state-dependent Riccati equation control on the inverted pendulum

直线倒立摆作为一种典型的非线性系统,是一种经典的控制理论研究对象.本文将状态依赖的Riccati方程(SDRE)方法与极点配置方法结合,进行倒立摆非线性控制的研究.该方法与SDRE相比,不再需要实时计算Riccati方程,同时克服了线性最优控制(LQR),线性鲁棒(H∞)控制等控制域不足的问题,可实现几乎任意初始摆角的稳定控制,而且在稳定点附近保持与某期望的线性控制方法完全相同.实验表明了该控制方法的有效性和对扰动的鲁棒性.最后讨论了SDRE进行一致性起摆控制的硬件可行性,以及系统对于传感器零点漂移的鲁棒性.

The inverted pendulum is a typical nonlinear system and a traditional test object on control theories.This study combines the state-dependent Riccati equation(SDRE)method and the pole placement method to give a consistent swinging-up and stabilization control on the inverted pendulum.This method exempts the controller from real-time calculation of the Riccati equations,meanwhile,overcomes the problem that linear quadratic regulator(LQR)controls and linear robust controls have limited control domain.Therefore,this method can accomplish stable control given almost arbitrary initial pendulum angles.Meanwhile,this method converges to the expected linear control near the stable point.Test results validates the feasibility and robustness of this control method.Finally,this paper gives the discussion about consistent swinging-up control and the robustness to the zero drift of sensors.