摘要
主要研究欠驱动机器人Acrobot的最优控制,讨论控制有无约束两种情形下时间三类性能指标的最优控制问题.首先引进一种非线性等价变换,将系统转换为另一种易于设计控制律的形式,然后由极小值原理建立了最优控制律.在证明了双连杆最优控制律是一种非奇异控制后,利用拉萨尔定理分析最优控制律下的不变集.控制策略是使用最优控制律驱动系统运动至不变集邻域,该邻域满足可线性化条件时,线性化系统并用线性最优控制律进行控制.切换控制的全局稳定性由非光滑Lyapunov控制函数保证.最后给出了一类性能指标下的仿真结果,并与相关研究结果进行了对比,验证了该方法的有效性和优越性.
In this paper,we present a unified treatment of the optimal control of under-actuated two-link manipulators.Firstly,a nonlinear in-revertible transfer is introduced to simplify design of controller,then several optimal control law are established by maximum principle.Controller for swing-up area is based on performance index,while controller for attractive area is based on LQR(linear quadratic regulator).It is proved that optimal control is not singular,invariant sets is obtained by theoretical analysis.The strategy for Acrobat is to use optimal control law to pump manipulators into linear area,then switch control law to LQR,which drives system to up-straight position.Local and global stability were analyzed in detail under control strategy by use of LaSalle’s in-variance principle and WCLF(non-smooth control Lyapunov function).Simulation and comparison with previous results show that the proposed approach here is valid and of advantages.
作者
张志东
陈莉
欧国东
张志飞
ZHANG Zhidong;CHEN Li;OU Guodong;ZHANG Zhifei(Guangdong Raising Synthesis Energy Services Co.,Ltd,Foshan 528000,China;School of Automation,Foshan University of Science and Technology,Foshann 528000,China)
出处
《湖南理工学院学报（自然科学版）》
CAS
2019年第4期4-10,共7页
Journal of Hunan Institute of Science and Technology(Natural Sciences)
基金
国家自然科学基金项目(61803087)
