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首页> 外文期刊>Arabian Journal for Science and Engineering. Section A, Sciences >Nonlinear SPKF-Based Time-Varying LQG for Inverted Pendulum System
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Nonlinear SPKF-Based Time-Varying LQG for Inverted Pendulum System

机译：基于非线性SPKF的时变LQG的倒立摆系统

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摘要

This paper deals with the holing issue of nonlinear inverted pendulum (IP) system. Close to the equilibrium point, IP is considered as a linear system without disruption and linear control is sufficient. However, when the IP swings over a wide range, its nonlinear dynamics becomes significant and the stabilization of IP becomes challenging task due to the inconsistency between its nonlinear dynamics and the controllers designed based on linearized models. Hence, the need for sophisticated control becomes highly demanding. This paper proposes an optimal time-varying linear quadratic Gaussian controller (TV-LQG) that is able to overcome this inconsistency problem. The proposed TV-LQG utilizes a sigma-point Kalman filter (SPKF) and a linear quadratic regulator with a prescribed degree of stability. SPKF is a highly accurate nonlinear state estimator since it does not use any linearization for calculating the state prediction covariance and Kalman gains. This leads, instantaneously, to a more exact nonlinear state estimation. The estimated states are fed to the Jacobian method, which updates, at once, the system dynamics accordingly. Thus, the parameters of the proposed TV-LQG are optimized based on the updated system dynamics. The proposed controller is intensively tested using simulation experiments and compared to the traditional LQG, LQR self-adjusting control and LQR-fuzzy control. The results proved the robustness and competitiveness of the proposed scheme to enhance the performance of the nonlinear IP system.
机译：本文讨论了非线性倒立摆系统的孔洞问题。接近平衡点，IP被认为是没有干扰的线性系统，线性控制就足够了。但是，由于IP的非线性动力学与基于线性化模型设计的控制器之间的不一致，当IP波动很大时，其非线性动力学变得非常重要，IP的稳定性也成为具有挑战性的任务。因此，对复杂控制的需求变得非常苛刻。本文提出了一种能够克服这种不一致问题的最优时变线性二次高斯控制器（TV-LQG）。拟议的TV-LQG利用sigma-point卡尔曼滤波器（SPKF）和具有规定稳定性的线性二次调节器。 SPKF是一种高精度的非线性状态估计器，因为它不使用任何线性化来计算状态预测协方差和卡尔曼增益。这立即导致更精确的非线性状态估计。估计的状态被馈入Jacobian方法，该方法立即更新系统动态。因此，基于更新的系统动力学来优化所提出的TV-LQG的参数。拟议的控制器经过大量仿真实验测试，并与传统的LQG，LQR自调节控制和LQR模糊控制进行了比较。结果证明了所提出的方案的鲁棒性和竞争力，以增强非线性IP系统的性能。

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