CN108667673A - Fault detection method for nonlinear networked control systems based on event-triggered mechanism - Google Patents
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Abstract
本发明提供一种基于事件触发机制的非线性网络控制系统故障检测方法,涉及网络系统故障检测技术领域。该方法首先建立非线性网络控制系统的T‑S模糊模型、设置事件触发条件,建立模糊故障检测滤波器模型,建立故障加权系统,进而建立故障检测系统模型;并根据故障检测系统模型,选择合适的残差评价函数和检测阈值,检测非线性网络控制系统故障是否发生;最后根据故障检测系统稳定和故障检测滤波器存在的充分条件,进一步设计故障检测滤波器的参数矩阵和事件触发矩阵。本发明提供的基于事件触发机制的非线性网络控制系统故障检测方法,大大提高了对外部扰动及通讯延时的鲁棒性,事件触发机制的应用能够节省有限的网络资源和计算资源。
The invention provides a fault detection method for a nonlinear network control system based on an event trigger mechanism, and relates to the technical field of network system fault detection. This method first establishes the T-S fuzzy model of the nonlinear network control system, sets the event trigger conditions, establishes the fuzzy fault detection filter model, establishes the fault weighting system, and then establishes the fault detection system model; and according to the fault detection system model, selects the appropriate The residual evaluation function and detection threshold of the nonlinear network control system are used to detect whether the fault occurs in the nonlinear network control system. Finally, according to the sufficient conditions for the stability of the fault detection system and the existence of the fault detection filter, the parameter matrix and event trigger matrix of the fault detection filter are further designed. The non-linear network control system fault detection method based on the event trigger mechanism provided by the present invention greatly improves the robustness to external disturbances and communication delays, and the application of the event trigger mechanism can save limited network resources and computing resources.
Description
技术领域technical field
本发明涉及网络系统故障检测技术领域,尤其涉及一种基于事件触发机制的非线性网络控制系统故障检测方法。The invention relates to the technical field of network system fault detection, in particular to a fault detection method for a nonlinear network control system based on an event trigger mechanism.
背景技术Background technique
网络控制系统由于其安装维护低成本,安全性、可靠性高,通信结构灵活等优点,在复杂工业控制系统中获得了广泛关注。网络控制系统中,传感器、执行器和控制器通过一个共享的通讯网络相互联系。随着网络控制系统对于安全、稳定、高性能的要求不断提高,针对网络控制系统的故障检测问题成为了一个重要的研究领域。Due to its low cost of installation and maintenance, high security and reliability, and flexible communication structure, networked control systems have gained widespread attention in complex industrial control systems. In a networked control system, sensors, actuators, and controllers are interconnected through a shared communication network. With the increasing requirements of networked control systems for security, stability, and high performance, the problem of fault detection for networked control systems has become an important research field.
由于通信网络的引入和网络控制系统本身的特性,不可避免的为网络控制系统带来了新的问题和挑战,比如通信延时,数据丢包,数据错序,带宽有限等问题。目前大部分的网络控制系统的研究成果是针对于系统的时滞、丢包、乱序等问题而提出的控制器、滤波器的设计方法,而针对网络控制系统的故障诊断问题还是相对较少。另外,关于网络控制系统的故障检测的研究成果大多数是以线性系统作为研究对象,然而工业系统以及生活中的实际系统大多数都是非线性的,因此,研究非线性网络控制系统的故障检测问题具有非常重要的理论研究价值和实际应用前景。Due to the introduction of the communication network and the characteristics of the network control system itself, it inevitably brings new problems and challenges to the network control system, such as communication delay, data packet loss, data out-of-sequence, and limited bandwidth. At present, most of the research results of network control systems are the design methods of controllers and filters for the problems of time delay, packet loss, and disorder of the system, but there are relatively few fault diagnosis problems for network control systems. . In addition, most of the research results on fault detection of networked control systems are based on linear systems, but most of the industrial systems and practical systems in life are nonlinear. Therefore, the study of fault detection problems in nonlinear networked control systems It has very important theoretical research value and practical application prospect.
对于非线性网络控制系统的故障检测问题,大多数采用时间触发的方法,但在实际工作过程中,并非所有的采样数据和测量输出都需要被传输。因此,时间触发易造成有限网络带宽的浪费,进一步加剧网络诱导时延、数据丢包的发生。为了减少网络中“不必要”数据的传输,同时保证期望的系统性能,事件触发通讯机制受到了广泛关注。事件触发策略的基本思想是当预先设定的阈值被满足时,采样数据才会被传输。基于事件触发通讯机制的非线性网络控制系统故障检测,不仅可以及时准确的检测到故障是否发生,而且可以节省有限的网络资源,符合故障检测的发展趋势。For fault detection problems in nonlinear networked control systems, most of them use time-triggered methods, but in actual work, not all sampling data and measurement outputs need to be transmitted. Therefore, time triggering can easily lead to waste of limited network bandwidth, and further aggravate the occurrence of network-induced delay and data packet loss. In order to reduce the transmission of "unnecessary" data in the network while ensuring the expected system performance, event-triggered communication mechanisms have received extensive attention. The basic idea of the event-triggered strategy is that sampled data is transmitted only when a preset threshold is met. The fault detection of nonlinear networked control system based on the event-triggered communication mechanism can not only detect whether a fault occurs in time and accurately, but also save limited network resources, which is in line with the development trend of fault detection.
