摘要
移动机械臂因广阔的工作空间和灵活的操作能力而具有潜在的应用前景,近年来已引起国际学术界和工业界的高度重视。而移动机械臂是时变、强耦合的非线性系统,其运动过程中受到非完整性约束,实际的控制系统又受到参数不确定性、外扰动和未建模动态等因素的影响,其运动控制问题相当困难。另外,随着移动机械臂的任务不断趋向复杂化,对控制精度和运动控制范围提出更高的要求。因此,研究这类系统的大范围非线性控制问题有十分重要的理论价值和实践意义。
微分几何方法可在全局意义下精确实现系统的线性化和解耦问题,实现系统的大范围分析和综合。但是,由于抽象的微分几何理论缺乏面向非线性控制的系统理论,且它必须依赖于系统的精确数学模型,这严重制约了它在实际工程中的广泛应用。本文在系统总结微分几何方法的基础上,采用微分几何方法和滑模变结构控制相结合的非线性控制策略,实现了移动机械臂轨迹跟踪控制。仿真结果表明,这种策略既提高了系统的鲁棒性和控制精度,又解决了非线性系统滑模面不易构造的难题。
本文首先系统地总结了面向非线性控制应用的微分几何基本理论,讨论了非线性系统精确线性化和解耦控制的充要条件,给出系统精确性化和解耦问题求解的具体步骤。然后利用非完整系统理论和Lagrange建模方法建立了移动机械臂的统一数学模型,并分析了系统的可控性。
其次,通过两次构造非线性反馈律和微分同胚,利用微分几何控制方法实现了移动机械臂的输入输出精确解耦,并用零动态分析了系统的内部动态品质。在解耦线性化的基础上,设计了PD轨迹跟踪控制器,利用S函数建立了可移植性强、适合于时实动态仿真的移动机械臂控制系统仿真模型,并仿真分析了PD跟踪控制效果和系统的鲁棒性。
最后,针对系统鲁棒性差和滑模变结构控制的抖振问题,提出了两种改进方案,即基于改进趋近律的滑模变结构控制和基于动态切换函数的动态积分滑模变结构控制。仿真结果表明,它们很好地实现了移动机械臂的轨迹跟踪控制,且在动力学参数摄动+40%和未建模动态及外扰动两种情况下,系统的鲁棒性强较PD跟踪控制强很多,并削弱了控制的抖振现象。
Due to its vast workspace and flexible manipulation, a mobile manipulator has an extensive background of applications, and has attracted great attention in the international academic and industrial fields. And the mobile manipulator is time-varying, the strong coupling of nonlinear system, its course of the campaign is restricted by nonholonomic constraints. the practical control system could not exclude the influence of parameter perturbation and disturbances from the external environments or unmodelled dynamics etc,which to some extent make it difficult to control. In addition, as the complexity of its tasks increase, we need higher precision and larger scale of control. Therefore, the study of such systems and the large-scale nonlinear control issues has important theoretical and practical significance.
Differential geometric method makes it possible to be realized globally by the decoupling and exact linearization control strategy based on the new theory. However, the abstract differential geometric method is lack of system theory for nonlinear system and relies on the precise of the system, which to some extent limited its application. The paper systematically summed up the methods of differential geometry and presented the nonlinear control strategy which employs the sliding mode control approach and the differential geometric method to realize trajectory tracking of the mobile manipulator. The simulation results indicate that the presented strategy has not only promoted the system to be more robust and precise, also solved the problem of constructing the nonlinear sliding surfaces. The main topics are as follows:
Firstly, the paper summed up the differential geometry basic theory for the control of nonlinear system, discussed the necessary and sufficient conditions for exact linearization and decoupling control of the nonlinear system and presented the detailed steps. Next, Nonholonomic theory and a Lagrange approach are used to obtain unified mathematical model of the mobile manipulator, and analysis the system’s controllable.
Secondly, through the two nonlinear feedback law and diffeomorphism, realize control exact input and output decoupling for the mobile manipulator using of differential geometric method, and use zero dynamics to analyze the internal dynamic quality of the system, designed the PD tracking controller on the basis of the linear decoupling system. Next, build the substitutable simulation model using of the S-function, which is suitable for real-time dynamic simulation of the mobile manipulator control, then analyze PD tracking control and robustness of the mobile manipulator.
Finally, presented the two improvement methods for problems of poor robustness and chattering, they are the improved reaching law and the dynamic integration sliding mode variable structure control based on dynamic switching functions. The simulation results show that they achieve a good performance for trajectory tracking control of the mobile manipulator, and promote the system to be more robust to the kinetic parameters perturbation +40% and external disturbances than PD tracking control. Moreover, weaken the chattering problem of the mobile manipulator.
引文
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