一类欠驱动系统的频域反步法设计

摘要

现有的状态空间反步法存在着设计上的问题,如对非线性函数求导的项数过多,且鲁棒性较差.结合一类欠驱动系统的控制设计,提出一种频域反步设计方法.该方法不同于标准的反步法,不是在每一步加一个积分器,而是每一步设计一个输出反馈回路.这样系统将更为紧凑,也更便于实现.每一步的回路都采用H∞设计.为了解决线性化设计可能带来的非线性尖峰现象,控制回路中增加饱和设计.以无动态联系的欠驱动系统为例来进行讨论.因为这类系统是欠驱动系统设计的难点,其相对阶不能定义,且其未建模非线性不能用有界算子来描述,而且还起一种正反馈的作用.%The existing state-space backstepping method suffers from design problems. For example, the increasing of the terms of the required derivatives of nonlinear functions during the recursive design, and less robustness caused by the single loop implementation of the integrator backstepping design. A frequency-domain backstepping technique is proposed in the paper with applications to a class of underactu-ated systems. The new method is not like the standard backstepping design by adding one integrator at each design step. Instead, an output feedback loop was designed at each step. Thus the resulting system was more compact and can be implemented more easily. The H∞ design was used for each loop. A con trol saturation design is added to counteract the nonlinear peaking phenomenon caused by the linearized design. An underactuated system with no dynamic relations between the generalized coordinates was used as an application example. Because for such underactuated system, the relative degree of the system is not well defined, and the unmodeled nonlinearity cannot be described by a bounded-norm operator, and even it acts as a positive feedback.