基于指数保性能的比例-积分-时滞滑模观测器设计

传统状态观测器仅基于当前观测误差重构系统状态,未充分利用系统历史观测数据.针对存在匹配扰动的二阶不确定线性系统,设计一种比例-积分-时滞滑模观测器,实现不确定线性系统状态的鲁棒确切估计.首先,设计带记忆滑模函数,形式为历史观测误差和当前观测误差的线性组合,设计参数包括滑模面增益和人工时滞两部分,将滑模面中的时滞项基于泰勒级数展开,将截断误差表示为积分形式;然后,设计带记忆输出反馈等效控制律,采用时滞依赖型Lyapunov泛函,进行滑模动态指数稳定性分析和观测补偿;接着,将观测器参数设计转化为多目标优化问题,优化目标包括:系统状态衰减率、控制代价、高频噪声不灵敏度,基于粒子群算法,在上述3个优化目标间实现设计参数优化整定,在“快、准、稳”方面进行合理折衷选择;最后,在无源网络系统中,验证所提出滑模观测器的可行性和有效性.

Design of proportional-integral-retarded sliding mode observer based on exponential guarantee performance

Traditional state observers reconstruct the system state only based on the current observation errors, which ignore the system historical observation datas. For the perturbed second-order uncertain linear system, a proportional-integral-retarded sliding mode observer is proposed, which achieves robust and accurate estimation of system states. First, the memory sliding mode function is designed as the linear combination of historical and current observation errors, the design parameters include sliding mode surface gain and artificial time delay. Second, the delayed measurements in the sliding mode surface are expanded based on the Taylor series, and the truncation error is expressed as integral. The memory output feedback equivalent control law is designed based on the delayed dependent Lyapunov functional. On this basis, the dynamic exponential stability analysis and error compensation of sliding mode are performed. Then, the design of observer gains is transformed into a multi-objective optimization problem, with optimization goals: decay rate, control effort, and high-frequency noise insensitivity. Based on the particle swarm algorithm, the optimization of design parameters is realized between the above three optimization goals, and a reasonable compromise among the competitive goals including the rapidness, accuracy and stability. Finally, the feasibility and effectiveness of the proposed sliding mode observer is verified in a passive network system.