发明内容Contents of the invention
针对现有技术的缺陷,本发明提供一种基于事件触发机制的非线性网络控制系统故障检测方法,实现对非线性网络控制系统的故障进行检测。Aiming at the defects of the prior art, the present invention provides a fault detection method of a nonlinear network control system based on an event trigger mechanism, so as to realize fault detection of the nonlinear network control system.
基于事件触发机制的非线性网络控制系统故障检测方法,包括以下步骤:A fault detection method for a nonlinear networked control system based on an event-triggered mechanism, comprising the following steps:
步骤1、对具有过程故障、传感器故障和输出扰动的非线性网络控制系统,利用Takagi-Sugeno(即T-S)模糊模型方法进行建模分析,建立该非线性网络控制系统的T-S模糊模型;Step 1, to the nonlinear network control system with process failure, sensor failure and output disturbance, utilize Takagi-Sugeno (i.e. T-S) fuzzy model method to carry out modeling analysis, establish the T-S fuzzy model of this nonlinear network control system;
所述模糊模型方法所使用的模糊规则如下所示:The fuzzy rules used by the fuzzy model method are as follows:
Rule i:IF z1(t)is Mi1(z)and...and zp(t)is Mip(z),THENRule i: IF z 1 (t) is M i1 (z) and...and z p (t) is M ip (z), THEN
其中,i为模糊规则编号,z(t)=[z1(t),z2(t),...,zp(t)]为包含非线性网络控制系统中状态量信息的前件变量,p为前件变量的个数,Mij为模糊集合,j=1、2、…、p,x(t)为非线性网络控制系统的状态变量,y(t)为测量输出,ω(t)为外部扰动,f(t)为传感器检测的故障信号,Ai,Di,Fi,Ci,Ei,Gi为已知合适维数的矩阵;Among them, i is the number of the fuzzy rule, z(t)=[z 1 (t), z 2 (t), ..., z p (t)] is the antecedent containing the state quantity information in the nonlinear network control system variable, p is the number of antecedent variables, M ij is a fuzzy set, j=1, 2, ..., p, x(t) is the state variable of the nonlinear network control system, y(t) is the measurement output, ω (t) is the external disturbance, f(t) is the fault signal detected by the sensor, A i , D i , F i , C i , E i , G i are matrices with known appropriate dimensions;
所述建立的非线性网络控制系统的T-S模糊模型如下所示:The T-S fuzzy model of the nonlinear networked control system of described establishment is as follows:
其中,r为模糊规则的数量,wi(z(t))为非线性网络控制系统的隶属度函数;Among them, r is the number of fuzzy rules, w i (z(t)) is the membership function of the nonlinear network control system;
步骤2、设置事件触发条件,根据事件触发条件确定传感器的测量输出是否应该被传输至滤波器;Step 2. Set the event trigger condition, and determine whether the measurement output of the sensor should be transmitted to the filter according to the event trigger condition;
所述设置的事件触发条件如下所示:The event trigger conditions for the settings are as follows:
其中,h为传感器的采样时间间隔,ikh为传感器的采样信号传输时刻,ik+1h为下一采样信号被传输的时刻,Φ>0为需要被设计的加权矩阵,ek(ikh+jh)=y(ikh+jh)-y(ikh)为阈值误差,ε为事件触发参数、y(ikh)为传感器上一时刻采样信号的测量输出,y(ikh+jh)为传感器当前的测量输出;Among them, h is the sampling time interval of the sensor, i k h is the transmission time of the sensor’s sampling signal, i k+1 h is the time when the next sampling signal is transmitted, Φ>0 is the weighting matrix that needs to be designed, e k ( i k h+jh)=y(i k h+jh)-y(i k h) is the threshold error, ε is the event trigger parameter, y(i k h) is the measurement output of the sensor’s sampling signal at the previous moment, y (i k h+jh) is the current measurement output of the sensor;
当上一时刻采样信号y(ikh)被传输时,只有当前采样信号满足触发条件时,采样信号将会被传输至滤波器;When the sampling signal y(i k h) was transmitted at the last moment, only when the current sampling signal meets the trigger condition, the sampling signal will be transmitted to the filter;
步骤3、利用T-S模糊模型方法建立模糊故障检测滤波器模型;Step 3, utilizing the T-S fuzzy model method to establish a fuzzy fault detection filter model;
所述利用T-S模糊模型方法对模糊故障检测滤波器进行建模所使用的模糊规则如下所示:The fuzzy rules used for modeling the fuzzy fault detection filter by using the T-S fuzzy model method are as follows:
Rulej:IF z1(ikh)is Nj1 and...and zp(ikh)is Njp,THENRulej: IF z 1 (i k h)is N j1 and...and z p (i k h)is N jp ,THEN
其中,xf(t)为模糊故障检测滤波器的状态向量,为模糊滤波器的真实输入,zf(t)为残差信号,Afj,Bfj,Cfj和Dfj为待设计的模糊滤波器的增益矩阵,j为模糊规则编号,Nji为模糊集合,z(ikh)=[z1(ikh),z2(ikh),...,zp(ikh)]为模糊故障检测滤波器的前件变量;Among them, x f (t) is the state vector of the fuzzy fault detection filter, is the real input of the fuzzy filter, z f (t) is the residual signal, A fj , B fj , C fj and D fj are the gain matrices of the fuzzy filter to be designed, j is the fuzzy rule number, N ji is the fuzzy Set, z (i k h)=[z 1 (i k h), z 2 (i k h), ..., z p (i k h)] is the antecedent variable of the fuzzy fault detection filter;
所述建立的模糊故障检测滤波器的模型如下所示:The model of the fuzzy fault detection filter set up is as follows:
其中,wj(z(ikh))为故障检测滤波器的隶属度函数;Among them, w j (z(i k h)) is the membership function of the fault detection filter;
步骤4、建立能够提升故障检测系统设计自由度的故障加权系统;Step 4. Establish a fault weighting system that can improve the design freedom of the fault detection system;
