Time-varying System Parameters Research Articles

Recursive formulation of the WKB solution for linear time-varying dynamic systems

This work proposes a new calculation algorithm of the Wentzel–Kramers–Brillouin (WKB) solution for slow linear time-varying (LTV) systems based on the recursive formulation. For a linear dynamic system with time-varying (TV) mass, damping or stiffness, the recursive relations in real function form among the components of the WKB solution are obtained. The integral terms within the sampling intervals that cannot be solved analytically are approximated by simple algebraic calculations with high precision. Thus, the conventional expression of the WKB solution involving complex numerical integral terms is reduced to an analytical recursive formulation. An explicit function relationship between the TV system parameters and the dynamic response can be obtained when the external excitation is given. In the premise of similar accuracy, the recursive formulation has much higher efficiency than the conventional calculation process, which is verified by applying the proposed method to a particular LTV dynamic system.

Extracting Inherent Model Structures and Identifying Parameters of Time-Varying Systems Using Local Linear Neuro-Fuzzy Networks

The main challenges in identifying time-varying systems are to extract the inherent model structure and formulate a generic approach for various time-varying processes. In this article, a local linear neuro-fuzzy networks based approach is proposed for the first time to tackle this issue. The basic idea is to utilize the superior approximation capability of the fuzzy neural networks to expand the unknown time-varying parameters so that various nonlinear and discontinuous processes can be captured. In addition, the local linear model tree optimization algorithm is incorporated in our approach to optimize the network architecture. On one hand, the least number of neurons corresponding to the time-varying parameters can be automatically determined, thus avoiding the superfluous bases and the troublesome overfitting problem; on the other hand, the optimized distribution of the neurons could significantly increase the interpretability of the results, thus contributing to locating the domains where the parameters exhibit strong nonlinearity or change sharply. Moreover, we demonstrate that our approach could simultaneously extract the parsimonious model structure while identifying the time-varying parameters, without adding additional procedures or increasing computation burden. Considering the generality and the unique merits, our proposed approach could significantly advance the applications of artificial neural network techniques in system identification.

Modal assurance distribution of multivariate signals for modal identification of time-varying dynamic systems

Most time–frequency representations (TFRs) and signal analysis methods used for the identification of dynamic systems through non-parametric techniques are based on univariate signals. However, combining the information obtained from different sensors to investigate the overall behavior of the monitored structure is not trivial, as different recordings may show different features. Moreover, methods based upon the analysis of the energy density distribution in the time–frequency plane generally suffer from problems related to crossing and closely-spaced modes. In this paper, a new time–frequency representation of multivariate and multicomponent signals based on the modal assurance criterion (MAC) is presented. The analysis of the modal assurance distribution (MAD) thus obtained enables the extraction of decoupled modal responses, which can then be used to evaluate the instantaneous modal parameters of time-varying systems. To this end, a decomposition algorithm based on modal assurance (DAMA) is proposed, employing the watershed segmentation of the MAD. The results for two case studies, a finite element model and a full-scale experimental benchmark, are shown, considering both the original MAD and two enhanced versions, here proposed to improve its readability. The results are compared with those obtained from modern and widely used techniques, showing the promising efficacy of the proposed method for signals with time-varying frequency and amplitude, even in the presence of narrow-band disturbances and white noise, as well as with vanishing modes.

Stabilization and tracking control of a time-variant linear hyperbolic PIDE using backstepping

We extend previous results regarding infinite-dimensional backstepping-based controller design for linear hyperbolic partial (integro-)differential equations (P(I)DEs), and derive a state-feedback controller for a PIDE system with time-varying system parameters. The system state converges to zero in the ∞-norm, in a finite time corresponding to the propagation time between the boundaries. Secondly, the controller is slightly modified to solve an output tracking problem. The derived controllers are demonstrated in simulations. The derived state-feedback controllers can also be combined with state observers into output-feedback controllers.

T-Source Inverter-Based Sensorless Speed Control for Permanent Magnet Synchronous Motor

Abstract Permanent magnet synchronous motors (PMSM) are used commonly in numerous industrial applications, for instance, in mechatronics, vacuum pumps, energy storage flywheels, automotive, centrifugal compressors, and robotics. Nowadays, the sensorless speed control of PMSM is getting more attention, and several studies are progressing because of its low cost and reliable features. Normally, the speed control methods in PMSM are achieved with the help of sensors for position or speed estimation and control. But, these sensors are easily prone to breakage. Also, the flexibility towards parameter variations is poor in the conventional speed control methods. So, a sensorless T-source inverter-based PMSM drive that integrates the Proportional Integral (PI) controller with an adaptive mechanism to cope with the time-varying system parameters is proposed in this article. A sensorless module, namely, a model reference adaptive system (MRAS), is employed to estimate the rotor position of PMSM based on its performance characteristics Simulation results are illustrated to investigate the performance of the proposed method with different speeds under no load and loaded conditions. Moreover, the proposed approach not only minimizes the cost and size of the motor but also maximizes the reliability and accuracy.

