Due to the probability of the packet dropout in the networked control systems, a balanced reduced-order fault detection filter is proposed. In this paper, we first analyze the packet dropout effects in the networked control systems. Then, in order to obtain a robust fault detector for the packet dropout, we use the balanced structure to construct a reduced-order model for residual dynamics. Simulation results are provided to testify the proposed method.

The background of the research is the increasing application of the wireless networks as medium in complex large-scale systems. In networked control systems (NCS), the control loops are close via communication networks. Hence, compared with traditional control systems, the NCS have many advantages, such as fewer system wiring, lower cost of maintenance, improvement of system flexibility, and application in the field of aerospace. So it has drawn more and more consideration in recent years. However, due to the insertion of the network, there appeared many challenging problems: the limited brand width of networked channel maybe cause impossibility of all information transmitted at the same time; due to the uncertainty, the information may be delayed or even dropped; the communication method of the networked system is the digital communication, so there may exist quantization error.

Since some packets have the probability of dropout in the channel, the detection of the faults may cause the false alarm for the NCS. Much work has been done to deal with this problem. In order to deal with the false alarm of the fault detection, the structure of standard model-based residual generator is suggested in [

For the fault detection system, the big Hankel singular values are more robust to the data packet dropout compared with the small ones; that is, the data packet dropout is easier to disturb the small Hankel singular values than the big ones. So we can improve the robust performance of the fault detection by the reduce-order model, that is, removing the small Hankel singular values. In this paper, in order to minimize the influence of the data packet dropout on the fault detection, we first analyze the packet dropout effects in the NCS. Then, based on the balanced structure, we construct a reduced-order fault detection filter and obtain the residual dynamics, which minimizes the ratio of maximum-to-minimum eigenvalues of the Gramian matrices. It has low parameter sensitivity to the data packet dropout and the measurement noise and improves the robust to the false alarm. At last, the simulation results are provided to corroborate the analytical theory.

Figure

The structure of networked control systems.

The networks are between the sensor and the controller, and they have the same sample time and are simultaneous. Since the communication is hold in the network environment, we assume that there exists packets loss in the communication link and the signal where the central catch is given as follow:

In this paper, we assume that the faults supervision stations and the central controller station are located together. Since the residual generator catches the input signal directly, in order to get the deviation, we must obtain the measurement output through the network. Hence, if there are some packets dropout which cause the network jam in the channel, some measurement output signal may be lost between the sensors and the supervision station. In order to obtain a robust residual generator and make the fault detection filter less sensitive to the packets dropout, we can remove the small Hankel singular values. So we design a reduced-order residual generator based on the balanced realization, and it is described as follow:

If we define that

We use the threshold selector to evaluate the residual generator (

In this section, based on balanced reduced-order model, we aim to find the optimal system parameters for the fault detection filter. Because it can minimize the effects of the measurement noises

Given the polynomial as

Define the matrix

Then we define

Now, the balanced realization system

The controllability Gramian

From (

In this section, we analyze the proposed algorithm in MATLAB. The first case of the NCS is the fourth-order system, and the matrices are given as

Since the dropout of the packets is random, we use two-state Markov jump system to describe the stochastic process [

By using (

The residual generators of the initial system given by (

Residual signal of the initial system given by (

Residual signal of the reduced-order system given by (

When the fault signal

Residual signal of the initial system given by (

Residual signal of the reduced-order system given by (

The second case system is the fifth-order system, and the matrices of the NCS are given as follows:

When the measurement noises

Residual signal of the initial system given by (

Residual signal of the reduced-order system given by (

Residual signal of the reduced-order system given by (

Residual signal of the initial system given by (

Residual signal of the reduced-order system given by (

Residual signal of the reduced-order system given by (

The packets dropout is inevitable in the NCS; we analyze the effects of this phenomenon for the fault detection systems. Since the balanced reduced-order model minimizes the ratio of maximum-to-minimum eigenvalues of the Gramian matrices and has low parameter sensitivity to the data packet dropout and the measurement noise, we propose a new structure of the fault detection for the NCS based on the balanced realization, which lead this structure to have a good packets dropout and measurement noise rejection. Simulation results show that the proposed method has a good performance for the NCS. For future work, the intelligent design could be further included in the scheme to deal with the case of system learning. For future work, the intelligent design [

The author declares that there is no conflict of interests.

This work was supported in part by the Key Project of Natural Science Foundation of Zhejiang Province under Grant no. LZ14F010002 and in part by the Public Welfare Project of Zhejiang Province under Grants nos. 2012C21048 and 2012C23040.