Actuators fault detection using unknown input observer in hydraulic system

Early and accurate fault detection and diagnosis (FDD) minimises downtime, increases the safety and reliability of plant operation, and reduces manufacturing costs. This paper presents a robust FDD strategy for a nonlinear system using a bank of unknown input observers (UIO). The approach is based on structure residual generation that provides not only decoupling of faults from model uncertainties and unknown input disturbance but also decoupling the effect of a fault from the effects of other faults. The generated residual was evaluated through the statistical threshold to avoid fault missing or false alarm. The performance of the robust FDD scheme was assessed by some sensor fault scenarios created in a continuous stirred-tank reactor (CSTR). The simulation result showed the effectiveness of the proposed approach.

Unknown input observers (UIO) are well-known in the literature for linear systems, in particular in the fault detection and identification area. Their particularity rests in the possibility of obtaining an exact asymptotic estimation of the state or a functional of it despite of completely unknown input disturbances. However, conditions for this to be possible are very restrictive, what reduces considerably the applicability and usefulness of UIOs. In the paper a method to reduce the severity of such conditions is proposed. The cause for the highly restrictive conditions for UIOs lies in the fact that the unknown input is assumed to be completely arbitrary, i.e. no knowledge about it is assumed. However, in practice some information about them is available, and one could use it to design an observer that is robust to such kinds of inputs. We propose the use of a linear model of the unknown inputs and an observer robust to such kinds of inputs is designed. This reduces the necessary conditions for its existence. It is intuitively clear that the more information on the disturbances is known the less restrictive the conditions for the existence of a robust observer are, as is shown in the paper.

This study investigates the problem of robust fault diagnosis for nonlinear systems subjected to actuator faults and unknown input disturbances. A novel adaptive fast smooth super-twisting observer based on the super-twisting and adaptive dual-layer algorithms is presented, and a robust fault-diagnosis scheme based on an adaptive threshold is proposed to take the estimation error generated by the observer as the residual. In the adaptive fast smooth super-twisting observer, additional fractional powers less than 1 and linear terms are added to improve the smoothness and rapidity of the observer. The finite-time stability of the adaptive fast smooth super-twisting observer is then analyzed based on the Moreno–Lyapunov function algorithm, and rigorous proof confirms that the estimation-error dynamic is robust to unknown input disturbances and can converge to a region of zero in finite time. Finally, simulations of the rigid spacecraft attitude kinematics and dynamics are used to validate the effectiveness of the developed adaptive fast smooth super-twisting observer and the designed robust fault-diagnosis scheme.

The H∞ and sliding mode observers are important in integer-order dynamic systems. However, these observers are not well explored in the field of fractional-order dynamic systems. In this paper, the H∞ filter and the fractional-order sliding mode unknown input observer are developed to estimate state of the linear time-invariant fractional-order dynamic systems with consideration of proper initial memory effect. As the first result, the fractional-order H∞ filter is introduced, and it is shown that the gain from the noise to the estimation error is bounded in the sense of the H∞ norm. Based on the extended bounded real lemma, the H∞ filter design is formulated in a linear matrix inequality form, and it will be seen that numerical methods to solve convex optimization problems are feasible in fractional-order systems (FOSs). As the second result of this paper, not only state but also unknown input disturbance are estimated by fractional-order sliding-mode unknown input observer, simultaneously. In this paper, it is shown that the design and stability analysis of the two estimation techniques are not related with the initial history. Through two numerical examples, the performance of the fractional-order H∞ filter and the fractional-order sliding-mode observer is illustrated with consideration of the initialization functions.

Fault detection in a three-tank hydraulic system using unknown input observer and extended Kalman filter

Robust fault detection for uncertain switched systems

In this paper, we consider the problem of designing a special type of observer to estimate the state and unknown input disturbance for linear time-invariant positive systems. Although positive observers have been designed for positive systems, they are unable to estimate the states when unknown inputs or disturbances are present in the systems. To realize simultaneous estimation of states and unknown inputs, we first design positive unknown input observers (PUIO) for positive linear systems, which is the main contribution of this paper. Then, we provide a procedure to estimate the unknown disturbance. The PUIO design can be performed with the aid of a positive stabilization scheme via LMI. A critical step in the design process is the requirement of imposing a condition on positivity of the generalized inverse of a certain design matrix. We show that this can easily be accomplished with the aid of a unique result, which makes the design of PUIO possible. An alternative LMI with less restrictive assumption is also included to design PUIO. Finally, theoretical results are supported by numerical examples.

The actuator fault detection for an unmanned aerial vehicle( UAV) longitudinal system with unknown atmospheric disturbances and stochastic noise was studied. Based on introducing a nonlinear longitudinal model of the fixed UAV,a residual generation was designed by employing a nonlinear unknown input observer( NUIO) which is based on cubature Kalman filter( CKF). The unknown input observer structure was constructed to decouple the unknown disturbances from residual. At the same time,the CKF was applied to calculate the gain matrix to achieve the requirement of robustness to noise. Finally,the occurrence of fault can be detected based on chi-square test about the residual sequence. The simulation results show that the proposed method can decouple the unknown disturbances from residual effectively and achieve the fast and accurate actuator fault detection.

Bond-Graph-Based Multivariable non linear UlO-type estimation

The distribution system's nonlinear loads cause low total harmonic distortion (THD), low distortion power factor, and localized communication interference, among other poor power quality metrics. Shunt active power filter (SAPF) capacity to function depends on the controller's ability to follow the reference signal. To manage larger systems with several inputs and outputs, it would be challenging task to design PID controllers, because excessive controller gains would need to be tuned. Also, every control loop would operate independently of one another, as if there were no interactions between the two loops. This paper proffers Model prediction control for Shunt active power filter (SAPF), which can manage systems with several inputs and outputs that may interact with one another. Luenberger observer (LO) and Proportional Integral observer (PIO) fail to estimates the actual states of SAPF to SAPF, as shown even in the presence of three unknown disturbances, i.e step, triangular and noise type. The proposed unknown input observer (UIO) in the presence of three unknown disturbances perfectly tracks the reference signal. Apart from state estimation, the proposed observer also estimates all the unknown disturbances, when compared to PIO. The results have been simulated in MATLAB environment.