所述故障加权系统如下公式所示:The fault weighting system is shown in the following formula:
其中,f(s)为故障信号,W(s)为加权矩阵,为加权后的故障信号;Among them, f(s) is the fault signal, W(s) is the weighting matrix, is the weighted fault signal;
故障信号f(s)和加权矩阵W(s)的状态空间形式如下公式所示:The state space form of fault signal f(s) and weighting matrix W(s) is shown in the following formula:
其中,xw(t)为状态空间向量,fw(t)为加权后的故障信号,Aw,Bw,Cw和Dw为常数矩阵;Among them, x w (t) is a state space vector, f w (t) is a weighted fault signal, A w , B w , C w and D w are constant matrices;
步骤5、根据非线性网络控制系统的T-S模糊模型、事件触发条件、滤波器的T-S模糊模型以及故障加权矩阵建立故障检测系统模型;Step 5, establish a fault detection system model according to the T-S fuzzy model of the nonlinear network control system, the event trigger condition, the T-S fuzzy model of the filter and the fault weighting matrix;
所述建立的故障检测系统模型如下公式所示:The established fault detection system model is shown in the following formula:
其中,为故障检测系统残差误差, in, is the residual error of the fault detection system,
步骤6、根据故障检测系统模型,选择合适的残差评价函数和检测阈值,通过对比残差评价函数和检测阈值的数值大小,检测非线性网络控制系统故障是否发生;Step 6. Select an appropriate residual evaluation function and detection threshold according to the fault detection system model, and detect whether a nonlinear network control system fault occurs by comparing the numerical values of the residual evaluation function and the detection threshold;
所述残差评价函数H(zf)和检测阈值Jth如下公式所示:The residual evaluation function H(z f ) and the detection threshold J th are shown in the following formulas:
基于残差评价函数和检测阈值,通过以下关系判断非线性网络控制系统故障是否发生:Based on the residual evaluation function and the detection threshold, the following relationship is used to judge whether a fault occurs in the nonlinear networked control system:
当残差评价函数大于检测阈值时,则非线性网络控制系统发生了故障,故障检测系统报警;反之,非线性网络控制系统正常工作,不报警;When the residual evaluation function is greater than the detection threshold, the nonlinear networked control system has a fault, and the fault detection system alarms; otherwise, the nonlinear networked control system works normally and does not alarm;
步骤7、构造模糊Lyapuonv函数,利用Lyapunov稳定性理论、相关引理和线性矩阵不等式,得到故障检测系统稳定和故障检测滤波器存在的充分条件,进一步设计故障检测滤波器的参数矩阵Afj,Bfj,Cfj和Dfj和事件触发矩阵Φ。Step 7. Construct the fuzzy Lyapuonv function, use the Lyapunov stability theory, related lemmas and linear matrix inequalities to obtain sufficient conditions for the stability of the fault detection system and the existence of the fault detection filter, and further design the parameter matrix A fj of the fault detection filter, B fj , C fj and D fj and the event trigger matrix Φ.
由上述技术方案可知,本发明的有益效果在于:本发明提供的基于事件触发机制的非线性网络控制系统故障检测方法,在非线性网络控制系统建模过程中,同时考虑了过程故障,传感器故障,和外部扰动对网络控制系统的影响。在故障诊断过程中,考虑并解决了网络系统中的通讯时延,数据丢包,和数据乱序等问题。其中滤波器模糊模型的前件变量和网络控制系统模糊模型的前件变量异步,可以提升滤波器设计的灵活性,减少成本;模糊Lyapunov函数的应用降低了系统的保守性。与现有的技术相比,使用本发明设计的事件触发模糊H∞滤波器进行故障检测,一方面,该技术不仅大大提高了对非线性网络控制系统的故障敏感度,而且对外部扰动及数据丢包具有更强的鲁棒性,能够有效的解决非线性网络控制系统的故障检测问题;另一方面,事件触发通讯机制的引入,能够有效的减少网络带宽的使用,节省有限的网络资源,同时还可以节省计算资源。It can be known from the above technical solution that the beneficial effect of the present invention lies in that the event-triggered mechanism-based nonlinear network control system fault detection method provided by the present invention takes into account process faults and sensor faults during the modeling process of the nonlinear network control system. , and the impact of external disturbances on the networked control system. In the process of fault diagnosis, problems such as communication delay, data packet loss, and data disorder in the network system are considered and solved. The antecedent variables of the fuzzy model of the filter and the fuzzy model of the network control system are asynchronous, which can improve the flexibility of the filter design and reduce the cost; the application of the fuzzy Lyapunov function reduces the conservatism of the system. Compared with the existing technology, using the event-triggered fuzzy H ∞ filter designed by the present invention for fault detection, on the one hand, this technology not only greatly improves the fault sensitivity to the nonlinear network control system, but also is sensitive to external disturbances and data Packet loss is more robust and can effectively solve the problem of fault detection in nonlinear network control systems; on the other hand, the introduction of event-triggered communication mechanisms can effectively reduce the use of network bandwidth and save limited network resources. At the same time, it can save computing resources.
