A double window state observer for detection and isolation of abrupt changes in parameters

Abstract

The paper presents a new method for diagnosis of a process fault which takes the form of an abrupt change in some real parameter of a time-continuous linear system. The abrupt fault in the process real parameter is reflected in step changes in many parameters of the input/output model as well as in step changes in canonical state variables of the system. Detection of these state changes will enable localization of the faulty parameter in the system. For detecting state changes, a special type of exact state observer will be used. The canonical state will be represented by the derivatives of the measured output signal. Hence the exact state observer will play the role of virtual sensors for reconstruction of the derivatives of the output signal. For designing the exact state observer, the model parameters before and after the moment of fault occurrence must be known. To this end, a special identification method with modulating functions will be used. A novel concept presented in this paper concerns the structure of the observer. It will take the form of a double moving window observer which consists of two signal processing windows, each of width T . These windows are coupled to each other with a common edge. The right-hand side edge of the left-side moving window in the interval [t − 2T, t − T ] is connected to the left-hand side edge of the right-side window which operates in the interval [t − T, t]. The double observer uses different measurements of input/output signals in both the windows, and for each current time t simultaneously reconstructs two values of the statethe final value of the state in the left-side window zT (t − T ) and the initial value of the state z0(t − T ) in the right-side window. If the process parameters are constant, the values of both the states on the common joint edge are the same. If an abrupt change (fault) in some parameter at the moment tA = t − T occurs in the system, then step changes in some variables of the canonical state vector will also occur and the difference between the states will be detected. This will enable localization of the faulty parameter in the system.

Limiting Energy Consumption by Decreasing Packets Retransmissions in 5G Network

“…For this reason, the MPTCP with OFN could give a valuable solution in critical network connections. The presented algorithm is able to provide a better energy management and higher transmission security and reliability without generating higher costs in the implementation process [33][34][35].…”

An Adaptive Identification Method Based on the Modulating Functions Technique and Exact State Observers for Modeling and Simulation of a Nonlinear Miso Glass Melting Process

“…MFM related approaches were also used for state observation. Examples of such applications can be found in the works of Byrski and Byrski (2016) or Jouffroy and Reger (2015).…”

“…Instead of this type of the differential state estimators, in the paper the exact state observers will be used. From the theory of exact state integral observers (Byrski and Byrski, 2016) it is known that such observers, for any final observation interval T (assumed in advance), can calculate the actual value of the observed state x k (t 1 ) at the final moment t 1 of the observation window [t 1 − T, t 1 ]. For the simulation and prediction of the state in the next time interval [t 1 , t 1 + T ] and hence for simulation of the unmeasured individual outputs y k (t) of the SISO k models in this interval, one needs to know the exact value of the state x k (t 1 ) at the beginning of this interval.…”

Robust Multiple Sensor Fault–Tolerant Control For Dynamic Non–Linear Systems: Application To The Aerodynamical Twin–Rotor System

“…A number of suitable fault estimation methods, essentially observer-based (Aouaouda et al, 2015;López-Estrada et al, 2015;Byrski and Byrski, 2016), Kalman filter-based (Foo et al, 2013;Pourbabaee et al, * Corresponding author 2016), or parameter identification-based (Cai et al, 2016) are used. In the work of Seron and De Doná (2015), a fault estimation scheme for non-linear systems that can be modeled in a linear parameter varying form is presented.…”