Time-Varying FOPDT system identification with unknown disturbance input

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

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.

It is of importance to design observers for multi‐variable non‐linear systems with unknown parameters and partially driven by unknown inputs. Such a problem arises in systems subject to disturbances or with inaccessible inputs and in many applications such as parameter identification, fault detection and isolation or cryptography. In this study, the problem of fixed‐time observation for non‐linear dynamical systems with unknown parameter and inputs is studied. Conditions on full/partial state and parameters identification are provided by the way of an observation algorithm based on differential geometry theory. Then, a uniform differentiator for estimating simultaneously the states and unknown parameters in fixed time while avoiding observability singularities is designed. An example on topology identification of network systems is described to show the effectiveness of the proposed method.

SummaryThis paper generalizes Kalman filtering with an intermittent unknown input problem to be left invertible discrete‐time stochastic linear systems with zero, one, or more structural delays. Contrary to the state filtering–based system inversion where the unknown input vector is reconstructed with a time delay that is equal to the structural delay of the plant, we propose an optimal state filtering by reconstructing some linear combinations of the unknown input vector with a time delay less than the structural delay. Designed under a sequential unknown input decoupling constraint, which has never been previously studied in the literature, all presented filters are very computationally efficient. The proposed state filtering is used to solve the autonomous distributed state filtering problem in large‐scale networked control systems when the unknown input vector represents interactions between subsystems and when each subsystem receives intermittent information about the interaction from unreliable networks. The stochastic stability conditions of the extended intermittent unknown input Kalman filter are established when the arrival binary sequence of packet dropouts follows a random Bernoulli process.

Joint unknown input observer for descriptor system based on interval observer

An observer is designed for strongly detectable systems with unbounded unknown inputs. The design scheme is based on three steps. First, the system is extended taking the unknown inputs (and possibly some of their derivatives) as new states. Then, using a high-order sliding mode differentiator (HOSMD), a new output of the system is generated in order to fulfill the Hautus condition. Finally, the system is decomposed into two subsystem, the first one being unaffected directly by the unknown inputs, and the second subsystem being obtained directly from the system output. Thus, a Luenberger observer is designed for the first subsystem. This procedure allows one to estimate the state and the unknown inputs using the least number of differentiations possible. Some simulations are given to show the effectiveness of the proposed observer.

In this paper, a differential neural network (DNN) implemented as a robust observer estimates the dynamics of perturbed uncertain nonlinear systems affected by exogenous unknown inputs. In the first stage, the identification error converges into a neighborhood around the origin. Then, the second-order sliding mode supertwisting algorithm implemented as a robust exact differentiator reconstructed the unknown inputs. The approach proposed in this paper can be applied in the case of full access to the state vector (identification problem) and in the case of partial access to the state vector (estimation problem). In the second case, the nonlinear system under study must have well-defined full relative degree with respect to the unknown input. Numerical examples showed the effectiveness of the proposed algorithm. The first example tested the DNN working as an identifier into a mathematical model describing the dynamics of a spatial minisatellite. The second example (with a DNN implemented as an observer) tested the methodology of this paper over a single link flexible robot manipulator represented in a canonical (Brunovsky) form. In both examples, the mathematical models served as data generators in the testing of the neural networks. Even when not exact mathematical description of both models was used in the input estimation, the accuracy obtained with the DNN is comparable with the case of applying a high-order differentiator with complete knowledge of the plant.

This paper presents an online self-tuning Smith Predictor for the First Order Plus Dead Time Model (FOPDT). It can tune time delay through oscillated input and output. Realtime phase difference detection is used to obtain the phase difference between the input and the output. An online tuner is used to minimize the phase difference. Once the phase difference is minimized, the exact time delay is completely compensated. Our method is suitable for both systems with constant time delay or variant time delay.

Robust fault detection for uncertain switched systems

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.

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.

In this paper, we focus on the problem of the robust fault diagnosis of four tank hydraulic system in the presence of both unknown input disturbance and sensor noise. Fault detection can be investigated by generating residuals. These residuals can be generated using different methods. One of the finest methods for generating residuals is to use unknown input observers (UIO). Faults can be detected and isolated simply with the help of the generated residuals, where the. Simulation results on a hydraulic system demonstrate that the effectiveness of the proposed approach.

Unknown input based observer synthesis for an interval type-2 polynomial fuzzy system with time delays and uncertainties

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.

Optimal joint estimation and identification theorem to linear Gaussian system with unknown inputs