附图说明Description of drawings
图1为本发明实施例提供的基于事件触发机制的非线性网络控制系统故障检测方法的流程图;Fig. 1 is the flow chart of the non-linear network control system fault detection method based on the event triggering mechanism provided by the embodiment of the present invention;
图2为本发明实施例提供的残差信号的示意图;FIG. 2 is a schematic diagram of a residual signal provided by an embodiment of the present invention;
图3为本发明实施例提供的残差评价函数和检测阈值随时间变化的示意图;Fig. 3 is a schematic diagram of a residual evaluation function and a detection threshold changing with time according to an embodiment of the present invention;
图4为本发明实施例提供的有故障和无故障时的残差评价函数随时间变化的示意图;Fig. 4 is a schematic diagram of the variation of the residual evaluation function with time when there is a fault and when there is no fault according to an embodiment of the present invention;
图5为本发明实施例提供的事件触发策略的释放时间和释放间隔之间的关系示意图。FIG. 5 is a schematic diagram of the relationship between the release time and the release interval of the event-triggered policy provided by the embodiment of the present invention.
具体实施方式Detailed ways
下面结合附图和实施例,对本发明的具体实施方式作进一步详细描述。以下实施例用于说明本发明,但不用来限制本发明的范围。The specific implementation manners of the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.
本实施例,使用本发明的基于事件触发机制的非线性网络控制系统故障检测方法对非线性网络控制系统进行故障检测。In this embodiment, the fault detection method of the nonlinear network control system based on the event-triggered mechanism of the present invention is used to detect the fault of the nonlinear network control system.
基于事件触发机制的非线性网络控制系统故障检测方法,如图1所示,包括以下步骤:The fault detection method for nonlinear networked control systems based on event-triggered mechanism, as shown in Figure 1, includes the following steps:
步骤1:对具有过程故障、传感器故障和输出扰动的非线性网络控制系统,利用Takagi-Sugeno (T-S)模糊模型方法进行建模分析,建立该非线性网络控制系统的T-S模糊模型;Step 1: For a nonlinear networked control system with process faults, sensor faults and output disturbances, the Takagi-Sugeno (T-S) fuzzy model method is used for modeling and analysis, and the T-S fuzzy model of the nonlinear networked control system is established;
所述模糊模型方法所使用的模糊规则如下所示:The fuzzy rules used by the fuzzy model method are as follows:
Rule i:IF z1(t)is Mi1(z)and...and zp(t)is Mip(z),THENRule i: IF z 1 (t) is M i1 (z) and...and z p (t) is M ip (z), THEN
其中,i为模糊规则编号,z(t)=[z1(t),z2(t),...,zp(t)]为包含非线性网络控制系统中状态量信息的前件变量,p为前件变量的个数,Mij为模糊集合,j=1、2、…、p,x(t)为非线性网络控制系统的状态变量,y(t)为测量输出,ω(t)为外部扰动,f(t)为应用传感器检测的故障信号,Ai,Di,Fi,Ci,Ei,Gi为已知合适维数的矩阵;Among them, i is the number of the fuzzy rule, z(t)=[z 1 (t), z 2 (t), ..., z p (t)] is the antecedent containing the state quantity information in the nonlinear network control system variable, p is the number of antecedent variables, M ij is a fuzzy set, j=1, 2, ..., p, x(t) is the state variable of the nonlinear network control system, y(t) is the measurement output, ω (t) is the external disturbance, f(t) is the fault signal detected by the applied sensor, A i , D i , F i , C i , E i , G i are matrices with known appropriate dimensions;
所述建立的非线性网络控制系统的T-S模糊模型如下所示:The T-S fuzzy model of the nonlinear networked control system of described establishment is as follows:
其中,r为模糊规则的数量,wi(z(t))为非线性网络控制系统的隶属度函数;Among them, r is the number of fuzzy rules, w i (z(t)) is the membership function of the nonlinear network control system;
该T-S模糊模型为包括过程故障、传感器故障以及外部扰动的非线性网络控制系统模型,是一种更为广泛的形式。令故障信号其中,fp(t)和fs(t)分别表示过程故障和传感器故障;定义Fi=[Fpi 0|和Gi=[0 Gsi],其中,Fpi和Gsi分别为故障的系数矩阵。当Fi=[Fpi 0],Gi=[0 0]时,建立的T-S模糊模型中的故障信号f(t)代表过程故障;当Fi=[0 0],Gi=[0 Gsi]时,建立的T-S模糊模型中的故障信号f(t)代表传感器故障。本实施例中的故障信号包括传感器故障和过程故障。The TS fuzzy model is a nonlinear network control system model including process faults, sensor faults and external disturbances, which is a more extensive form. fault signal Among them, f p (t) and f s (t) represent process fault and sensor fault respectively; define F i =[F pi 0| and G i =[0 G si ], where F pi and G si are faults coefficient matrix. When F i =[F pi 0], G i =[0 0], the fault signal f(t) in the established TS fuzzy model represents the process fault; when F i =[0 0], G i =[0 G si ], the fault signal f(t) in the established TS fuzzy model represents the sensor fault. The fault signals in this embodiment include sensor faults and process faults.