A combined data‐driven and observer‐design methodology for fault detection and isolation (FDI) in hybrid process systems with switching operating modes is proposed. The main contribution is to construct a unified framework for FDI by integrating Gaussian mixture models (GMM), subspace model identification (SMI), and results from unknown input observer (UIO) theory. Initially, a GMM is built to identify and describe the multimodality of hybrid systems using the recorded input/output process data. A state‐space model is then obtained for each specific operating mode based on SMI if the system matrices are unknown. An UIO is designed to estimate the system states robustly, based on which the fault detection is laid out through a multivariate analysis of the residuals. Finally, by designing a set of unknown input matrices for specific fault scenarios, fault isolation is performed through the disturbance‐decoupling principle from the UIO theory. A significant benefit of the developed framework is to overcome some of the limitations associated with individual model‐based and data‐based approaches in dealing with the problem of FDI in hybrid systems. Finally, the validity and effectiveness of the proposed monitoring framework are demonstrated using a numerical example, a simulated continuous stirred tank heater process, and the Tennessee Eastman benchmark process. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2805–2814, 2014

In this paper, two controllers with a compound disturbance observer are proposed for a two-wheeled inverted robot (TWIR) with model uncertainty and unknown input disturbance. First, an equivalent linear model of the TWIR with uncertainty and input disturbance is proposed using the Taylor series expansion for the nonlinear model of the TWIR at an equilibrium point, in which the nonlinear part of the Taylor series and the model uncertainty are combined with unknown input disturbance as compound input disturbance. Then, the compound input disturbance is estimated by using the Newton method and reference model. As the estimated compound disturbance is used to compensate for the compound disturbance, the equivalent linear system becomes closely definite without compound input disturbance. Finally, two controllers are proposed using the equivalent linear system. Stability analysis of the proposed control methods is also given. To illustrate the proposed methods, some simulations for the TWIR are performed and compared with the existing methods. The main contribution of this work includes the following: (i) simple controllers based on compound input disturbance observer for trajectory tracking and balancing of TWIRs with unknown input disturbance and model uncertainty are proposed; (ii) the stability of proposed closed-loop control systems is proved; (iii) our proposed methods are simulated and compared with the existing methods.

The Time-Varying First Order Plus Dead Time (TV-FOPDT) model is an extension of the conventional FOPDT by allowing the system parameters, which are primarily defined on the transfer function description, i.e., the DC-gain, time constant and time delay, to be time dependent. The TV-FOPDT identification problem turns to estimate these time-varying parameters based on measured control input and system output. This work considers a TV-FOPDT identification problem in the presence of an unknown disturbance input. By regarding the unknown input as one extra system parameter, the considered identification problem is formulated as a Stochastic Mixed Integral Programming (SMIP) problem after discretizing the original problem. The sliding window technique with forgetting factor is employed to cope with time resolution issue, and the Least Mean Square (LMS) method is used to obtain the optimal solution of each individual optimization problem based on different time delay assumptions. The proposed method is firstly tested through a number of numerical examples, and then it is applied to estimate a TV-FOPDT model of the superheat dynamic of a supermarket refrigeration system.

In this paper, interval observer‐based consensus control is developed for multi‐agent systems with unknown input signals, sensor noises, and stealthy attack signals. Compared with the conventional robust observer, the interval observer has more relaxed preconditions for the systems, so the interval observer is more extensive. First, design an interval observer for each subsystem and linearly transform into a form that is easy to obtain the coefficient matrices of the interval observer. Then, based on the upper bound estimation of the observer, design a consensus control protocol, and the technique is used to suppress the unknown input signals. Finally, a numerical simulation example is presented to illustrate the feasibility and correctness of the developed method.

An approach for nonlinear unknown input observer (NUIO) design is proposed for a class of nonlinear systems representable by a Takagi—Sugeno (TS) fuzzy system. The proposed NUIO design for TS fuzzy systems is carried out for two cases: (1) the premise variables do not depend on the unmeasured state variables; and (2) the premise variables depend on the unmeasured state variables. Sufficient conditions for the existence of NUIOs are derived, and a linear matrix inequality (LMI)-based design strategy is presented for NUIO design purposes. The proposed NUIO design approach is then applied to solve actuator fault detection and isolation problems for nonlinear systems described by TS fuzzy systems. To this end, a system structure with two groups of inputs where one group of inputs is treated as unknown inputs is developed. Based on the system structure, a bank of NUIOs are then designed using the developed NUIO design approach in order to investigate the following fault diagnosis problems. (1) How can the NUIOs be used for detecting faults? (2) Under what conditions is it possible to isolate single and/or multiple faults? (3) What is the maximum number of faults that can be isolated simultaneously? (4) How can multiple fault isolation be achieved? In this article we present a NUIO-based fault-detection scheme for problem (1), give sufficient conditions for problem (2), determine the maximum number of faults that can be isolated for problem (3), and propose a fault-diagnosis scheme using a bank of NUIOs to solve problem (4). As an illustrative example, Lorenz’s chaotic system with multi-inputs is chosen to show the effect of the designed NUIOs and the proposed fault detection and isolation scheme. Simulation results show that accurate state estimation is achieved and actuator faults can be detected and isolated successfully.