经典PID对机器人操纵器的全局可调节性研究
On Global Regulatability of Robot Manipulators by Classical PID
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中文总结 AI 辅助
本文针对具有可变相对阶的不确定多输入多输出非线性系统，提出通道式扩展PID控制器，证明其参数可独立设计，实现系统半全局稳定与设定点调节，为工程逐通道调参提供理论支撑。
中文摘要 AI 辅助
本文研究一类采用扩展PID（EPID）控制的不确定多输入多输出（MIMO）非线性系统，重点关注具有明确定义的向量相对阶（各通道分量可不同）的系统，该设置在现有PID类控制文献中受关注较少。我们开发了一种通道式EPID控制器，其中每个控制输入由对应跟踪误差的比例、积分和微分项构成，最高导数阶数根据该通道的相对阶确定。在未知非线性项满足适当增长条件下，我们构建了由规定初始状态界、不确定性和参考信号指定的EPID参数容许集。我们证明，从该集合中选择的任意参数都能保证闭环系统的半全局稳定性，并实现期望的设定点调节。这些结果表明，EPID参数可针对每个通道独立设计，为强耦合且不确定的MIMO系统（包括飞行控制系统）中逐通道调参的常见工程实践提供了理论依据。
英文摘要
A long-standing open problem in robot manipulator control is whether global regulation can be achieved by classical PID control. This paper provides an answer to this question for classical PID controllers with triple parameters (k_p,k_i,k_d) in R^3. We find and prove that for one-degree-of-freedom manipulators, the classical PID control guarantees global stability and asymptotic regulation under standard structural assumptions, and further derive explicit quantitative design conditions for the PID gains. However, for multi-degree-of-freedom cases, we can construct a robot manipulator satisfying the same structural assumptions for which no choice of PID gains (k_p,k_i,k_d) can achieve global asymptotic regulation. These results provide a fundamental understanding of the abovementioned open problem, revealing both the fundamental capability and intrinsic limitation of the classical PID control for robot manipulator dynamics.
发表机构
- State Key Laboratory of Mathematical Sciences, AMSS, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）
- School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）
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