步骤2:设置事件触发条件,根据事件触发条件确定传感器的测量输出是否应该被传输至滤波器;Step 2: Set the event trigger condition, and determine whether the measurement output of the sensor should be transmitted to the filter according to the event trigger condition;
设置的事件触发条件如下所示:The set event trigger conditions are as follows:
其中,h为传感器的采样间隔,ikh为传感器的采样信号传输时刻,ik+1h为下一采样信号被传输的时刻,Φ>0为需要被设计的加权矩阵,ek(ikh+jh)=y(ikh+jh)-y(ikh)为阈值误差,ε为事件触发参数、y(ikh)为传感器上一时刻采样信号的测量输出,y(ikh+jh)为传感器当前的测量输出;Among them, h is the sampling interval of the sensor, i k h is the transmission moment of the sensor’s sampling signal, ik +1 h is the moment when the next sampling signal is transmitted, Φ>0 is the weighting matrix that needs to be designed, e k (i k h+jh)=y(i k h+jh)-y(i k h) is the threshold error, ε is the event trigger parameter, y(i k h) is the measurement output of the sensor’s sampling signal at the last moment, y( i k h+jh) is the current measurement output of the sensor;
当上一时刻采样信号y(ikh)被传输时,只有当前采样信号满足触发条件时,采样信号将会被传输至滤波器;When the sampling signal y(i k h) was transmitted at the last moment, only when the current sampling signal meets the trigger condition, the sampling signal will be transmitted to the filter;
将事件触发条件应用到故障检测过程中,下一触发时刻不仅与所选择的触发参数有关,而且与上一时刻被传输的采样器的测量输出有关。事件触发机制的使用,可以有效地减少数据传输,节省有限的网络资源。与此同时,事件触发条件在每一个触发时刻只需要计算阈值,即εyT(ikh)Φy(ikh)在时间间隔(ikh,ik+1h]内是一个常数,所以该事件触发机制在节省网络资源的同时,也可以节省计算资源。Applying the event trigger condition to the fault detection process, the next trigger moment is not only related to the selected trigger parameters, but also related to the measured output of the sampler transmitted at the last moment. The use of the event trigger mechanism can effectively reduce data transmission and save limited network resources. At the same time, the event trigger condition only needs to calculate the threshold value at each trigger moment, that is, εy T (i k h)Φy(i k h) is a constant in the time interval (i k h, i k+1 h], Therefore, the event trigger mechanism can save computing resources while saving network resources.
步骤3:考虑到事件触发机制和网络诱导延时的影响,利用T-S模糊模型方法建立模糊故障检测滤波器模型;Step 3: Considering the influence of the event trigger mechanism and network-induced delay, the fuzzy fault detection filter model is established by using the T-S fuzzy model method;
利用T-S模糊模型方法对模糊故障检测滤波器进行建模所使用的模糊规则如下所示:The fuzzy rules used to model the fuzzy fault detection filter using the T-S fuzzy model method are as follows:
Rule j:IF z1(ikh)is Nj1 and...and zp(ikh)is Njp,THENRule j: IF z 1 (i k h)is N j1 and...and z p (i k h)is N jp ,THEN
其中,xf(t)为模糊故障检测滤波器的状态向量,为模糊滤波器的真实输入,zf(t)为残差信号,Afj,Bfj,Cfj和Dfj为待设计的模糊滤波器的增益矩阵,j为模糊规则编号,Nji为模糊集合,z(ikh)=[z1(ikh),z2(ikh),...,zp(ikh)]为模糊故障检测滤波器的前件变量;Among them, x f (t) is the state vector of the fuzzy fault detection filter, is the real input of the fuzzy filter, z f (t) is the residual signal, A fj , B fj , C fj and D fj are the gain matrices of the fuzzy filter to be designed, j is the fuzzy rule number, N ji is the fuzzy Set, z (i k h)=[z 1 (i k h), z 2 (i k h), ..., z p (i k h)] is the antecedent variable of the fuzzy fault detection filter;
建立的模糊故障检测滤波器模型如下所示:The established fuzzy fault detection filter model is as follows:
其中,wj(z(ikh))为故障检测滤波器的隶属度函数;Among them, w j (z(i k h)) is the membership function of the fault detection filter;
故障检测滤波器用来产生残差信号,残差信号在故障检测系统中十分重要,它被用来决定当前的网络控制系统中是否有故障发生。不同于传统的并行分布补偿策略,故障检测滤波器的前件变量z(ikh)与网络控制系统的前件变量z(t)不相等。因此,采用异步前件变量的故障检测滤波器在实际应用中可以提升设计的灵活性,减少设计成本。The fault detection filter is used to generate the residual signal. The residual signal is very important in the fault detection system. It is used to determine whether there is a fault in the current network control system. Different from the traditional parallel distributed compensation strategy, the antecedent variable z(i k h) of the fault detection filter is not equal to the antecedent variable z(t) of the NCS. Therefore, the fault detection filter using asynchronous antecedent variables can improve design flexibility and reduce design cost in practical applications.
