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

DOI编号  10.7641/CTA.2019.90229
2020,37(4):739-746

 作者 单位 E-mail 王志晟 清华大学电机工程与应用电机系 delbert.wang@outlook.com 张雪敏 清华大学电机工程与应用电机系 delbert.wang@outlook.com 梅生伟 清华大学电机工程与应用电机系

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 optimal (LQR) controls and linear robust controls have limited control domain. As a result, this method can accomplish stable control given almost arbitrary initial pendulum angles, and converge 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.