采用代数建模方法的自适应观测器设计
Adaptive Observer Design Based on an Algebraic Modelling Approach

针对伴有未知输入的一类线性时不变系统,当观测器匹配条件不满足时,研究了自适应观测器的设计问题。通过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,并假设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的增广系统;对于该增广系统讨论了自适应观测器的存在条件,给出了自适应观测器的设计方法,这种自适应观测器不仅可以观测原系统的状态,还可以重构、匹配未知输入。将该设计方法应用于一类机器人系统,虽然系统未知输入初值和观测器重构的未知输入初值相差很大,但是观测器重构的未知输入值能够很快地跟踪上系统实际的未知输入值;虽然这是一种有界误差跟踪,但是误差可以控制在很小的范围内,并不影响实际应用。仿真结果表明,所提方法是有效的。
This paper studies the problem of designing adaptive observers for linear time？？invariant systems with unknown inputs when the observer matching condition is not satisfied. The unknown inputs are divided into two parts: one is matched and the other is mismatched. Under the assumption that the mismatched unknown inputs are deterministic and can be expressed as the response of a fictitious autonomous system, an augmented system consisting of the original system and the mismatched unknown inputs dynamical system is constructed so that the observer matching condition can be satisfied. For the augmented system, the procedure to design this adaptive observer is given, and it is able to not only observe the state of original system but also reconstruct the matched unknown inputs. Such adaptive observer is applied to a kind of robot system and the simulation results demonstrate the effectiveness of the proposed approach