步骤4:建立能够提升故障检测系统设计自由度的故障加权系统;Step 4: Establish a fault weighting system that can improve the design freedom of the fault detection system;
所述故障加权系统如下公式所示:The fault weighting system is shown in the following formula:
其中,f(s)为故障信号,W(s)为加权矩阵,为加权后的故障信号;Among them, f(s) is the fault signal, W(s) is the weighting matrix, is the weighted fault signal;
故障信号f(s)和加权矩阵W(s)的状态空间形式如下公式所示:The state space form of fault signal f(s) and weighting matrix W(s) is shown in the following formula:
其中,xw(t)为状态空间向量,fw(t)为加权后的故障信号,Aw,Bw,Cw和Dw为已知常数矩阵;Among them, x w (t) is a state space vector, f w (t) is a weighted fault signal, A w , B w , C w and D w are known constant matrices;
步骤5、根据非线性网络控制系统的T-S模糊模型、事件触发条件、滤波器的T-S模糊模型以及故障加权矩阵建立故障检测系统模型;Step 5, establish a fault detection system model according to the T-S fuzzy model of the nonlinear network control system, the event trigger condition, the T-S fuzzy model of the filter and the fault weighting matrix;
所述建立的故障检测系统模型如下公式所示:The established fault detection system model is shown in the following formula:
其中,为故障检测系统残差误差, in, is the residual error of the fault detection system,
在该故障检测系统中,网络诱导延时、过程故障、传感器故障和外部扰动同时包含在内。在实际应用中,故障和扰动极有可能是同时存在的,而数据在网络传输过程中,网络诱导延时又是不可避免的。In this fault detection system, network-induced delays, process faults, sensor faults, and external disturbances are simultaneously included. In practical applications, faults and disturbances are likely to exist at the same time, and network-induced delays are unavoidable during data transmission over the network.
步骤6、根据故障检测系统模型,选择合适的残差评价函数和检测阈值,通过对比残差评价函数和检测阈值的数值大小,检测非线性网络控制系统故障是否发生;Step 6. Select an appropriate residual evaluation function and detection threshold according to the fault detection system model, and detect whether a nonlinear network control system fault occurs by comparing the numerical values of the residual evaluation function and the detection threshold;
残差评价函数H(zf)和检测阈值Jth如下公式所示:The residual evaluation function H(z f ) and the detection threshold J th are shown in the following formulas:
基于残差评价函数和检测阈值,通过以下关系判断非线性网络控制系统故障是否发生:Based on the residual evaluation function and the detection threshold, the following relationship is used to judge whether a fault occurs in the nonlinear networked control system:
当残差评价函数大于检测阈值时,则非线性网络控制系统发生了故障,故障检测系统报警;反之,非线性网络控制系统正常,不报警。在检测阈值的选定过程中,选择在没有故障的情况下残差评价函数的最大值作为检测阈值,即当系统中仅仅存在扰动时,无论扰动有多大,故障检测系统都不会报警。这样,故障检测系统就可以在存在扰动的环境下,准确检测故障。When the residual evaluation function is greater than the detection threshold, the nonlinear networked control system has a fault, and the fault detection system alarms; otherwise, the nonlinear networked control system is normal and does not alarm. In the selection process of the detection threshold, the maximum value of the residual evaluation function is selected as the detection threshold under the condition of no fault, that is, when there is only disturbance in the system, no matter how big the disturbance is, the fault detection system will not alarm. In this way, the fault detection system can accurately detect faults in a disturbed environment.
