Fault reconstruction for delay systems via least squares and time‐shifted sliding mode observers

Abstract

In this article, we address the problem of fault reconstruction in delayed systems by introducing a time-shifted sliding mode observer (SMO). While time-varying delays of arbitrary duration are considered in the measured output signal, the actuator fault is parametrized as a weighted sum of known regressor functions with unknown coefficients. The prediction scheme utilizes the variation of constants formula to obtain the present time estimate of the unmeasured state. The fault is also identified at present time by means of the continuous-time Least Squares approaches. Ideal sliding mode can be guaranteed in theory, even in the presence of such adverse delays, since there is no chattering in the output estimation error of the SMO. An application to petroleum engineering with numerical simulations is presented to show the effectiveness of the proposed method.

Luenberger‐typecubic observers for state estimation of linear systems

“…For any Q = Q T > 0, there exists a unique solution P = P T > 0 to (9) if the pair (A, C) is observable. 36 If 9holds, (8) will be fulfilled if:…”

“…As a result, in many applications requiring the whole state variable vector, it is inevitable to use an observer to construct the state variable from the measured output. 1 Observers may be used for observer-based feedback control, [4][5][6][7][8] fault detection [9][10][11][12][13][14] and parameter estimation. 1 Unknown or partially known input, 3,10 robust, 7,15 optimal 2,15 and functional 16 observers have been investigated in the literature for linear 16 as well as descriptor, 3,16 delayed, 9 time varying, 2 linear parameter varying 13,14 and nonlinear systems.…”

“…1 Observers may be used for observer-based feedback control, [4][5][6][7][8] fault detection [9][10][11][12][13][14] and parameter estimation. 1 Unknown or partially known input, 3,10 robust, 7,15 optimal 2,15 and functional 16 observers have been investigated in the literature for linear 16 as well as descriptor, 3,16 delayed, 9 time varying, 2 linear parameter varying 13,14 and nonlinear systems. 1,[4][5][6][7][8]11,12 The literature of linear observers for linear systems is very mature.…”

Composite‐observer‐based sampled‐data control for uncertain upper‐triangular nonlinear time‐delay systems and its application

“…The stabilization problem for nonlinear systems is one of the most important issues in the field of control, and many results have been reported. Backstepping technique 1‐4 and sliding‐mode‐control method 5‐10 as important tools, have been extensively studied. In particular, a novel time shift approach for actuator fault reconstruction of systems with arbitrary measurement delays was proposed based on sliding mode observer in Reference 9.…”

Adaptive fault‐tolerant control of an axially moving system with time‐varying constraints

“…However, in the physical system, some unknown interference or, more precisely, unmodeled disturbance can lead to unknown consequences, producing actuator failures and resulting in losing ideal control effect [19][20][21][22][23][24]. In [25], system uncertainties mainly come from inaccuracy of system structure and control input channels.…”