Zero-assignment and complex coefficient gain design of generalized proportional-integral observer for robust fault detection

A generalized proportional‐integral observer for fault detection: An approximate input disturbance decoupling approach

“…Lemma 1. . 12 For an observable discrete-time LTI system (1) subject to periodic input disturbance at frequencies {𝜔 d1 , 𝜔 d2 … 𝜔 dn } with a corresponding ADD-GPIO (3), if the gain matrix K takes the following form:…”

“…It facilitates the quantitative analysis of the degree of difference between the two transfer functions at the given frequencies. Therefore, in this article, (12) is chosen as the objective function to optimize the degree of difference between G d (z) and G f (z).…”

“…Since the precursory work of Isermann, 1 Ye et al 2 model‐based fault detection (FD) has been a promising research area for the last few decades 3 . In particular, observer‐based fault detection methods have been intensively studied 4‐6 and numerous fault detection methods based on classical observers have been proposed till now, such as Luenberger observer, 7 Kalman filter, 8 Unknown Input Observer (UIO), 9 sliding‐mode observer, 10 proportional‐integral observer, 11 and recently, the generalized proportional‐integral observer (GPIO) 12,13 . The basic idea is to construct an appropriate observer to generate a favourite fault‐sensitive residual signal, so that a fault can be relatively easily detected by evaluating the residual's features, such as change patterns and magnitudes.…”

“…This allows us to target different treatments of perturbations and faults for the same transfer function matrix, attenuating the periodic disturbance through zero configuration and improving sensitivity to faults through pole optimization. A complex coefficient vector 12 was proposed to decouple the fault detection residual from the periodic disturbance. However, the introduction of the complex coefficient vector increased the design complexity of the system.…”

“…3 In particular, observer-based fault detection methods have been intensively studied 4-6 and numerous fault detection methods based on classical observers have been proposed till now, such as Luenberger observer, 7 Kalman filter, 8 Unknown Input Observer (UIO), 9 sliding-mode observer, 10 proportional-integral observer, 11 and recently, the generalized proportional-integral observer (GPIO). 12,13 The basic idea is to construct an appropriate observer to generate a favourite fault-sensitive residual signal, so that a fault can be relatively easily detected by evaluating the residual's features, such as change patterns and magnitudes. However, many automation systems in industries are subject to semi-stationary periodic disturbances, such as repetitive tasks, 14 periodic load changes, 15 vibrations, 16 the interference caused by the alternating current power supply or its harmonics.…”