基于代数方法的一类不确定系统的滑模观测器设计

摘要

This paper considers the problem of designing sliding-mode observers for linear invariant systems with unknown inputs when the observer matching condition is not satisfied. The unknown inputs can be divided into two parts, one is matched unknown inputs and the other is unmatched unknown inputs. Using an algebraic unknown inputs modelling technique, the mismatched part can be expressed as a dynamical system. Therefore, an augmented system consisting of the original system model and the unmatched unknown inputs model is constructed such that the observer matching condition can be satisfied. For the augmented system, a sliding-mode observer is designed which is able to asymptotically track the original states. The simulation results to a single flexible joint robot link model demonstrate the effectiveness of the proposed approach.%在不满足观测器匹配条件的情况下，针对伴有未知输入的一类线性时不变系统，研究了滑模观测器的设计。首先，将未知输入划分为匹配未知输入和不匹配未知输入两部分，通过使用代数方法，不匹配未知输入可以表述为一个动态系统，从而可得一个满足匹配条件，由原系统和不匹配未知输入系统构成的增广系统。针对该增广系统设计滑模观测器，可以渐近跟踪原系统的状态。针对一类伴有未知扰动的柔性关节机器人系统，使用该文方法设计滑模观测器，仿真结果表明该方法是有效的。