步骤7:构造模糊Lyapuonv函数,利用Lyapunov稳定性理论、相关引理和线性矩阵不等式,得到故障检测系统稳定和故障检测滤波器存在的充分条件,并进一步设计故障检测滤波器的参数和事件触发矩阵;Step 7: Construct the fuzzy Lyapuonv function, use the Lyapunov stability theory, correlation lemma and linear matrix inequality to obtain sufficient conditions for the stability of the fault detection system and the existence of the fault detection filter, and further design the parameters of the fault detection filter and the event trigger matrix ;
步骤7.1:构建模糊Lyapunov函数V(t),并将模糊Lyapunov函数V(t)对时间求导,得到故障检测系统稳定且故障检测滤波器存在的充分条件,即1)当时,滤波器残差系统是渐进稳定的;2)在零初始条件下,滤波器残差误差信号满足其中γ>0是H∞衰减水平, Step 7.1: Construct the fuzzy Lyapunov function V(t), and derive the fuzzy Lyapunov function V(t) with respect to time, and obtain the sufficient conditions for the stability of the fault detection system and the existence of the fault detection filter, that is, 1) when When , the filter residual system is asymptotically stable; 2) Under zero initial conditions, the filter residual error signal satisfies where γ>0 is the H ∞ attenuation level,
构建的模糊Lyapunov函数如下:The constructed fuzzy Lyapunov function is as follows:
其中, in,
对于非线性网络控制系统的故障检测问题,假设已知的正实数φk(k=1,...,r)满足在给定常数γ,τ1,τ3,ε和已知滤波器增益矩阵Afj,Bfj,Cfj,Dfj的情况下,故障检测系统是渐进稳定的并且满足H∞性能,当且仅当存在对称矩阵Z1和对称正定矩阵Pk>0,Φ>0,M>0,Rκ>0,使得下列不等式成立,For the fault detection problem of nonlinear networked control system, it is assumed that the known positive real number φ k (k=1,...,r) satisfies Given constants γ, τ 1 , τ 3 , ε and known filter gain matrices A fj , B fj , C fj , D fj , the fault detection system is asymptotically stable and satisfies the H ∞ performance when and Only when there are symmetric matrix Z1 and symmetric positive definite matrix P k > 0, Φ > 0, M > 0, R κ > 0, so that the following inequalities hold,
其中,in,
H1=[I0 0],Ξ23=(3-m)(R2-S2),Ξ25=(m-2)(R3-S3),Ξ33=Q1-M-R1-R2,Ξ34=Q3+(3-m)S2+(m-2)R2,Ξ44=Q2-Q1-R2-R3,Ξ45=(3-m)R3+(m-2)S3-Q3,Ξ55=-Q2-R3,Ξ66=(ε-1)Φ,Ξ77=-γ2I,Ξ88=-γ2I,D1i=[Di Fi],E1i=[Ei Gi], H 1 =[I0 0], Ξ23=(3-m)(R 2 -S 2 ), Ξ 25 =(m-2)(R 3 -S 3 ), Ξ 33 =Q 1 -MR 1 -R 2 , Ξ 34 =Q 3 +(3-m)S 2 +(m-2)R 2 , Ξ 44 =Q 2 -Q 1 -R 2 -R 3 , Ξ 45 =(3-m)R 3 +(m-2)S 3 -Q 3 , Ξ 55 =-Q 2 -R 3 , Ξ 66 =(ε-1)Φ, Ξ 77 =-γ 2 I, Ξ 88 =-γ 2 I, D 1i =[D i F i ], E 1i =[E i G i ],
Ψ22=diag{-R1,-R2,-R3,-εΦ,-I}。 Ψ 22 =diag{-R 1 , -R 2 , -R 3 , -εΦ, -I}.
步骤7.2:设计故障检测滤波器的参数矩阵和事件触发矩阵Φ;Step 7.2: Design the parameter matrix and event trigger matrix Φ of the fault detection filter;
定义 definition
其中, in,
进而定义如下倒转矩阵:Then define the inversion matrix as follows:
用J2=diag{J,I,I,I,I,I,I,I,I,I}前乘(10)式,用后乘(10)式,然后定义Multiply the formula (10) by J 2 =diag{J, I, I, I, I, I, I, I, I, I}, and use Multiply (10) and then define
Xk=U1k, X k =U 1k ,
从而得到thus get
其中,in,
Υ66=(ε-1)Φ,Υ77=Υ88=diag{-γ2I,-γ2I}, Υ 66 = (ε-1)Φ, Y 77 = Y 88 = diag{-γ 2 I,-γ 2 I},
H3=[0 I], H 3 =[0 I],
F22=diag{-R1 -R2 -R3 -εΦ -I}。正实数φk(k=1,...,r)满足τ1,τ3,ε,h,γ为已知常数,Z2为对称矩阵,U1l>0,U1k>0,Xk>0,V>0,Y>0,M>0,Rk>0(k=1,2,3)为对称正定矩阵, F 22 =diag{-R 1 -R 2 -R 3 -εΦ -I}. A positive real number φ k (k=1,...,r) satisfies τ 1 , τ 3 , ε, h, γ are known constants, Z 2 is a symmetric matrix, U 1l >0, U 1k >0, X k >0, V>0, Y>0, M>0, R k > 0 (k=1, 2, 3) is a symmetric positive definite matrix,
由于U(k)>0,根据Schur补引理,Since U(k)>0, according to Schur's complement lemma,
Xk-Y>0 (13)X k -Y>0 (13)
根据(11)式,得到: According to formula (11), get:
同步骤7.1相同,得到:Same as step 7.1, get:
进而得出,如果条件(12)-(14)有可行性解,则故障检测滤波器可以保证故障检测系统是渐进稳定的并且满足H∞性能;Furthermore, if the conditions (12)-(14) have feasible solutions, the fault detection filter can ensure that the fault detection system is asymptotically stable and satisfies the H ∞ performance;
定义从到zf(t)的映射算子为进一步得出 defined from The mapping operator to z f (t) is further draw
其中in
用(15)式中的矩阵来代替(11)中对应的矩阵,得到Substituting the matrix in (15) for the corresponding matrix in (11), we get
因此,H∞故障检测滤波器的参数为目前为止,基于事件触发故障检测滤波器的设计方案已经完成。Therefore, the parameters of the H ∞ fault detection filter are So far, the design scheme of fault detection filter based on event triggering has been completed.