Finite-time synchronization of uncertain complex dynamic networks with time-varying delay

This study investigates the finite-time synchronization of uncertain nonlinear complex dynamic networks with time-varying delay. For a class of complex network models with time-varying delay and uncertain system parameters, the time delay changes infrequently, uncertain terms are unknown but bounded, and the matching conditions are satisfied. The coupling relationship between nodes is a nonlinear function with time delay, and the function satisfies the Lipschitz condition. A new criterion for the finite-time synchronization of a class of complex dynamical networks with variable delay is obtained, and the upper bound of the time for the system to achieve synchronization is presented by constructing a suitable Lyapunov–Krasovskii function, designing a nonlinear controller, and combining analysis techniques, such as matrix inequality. Finally, the validity of finite-time synchronization is verified through computer simulation.

On the combination of kernel principal component analysis and neural networks for process indirect control

ABSTRACT A new adaptive kernel principal component analysis (KPCA) for non-linear discrete system control is proposed. The proposed approach can be treated as a new proposition for data pre-processing techniques. Indeed, the input vector of neural network controller is pre-processed by the KPCA method. Then, the obtained reduced neural network controller is applied in the indirect adaptive control. The influence of the input data pre-processing on the accuracy of neural network controller results is discussed by using numerical examples of the cases of time-varying parameters of single-input single-output non-linear discrete system and multi-input multi-output system. It is concluded that, using the KPCA method, a significant reduction in the control error and the identification error is obtained. The lowest mean squared error and mean absolute error are shown that the KPCA neural network with the sigmoid kernel function is the best.

Adaptive Backstepping Based Fault-tolerant Control for High-speed Trains with Actuator Faults

In this paper, the fault-tolerant control problem is addressed for high-speed trains with unknown time-varying system parameters, traction system actuator faults and disturbances. To represent the unknown time-varying system parameters in mathematical form, a new piecewise time-varying indicator including commonly used 0–1 case, is employed, which results in a piecewise time-varying nonlinear model with some unknown parameters and piecewise disturbances. For the healthy system with the time-varying indicator in the unknown forms and having known switching time instants, an adaptive backstepping controller is proposed to deal with the unknown system parameters and disturbances and achieve the position tracking. Further, the adaptive backstepping based fault-tolerant controller with adaptive laws is developed to guarantee the system states boundedness and the position tracking, in the presence of unknown actuator faults. Based on Lyapunov function, the stability of the closed-loop system is proved. Simulation studies on CRH2 (China Railway High-speed Train II) verify the performance of the proposed fault-tolerant control scheme.

Sliding Mode Variable Structure Control for Surface Permanent Magnet Synchronous Motors Based on a Fuzzy Exponential Reaching Law

In order to handle heavy chattering and negative robustness caused by time‐varying system parameters and external load disturbance of the speed control system, thereby having high‐precision control over surface permanent magnetic synchronous machine (PMSM), this paper combines the advantages of sliding mode variable structure control (SMVSC) and fuzzy control. Firstly, a fuzzy sliding mode variable structure control (FUZZY‐SMVSC) method is proposed, based on the vector control foundation framework of surface PMSM (SPMSM). It effectively reduces chattering while keeping sliding mode, according to the fuzzy rules formulated based on fuzzy control principle. Secondly, integral sliding mode surface is used and integration element is introduced into fuzzy control input, thereby reducing the static error of the conventional fuzzy control. Simulation and experimental results show that the proposed fuzzy sliding mode variable structure control reduces chattering by fuzzy reasoning and softening. Also, it still can maintain the strong robustness of sliding mode variable structure and ensures the fine dynamics of the system, against time‐varying system parameters and external load disturbance.

