Time-varying Output Constraint Control of High-order Strict-feedback Systems Based on Fully Actuated System Approach
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摘要: 针对输出受不对称时变约束的不确定高阶严反馈系统, 提出一种基于全驱系统方法的高阶自适应动态面输出约束控制方法. 所研究的高阶严反馈系统, 每个子系统都是高阶形式, 通过非线性转换函数将原输出约束系统转换为新的无约束系统, 从而将原系统输出约束问题转化为新系统输出有界的问题. 进一步结合全驱系统方法和自适应动态面控制, 直接将每个高阶子系统作为一个整体进行控制器设计, 而不需要将其转化为一阶系统形式, 有效简化了设计步骤; 同时通过引入一系列低通滤波器来获得虚拟控制律的高阶导数, 以代替复杂的微分运算. 基于Lyapunov稳定性理论证明闭环系统所有信号是一致最终有界的, 系统输出在满足约束的条件下能有效跟踪期望的参考信号, 且可通过调整参数使得系统跟踪误差收敛到零附近的足够小的邻域内. 最后, 通过对柔性关节机械臂系统进行仿真, 验证了所提出控制方法的有效性.Abstract: A high-order adaptive dynamic surface output constraint control method based on fully actuated system approach is proposed for uncertain high-order strict-feedback systems with asymmetric time-varying output constraints. The high-order strict-feedback system studied in this paper, each subsystem is a high-order form. The original output constraint system is transformed into a new unconstrained system by nonlinear transformation function, so that the original system output constraint problem is transformed into the new system output bounded problem. Furthermore, combined with the fully actuated system approach and the adaptive dynamic surface control method, the controller is designed directly for each high-order subsystem as a whole without converting it into a first-order system form, which effectively reduces the design steps. At the same time, a series of low-pass filters are introduced to obtain the high-order derivative of the virtual control law to replace the complex differential operation. Based on Lyapunov theory, it is proved that all signals of the closed-loop system are uniformly ultimately bounded. The system output can effectively track the desired reference signal without violating the constraints, and the system tracking error can be converged to any small neighborhood of the origin by adjusting the parameters. Finally, the effectiveness of the control method is verified by simulating the flexible joint manipulator system.
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图 5 参数估计${\hat{\theta} _1}(h)$, ${\hat{\theta} _1}(f1)$, ${\hat{\theta} _1}(f2)$(情况1)
Fig. 5 Parameter estimation ${\hat{\theta} _1}(h)$, ${\hat{\theta} _1}(f1)$, and ${\hat{\theta} _1}(f2)$(Case 1)
图 6 参数估计${\hat{\theta} _2}(h)$, ${\hat{\theta} _2}(f1)$, ${\hat{\theta} _2}(f2)$(情况1)
Fig. 6 Parameter estimation ${\hat{\theta} _2}(h)$, ${\hat{\theta} _2}(f1)$, and ${\hat{\theta} _2}(f2)$(Case 1)
图 10 参数估计${\hat{\theta} _1}(h)$, ${\hat{\theta} _1}(f1)$, ${\hat{\theta} _1}(f2)$(情况2)
Fig. 10 Parameter estimation ${\hat{\theta} _1}(h)$, ${\hat{\theta} _1}(f1)$, and ${\hat{\theta} _1}(f2)$(Case 2)
图 11 参数估计${\hat{\theta} _2}(h)$, ${\hat{\theta} _2}(f1)$, ${\hat{\theta} _2}(f2)$(情况2)
Fig. 11 Parameter estimation ${\hat{\theta} _2}(h)$, ${\hat{\theta} _2}(f1)$, and ${\hat{\theta} _2}(f2)$(Case 2)
表 1 三种算法运算时间对比(s)
Table 1 Comparison of operation time of three algorithms (s)
本文方法 一阶BLF方法 一阶NM方法 情况1 44.380383 58.879631 49.213382 情况2 35.173545 47.965324 41.693068 
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