步骤7.3提供了联合设计事件触发矩阵Φ和模糊故障检测滤波器的充分条件,线性矩阵不等式(LMIs)(12)-(14)存在可行性解,则故障检测滤波器参数Afj,Bfj,Cfj,Dfj和事件触发矩阵Φ被获得。通过MATLAB中的LMI工具包,求解线性矩阵不等式,获得故障检测滤波器的参数和事件触发矩阵。Step 7.3 provides sufficient conditions for the joint design of the event trigger matrix Φ and the fuzzy fault detection filter. There are feasible solutions to the linear matrix inequalities (LMIs) (12)-(14), then the fault detection filter parameters A fj , B fj , C fj , D fj and event trigger matrix Φ are obtained. Through the LMI toolkit in MATLAB, the linear matrix inequality is solved to obtain the parameters of the fault detection filter and the event trigger matrix.
本实施例中所采用的非线性网络控制系统的参数设置如下所示:The parameter setting of the nonlinear network control system adopted in this embodiment is as follows:
C1=[1 0],C2=[1 0],E1=0.5,E2=0.5,G1=0.1,G2=0.1。C 1 =[1 0], C 2 =[1 0], E 1 =0.5, E 2 =0.5, G 1 =0.1, G 2 =0.1.
模糊装置的隶属度函数选择为:w2(z(t))=1-w1(z(t));故障加权系统的参数设置为:Aw=0.1,Bw=0.25,Cw=0.2,Dw=0.65;The membership function of the fuzzy device is chosen as: w 2 (z(t))=1-w 1 (z(t)); The parameters of the fault weighting system are set as: A w =0.1, B w =0.25, C w =0.2, D w =0.65;
外部扰动信号ω(t)设置为:The external disturbance signal ω(t) is set as:
同时,故障信号如下所示:Meanwhile, the fault signal looks like this:
令采样间隔h=10ms,τ1=0.002,τ3=0.2,φ1=φ2=0.1,ε=0.1。通过计算,H∞衰减水平的最小值γ=0.6501。利用MATLAB中的LMI工具箱,令γ=1,得到对应的事件触发加权矩阵Φ=3.7474。令初始状态x(0)=[0 0]T,xf(0)=[0 0]T,xw(0)=0,则本实施例中,故障检测系统的残差信号如图2所示,残差评价函数和检测阈值随时间的变化如图3所示,对于该故障检测系统,选择检测阈值仿真结果显示,由此可得,故障在发生后的0.8s被检测到。Let the sampling interval h=10ms, τ 1 =0.002, τ 3 =0.2, φ 1 =φ 2 =0.1, ε=0.1. By calculation, the minimum value of H ∞ attenuation level γ=0.6501. Using the LMI toolbox in MATLAB, let γ=1, and get the corresponding event-triggered weight matrix Φ=3.7474. Let the initial state x(0)=[0 0] T , x f (0)=[0 0] T , x w (0)=0, then in this embodiment, the residual signal of the fault detection system is shown in Figure 2 As shown, the change of the residual evaluation function and detection threshold with time is shown in Figure 3. For this fault detection system, the detection threshold The simulation results show that, It can be seen that the fault was detected 0.8s after it occurred.
本实施例还提供了如图4所示的在有故障和无故障时的残差评价函数随时间的变化图,该图证明了残差信号不仅能够检测到故障是否发生,而且能够区分故障和扰动对系统的影响。本实施例还提供了如图5所示的事件触发策略的释放时刻和释放间隔,从图中可以看出,在仿真时间的40s内,事件触发仅仅触发了179次,相对于时间触发的2000次,触发次数明显减少。当故障发生时,事件触发显著增加,保证了故障检测的可靠性。由此可知,设计的故障检测滤波器不仅能够及时检测故障,而且能够有效地降低有限带宽的使用。This embodiment also provides the time-varying diagram of the residual evaluation function when there is a fault and no fault as shown in Figure 4, which proves that the residual signal can not only detect whether a fault occurs, but also distinguish between faults and faults. The impact of disturbances on the system. This embodiment also provides the release time and release interval of the event trigger strategy as shown in Figure 5. It can be seen from the figure that within 40s of the simulation time, the event trigger is only triggered 179 times, compared to the 2000 times of the time trigger times, the number of triggers is significantly reduced. When a fault occurs, event triggering increases significantly, ensuring the reliability of fault detection. It can be seen that the designed fault detection filter can not only detect faults in time, but also effectively reduce the use of limited bandwidth.
最后应说明的是:以上实施例仅用以说明本发明的技术方案,而非对其限制;尽管参照前述实施例对本发明进行了详细的说明,本领域的普通技术人员应当理解:其依然可以对前述实施例所记载的技术方案进行修改,或者对其中部分或者全部技术特征进行等同替换;而这些修改或者替换,并不使相应技术方案的本质脱离本发明权利要求所限定的范围。Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: it can still be Modifications are made to the technical solutions described in the foregoing embodiments, or equivalent replacements are made to some or all of the technical features; these modifications or replacements do not make the essence of the corresponding technical solutions depart from the scope defined by the claims of the present invention.
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