A Bayesian estimator of operational modal parameters for linear time-varying mechanical systems based on functional series vector TAR model

Operational modal analysis of time-varying mechanical dynamic systems is a useful but challenging task. This paper presents a Bayesian estimator for modal parameters of linear time-varying mechanical dynamic systems in the framework of the functional-series vector time-dependent autoregressive (FS-VTAR) model with output-only measurements. The proposed Bayesian estimator cannot only give the modal parameters with the estimation of mean value, but also supplies the uncertainty with the creditable interval estimation. A series of numerical examples have illustrated the advantages of the proposed Bayesian estimator against the overestimate, the better performance for the short data and the capability of supplying uncertainty of estimates. An experimental example validates the proposed estimator further.

On the Asymptotic Stability of Nonlinear Time-Varying Switched Systems

This paper considers a class of nonlinear systems with switching from one nonstationary Lienard-type equation to another. For such a system, the asymptotic stability of a given equilibrium is studied using the method of Lyapunov functions and theory of differential inequalities. The switching law constraints that guarantee the desired property of the system are established. As shown below, these constraints generally depend on the rate of change of time-varying system parameters. Some illustrative examples are also given.

Iterative learning control for image feature extraction with multiple-image blends

In this paper, a novel method of image extraction is proposed. Firstly, the image information is embedded into the parameters of the chaotic system, and then the image is overlapped and embedded to complete the image hiding. This process is equivalent to a dynamic system with unknown time-varying parameters. Secondly, the D-type iterative learning control algorithm is used to extract the information hidden in the image, because iterative learning can be used to estimate the time-varying parameter system completely in the time interval. Finally, the numerical simulation shows that the algorithm can effectively extract the hidden information under various attacks.

Adaptive Actuator Compensation of Position Tracking for High-Speed Trains With Disturbances

In this paper, the adaptive fault compensation problem is investigated for high-speed trains in the presence of time-varying system parameters, disturbances, and actuator failures. To deal with the time-varying system parameters, a new time-varying indicator function instead of commonly used 0–1 function, is proposed to model the train dynamics as a piecewise model with unparameterizable time-varying disturbances, which can cover more time variations and help parametrization for adaptation. A backstepping adaptive controller is designed for the healthy system with unknown piecewise model parameters and known piecewise bounds on disturbances. For both the parameterizable and unparameterizable failures, the backstepping adaptive failure compensation with the adaptive laws are derived to achieve the position tracking under the known bound disturbances. The adaptive failure compensation for unknown bounds on disturbances is also discussed under the parameterizable failure. Through introducing the nonlinear damping in the proposed controller, the failure compensation controller is proposed for the model with unparameterizable system parameters to achieve an arbitrary degree of position tracking accuracy. The stability of the corresponding closed-loop system and asymptotic state tracking are proved via Lyapunov direct method, and validated using a high-speed train model.

A Dual Particle Filter-Based Fault Diagnosis Scheme for Nonlinear Systems

In this paper, a dual estimation methodology is developed for both time-varying parameters and states of a nonlinear stochastic system based on the particle filtering scheme. Our developed methodology is based on a concurrent implementation of state and parameter estimation filters as opposed to using a single filter to simultaneously estimate the augmented states and parameters. The convergence and stability properties of our proposed dual estimation strategy are shown formally to be guaranteed under certain conditions. The advantage of our developed dual estimation method is justified by handling simultaneously and efficiently both the state and time-varying parameters of a nonlinear system. This is accomplished in the context of a health monitoring scheme that employs a unified approach to fault detection (FD), isolation, and identification in a single framework. The performance capabilities of our proposed FD methodology is demonstrated and evaluated by its application to a gas turbine engine through providing state and parameter estimation objectives under simultaneous and concurrent component fault scenarios. Extensive simulation results are provided to substantiate and justify the superiority of our proposed FD methodology when compared with another well-known alternative diagnostic technique that is available in the literature.

Generalized Proportional Integral Observer-Based Robust Finite Control Set Predictive Current Control for Induction Motor Systems with Time-Varying Disturbances

During the past few years, finite control set predictive current control (PCC) method has attracted more and more attention in research and industry applications. However, PCC method could be improved by considering two points. First, the current reference used in the cost function of PCC control scheme is usually produced by a proportional and integration speed controller. Confront with load torque and time-varying system parameters, it is a better solution to design a disturbance estimation based feed-forward compensated controller. In this way, the current reference could be generated faster and more accurate. Second, the PCC method is model-based method which means the accuracy of the model parameters are essential. In real system, time-varying parameters existed almost always. This paper investigates a generalized proportional integral observer based PCC approach for dealing with load torque disturbance, time-varying parameter uncertainties. The effectiveness of the proposed method has also been confirmed by simulation and a lab-constructed experimental prototype.

