Quantitative Reconfigurability Evaluation for Control Systems in View of Time Properties
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摘要: 故障诊断时间和控制重构延时严重影响了控制系统的实际重构性能，然而目前缺乏相关研究.基于该现状，本文针对执行器快变偏差故障，重点考虑时间特性影响，结合能量与输入约束，对控制系统可重构性的定量评价问题展开了研究.首先，以基于观测器的故障诊断算法和控制重构方案为例，建立了重构系统模型；然后，以该模型为对象，通过对重构过程中关键时刻的分析，深入研究了系统故障后的动态特性，并综合考虑故障引起的状态偏差、资源浪费以及诊断误差，设计了用于描述故障系统性能下降程度的二次型性能指标；其次，利用Lyapunov稳定性理论，定量求解了性能指标关于时间的一般表达式，进而求得该指标在整个时域中的最优解；最后，基于最优性能指标，引入了可重构度的概念，实现了对控制系统可重构性的理论判定以及定量描述，并通过数值仿真验证了所提可重构性分析方法的有效性.Abstract: Due to the effect on actual reconfigurability of control systems caused by delays of fault diagnosis and controller reconfiguration, it is necessary to analyze system reconfigurability in the time domain. Given this, a quantitative analysis on time properties of reconfigurability is carried out for control systems with fast time-varying actuator bias fault in this paper. First of all, the observer-based fault diagnotor and reconfigurable controller are presented as an example to build the reconfigured system model. Then, the key instants for the whole fault-tolerant process are analyzed to describe the system post-fault properties and a quadratic index is designed to describe the performance degradation related to the nominal system. Next, the analytical expression of the quadratic index is deduced in terms of Lyapunov stability theory, based on which time management is optimized for the reconfiguration scheme. After that, the reconfigurability of the control system is quantitatively evaluated by giving the reconfigurability criteria and introducing the degree of reconfigurability. Finally, a numerical simulation is carried out to show the validity of the proposed analysis method.1) 本文责任编委 姜斌
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图 2 控制系统可重构性评价流程
Fig. 2 Flowchart of the quantitative reconfigurability evaluation for control systems
图 3 标称、故障与重构系统的输出响应
Fig. 3 Output discrepancies of nominal, fault and reconfigurated systems
图 4 ${t_d} = 34$s时, 性能指标${J_s}$随${t_r}$的变化曲线
Fig. 4 Cost index evolution for different ${t_r}$ (${t_d} = 34$s)
图 5 ${t_d} = {t_r}$时, 性能指标${J_s}$随${t_d}$的变化曲线
Fig. 5 Cost index evolution for different ${t_d}$ (${t_d} = {t_r}$)
图 6 性能指标${J_s}$关于不同${t_d}, {t_r}$的变化曲线
Fig. 6 Cost index evolution for different ${t_d}, {t_r}$
图 7 可重构性指标$\rho $关于不同${t_d}, {t_r}$的变化曲线
Fig. 7 Degree of reconfigurability for different ${t_d}, {t_r}$
图 8 ${t_{r1}}$与$t_r^*$两个不同重构时刻的系统输出响应
Fig. 8 Output discrepancies for two instants ${t_{r1}}, t_r^*$
图 9 ${t_{r1}}$与$t_r^*$两个不同重构时刻的系统输入响应
Fig. 9 Input discrepancies for two instants ${t_{r1}}, t_r^*$
图 10 ILO系统${t_d} = {t_r}$时, 性能指标${J_s}$随${t_d}$的变化曲线
Fig. 10 Cost index evolution for different ${t_d}$ (${t_d} = {t_r}$, ILO)
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