Design and stability analysis of semi-implicit cascaded proportional-derivative controller for underactuated cart-pole inverted pendulum system

IF 2.7 4区计算机科学 Q3 ROBOTICS

Robotica Pub Date : 2023-10-16 DOI:10.1017/s0263574723001352

Changyi Lei, Ruobing Li, Quanmin Zhu

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引用次数: 0

Abstract

Abstract This article proposes a control method for underactuated cartpole systems using semi-implicit cascaded proportional-derivative (PD) controller. The proposed controller is composed of two conventional PD controllers, which stabilizes the pole and the cart second-order dynamics respectively. The first PD controller is realized by transforming the pole dynamics into a virtual PD controller, with the coupling term exploited as the internal tracking target for the cart dynamics. Then, the second PD controller manipulates the cart dynamics to track that internal target. The solution to the internal tracking target relies on an equation set and features a semi-implicit process, which exploits the internal dynamics of the system. Besides, the design of second PD controller relies on the parameters of the first PD controller in a cascaded manner. A stability analysis approach based on Jacobian matrix is proposed and implemented for this fourth-order system. The proposed method is simple in design and intuitive to comprehend. The simulation results illustrate the superiority of proposed method compared with conventional double-loop PD controller in terms of convergence, with the theoretical conclusion of at least locally asymptotic stability.

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欠驱动车杆倒立摆系统半隐式级联比例导数控制器的设计与稳定性分析

提出了一种半隐式级联比例导数(PD)控制器控制欠驱动横极系统的方法。该控制器由两个传统的PD控制器组成，分别稳定极点和小车的二阶动力学。第一个PD控制器通过将极点动力学转化为虚拟PD控制器来实现，耦合项作为小车动力学的内部跟踪目标。然后，第二个PD控制器操纵购物车动态来跟踪该内部目标。内部跟踪目标的求解依赖于一个方程集，采用半隐式过程，利用了系统的内部动力学特性。此外，第二PD控制器的设计以级联的方式依赖于第一PD控制器的参数。针对该四阶系统，提出并实现了基于雅可比矩阵的稳定性分析方法。该方法设计简单，易于理解。仿真结果表明，与传统双环PD控制器相比，该方法在收敛性方面具有优越性，并得到了至少局部渐近稳定的理论结论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Robotica 工程技术-机器人学

CiteScore

4.50

自引率

22.20%

发文量

181

审稿时长

9.9 months

期刊介绍： Robotica is a forum for the multidisciplinary subject of robotics and encourages developments, applications and research in this important field of automation and robotics with regard to industry, health, education and economic and social aspects of relevance. Coverage includes activities in hostile environments, applications in the service and manufacturing industries, biological robotics, dynamics and kinematics involved in robot design and uses, on-line robots, robot task planning, rehabilitation robotics, sensory perception, software in the widest sense, particularly in respect of programming languages and links with CAD/CAM systems, telerobotics and various other areas. In addition, interest is focused on various Artificial Intelligence topics of theoretical and practical interest.