Robust backstepping control of double-rod cylinder for motion synchronization of mold oscillator

High-performance synchronization control of two double-rod cylinders used to oscillate the mold of a continuous casting machine is considered in this article. Friction between strand shell and mold plays an important role to achieve high-precision control of mold oscillator. A new friction model is proposed for exact system modeling and is proved useful. Using a force-distribution method to consider the coupling effect between two cylinders, mathematical models of each cylinder are presented and a simple robust backstepping control strategy is proposed, which can reduce the influences of time-varying system parameters and unmodeled uncertainties. The transient performance and stability of the proposed controller are rigorously proved. Simulation and experimental results show that proposed synchronization control method can achieve good performance for given tracking task.

Voltage stability assessment based on improved coupled single‐port method

This study proposes an improved coupled single-port method for the assessment of voltage stability based on phasor measurement unit (PMU) data. The impedance matching condition, i.e. the condition that the local load impedance and the Thevenin equivalent impedance are equal in magnitude at the loadability limit point, has been a fundamental assumption of many existing studies on voltage stability assessment. However, it is shown in this study that the impedance matching can happen either before or after the loadability limit point in certain cases. The authors have proven that the inaccuracy of the conventional impedance matching condition is due to the time-varying equivalent parameters of a power system. To deal with the dynamic nature of grid equivalence, they propose an innovative method to improve the conventional coupled single-port method. In the new method, voltage magnitude-to-load consumption sensitivity is used to adjust the equivalent parameters calculated by the coupled single-port method. Compared to conventional methods, the proposed method requires fewer PMU measurements and provides more accurate margin estimates. Case studies on extensive test systems validate the accuracy of the proposed method. The comparison between the conventional coupled single-port method and the developed method is also provided to demonstrate the effectiveness of the new method.

Event-Based Variance-Constrained ${\mathcal {H}}_{\infty }$ Filtering for Stochastic Parameter Systems Over Sensor Networks With Successive Missing Measurements.

This paper is concerned with the distributed filtering problem for a class of discrete time-varying stochastic parameter systems with error variance constraints over a sensor network where the sensor outputs are subject to successive missing measurements. The phenomenon of the successive missing measurements for each sensor is modeled via a sequence of mutually independent random variables obeying the Bernoulli binary distribution law. To reduce the frequency of unnecessary data transmission and alleviate the communication burden, an event-triggered mechanism is introduced for the sensor node such that only some vitally important data is transmitted to its neighboring sensors when specific events occur. The objective of the problem addressed is to design a time-varying filter such that both the requirements and the variance constraints are guaranteed over a given finite-horizon against the random parameter matrices, successive missing measurements, and stochastic noises. By recurring to stochastic analysis techniques, sufficient conditions are established to ensure the existence of the time-varying filters whose gain matrices are then explicitly characterized in term of the solutions to a series of recursive matrix inequalities. A numerical simulation example is provided to illustrate the effectiveness of the developed event-triggered distributed filter design strategy.

Optimal step size of least mean absolute third algorithm

This paper proposes an optimized least mean absolute third (OPLMAT) algorithm to improve the capability of the adaptive filtering algorithm against Gaussian and non-Gaussian noises when the unknown system is a time-varying parameter system under low signal–noise rate. The optimal step size of the OPLMAT is obtained based on minimizing the mean-square deviation at the current time. In addition, the mean convergence and steady-state error of the OPLMAT algorithm are derived theoretically, and the computational complexity of OPLMAT is analyzed. Furthermore, the simulation experimental results of system identification presented illustrate the principle and efficiency of the OPLMAT algorithm. Simulation results demonstrate that the proposed algorithm performs much better than the LMAT and NLMAT algorithms.

PARAMETER IDENTIFICATION OF NONLINEAR VIBRATION SYSTEMS BASED ON THE HILBERT-HUANG TRANSFORM

Parameters of time-varying damping systems and nonlinear vibration systems, such as the Duffing and Van der Pol vibration systems, were identified by the Hilbert-Huang transform (HHT) in this study. The nonlinear vibration signal was first decomposed into free vibration and forced vibration components by the empirical mode decomposition. Subsequently, the amplitude envelope and the instantaneous frequency of the decomposed components were computed by the empirical envelop method. Damping ratios and other parameters of the nonlinear vibration systems were finally identified by using the least square method. Compared with the results from the wavelet analysis, the proposed method is proven to be more effective through numerical simulations of three typical nonlinear vibration systems and is featured by a higher level of accuracy.