EID‐Estimation‐Based Periodic Disturbance Rejection for Sintering Ignition Process with Input Time Delay

This paper presents the design of a linear quadratic analog tracker (LQAT) based on the observer–Kalman-filter identification (OKID) method and the design of a modified functional observer-based equivalent input disturbance (EID) estimator for unknown square–non-square singular analog systems with unknown input and output disturbances. First, an equivalent mathematical model of the singular analog system is presented to simulate the time response of continuous-time linear singular analog systems to arbitrary inputs via the model conversion method. Then, for the unknown singular analog system, it constructs a linear quadratic analog tracker with state feedback and feed-forward gains based on the off-line OKID method. Furthermore, it extends the design methodology of the EID estimator for strictly proper regular systems with unknown matched–mismatched input and output disturbances to proper regular systems. It is important to mention that the newly developed modified functional observer for proper systems is used to estimate the unknown EID of singular analog systems and that the constraints on the dimensions of unknown disturbances can be eliminated by using the newly proposed EID estimation method. The contributions of this paper can be listed as follows: (1) based on both the OKID method and the discrete-to-continuous model conversion, the simulation of the time responses of the continuous-time linear singular models (which are not feasible using existing MATLAB toolboxes) become feasible; (2) for effective control of the unknown singular analog system, an off-line OKID method is proposed to design an LQAT with state feedback and feed-forward gains; and (3) based on the newly developed modified functional observer for the reduced-order proper regular system, the original EID estimator in the literature is newly extended to estimate the EID from the unknown strictly proper singular analog system, without the original dimensional constraints of the disturbances. It is important to mention that the disturbances of interest can be unknown matched–mismatched input and output disturbances.

In this paper, a robust H∞ control problem is considered for an uncertain singular system. An active disturbance rejection method called equivalent input disturbance (EID) is used to reduce the influence of exogenous disturbances and uncertainties on the system. At the first, there exists an EID, which can produces the same effect on the system as disturbances and uncertainties do in the control channel according to the EID concept. Then, an EID estimator is constructed to estimate the influence of EID on the system. Finally, based on Lyapunov stability theory, a static output feedback‐based robust H∞ controller combined with EID estimate is designed, guaranteeing that closed‐loop system is admissible (regular, impulse‐free, and stable) with a prescribed H∞ performance level. Compared with traditional H∞ control method, H∞ control based on EID method improve the control performance of the system. A numerical example demonstrates the validity of the method.

This paper develops a novel equivalent input disturbance (EID)-based adaptive sliding mode control (SMC) method for singularly perturbed systems (SPSs). Firstly, the block diagonalization approach is introduced to decompose the full-order SPSs exactly, and slow and fast subsystems are obtained by solving the upper and lower triangular matrices individually. Secondly, an EID is constructed to estimate the unknown disturbances with the observer gain and error system convergence analyzed. Then, depending on the decoupled reduced-order system models, a Lyapunov equation-based solution is adopted to construct a composite sliding surface. Finally, combined with the EID estimation, an adaptive SMC law is proposed to compensate the adverse effect of disturbances and the reachability condition is proven. The presented control strategy is free of any priori disturbances information while the satisfactory system performance can be guaranteed. Simulation results on two examples illustrate its superiority over the existing methods.

This paper describes a fault diagnosis method based on the equivalent-input-disturbance (EID) approach to power distribution feeders connected to a photovoltaic (PV) system. Node faults are treated as a system disturbance and are estimated using an EID estimator. First, a dynamic model that contains both the PV system and a power supply utility for the feeder is built. Second, an EID estimator is constructed to estimate the disturbance to the system on the control input channel. Third, a method for abstracting the amount caused by the PV system in the EID is presented to estimate the effect caused by faults. Simulation results demonstrate the validity and superiority of the method.

Compensation in Repetitive Control System for Aperiodic Disturbances and Input Dead Zone

In industrial processes, valve stiction often induces loop oscillations, and limits the control loop performance. To better control the plant with valve stiction, in this paper, the equivalent-input-disturbance (EID) approach is incorporated into the conventional PID control system to improve the ability of disturbance and nonlinearity rejection. The newly proposed method uses a classic two-parameter stiction model to represent the nonlinearity of valve stiction. According to the EID method, an EID estimator is constructed to estimate the influence of valve stiction on the system output. The controller is based on the basic proportional-integral-derivative (PID) control. And a simulation example is provided to demonstrate the validity of this method.

ABSTRACTIn this paper, the output tracking control problem for a class of switched nonlinear systems with multiple time-varying delays is studied based on equivalent-input-disturbance (EID) approach. More precisely, with the use of suitable Lyapunov-Krasovskii functional together with average dwell-time technique, an output feedback tracking controller is designed which makes that the states of resulting system can asymptotically track the desired trajectory. Further, the EID estimator is implemented to reject both matched and unmatched disturbances effectively without requiring any prior knowledge of the disturbances. Simulation results are presented to illustrate the effectiveness and potential of the developed EID-based output tracking control design technique. The results reveal the fact that the tracking controller based on EID provides a better tracking performance than the feedback controller based on sliding mode technique.

Using the bilinear and tuning bilinear approximation together with the interval arithmetic operation, the discrete-time uncertain model and robust digital redesign of sampled-data uncertain system with input time delay are presented. The system matrices characterizing the stale-space representation of the original uncertain system are assumed to be interval matrices. The developed discrete-time interval model tightly encloses the exactly discretized continuous-time input time-delay uncertain system, and it can be utilized for digital simulation. Based on bilinear approximation, a tuning bilinear approximation is presented to find the digitally redesign controller of the digitally controlled sampled-data uncertain system with input time delay. The digitally redesigned predictor controller is able to closely match the states of the digitally redesigned uncertain sampled-data system with those of the original continuous-time predictor controlled uncertain system.

In this paper, we present an improved delay-dependent absolute stability criterion for Lur’e systems with time delays. The guarantee of absolute stability is provided by Lyapunov-Krasovskii theorem with the Lyapunov functional containing the integral of sector-bounded nonlinearities. The Lyapunov functional terms involving delay are partitioned to be associated with each equidistant fragment on the length of time delay. Employing the Jensen inequality and S-procedure, the sufficient condition is derived from time derivative of the Lyapunov functional. Then, the absolute stability criterion expressed in terms of linear matrix inequalities (LMIs) can be efficiently solved using available LMI solvers. The bisection method is used to determine the maximum allowable time delays to ensure the stability of Lur’e systems in the presence of uncertain time-invariant delays. In addition, the stability criterion is extended to Lur’e systems subject to norm-bounded uncertainties by using the matrix eliminating lemma. Numerical results from two benchmark problems show that the proposed criteria give significant improvement on the maximum allowable time delays.

Software reliability growth models based on a nonhomogeneous Poisson process (NHPP) have been considered as one of the most effective among various models since they integrate the information regarding testing and debugging activities observed in the testing phase into the software reliability model. Although most of the existing NHPP models have progressed successfully in their estimation/prediction accuracies by modifying the assumptions with regard to the testing process, these models were developed based on the instantaneous fault-removal assumption. In this paper, we develop a generalized NHPP software reliability model considering quasi-renewal time-delay fault removal. The quasi-renewal process is employed to estimate the time delay due to identifying and prioritizing the detected faults before actual code change in the software reliability assessment. Model formulation based on the quasi-renewal time-delay assumption is provided, and the generalized mean value function (MVF) for the proposed model is derived by using the method of steps. The general solution of the MVFs for the proposed model is also obtained for some specific existing models. The numerical examples, based on a software failure data set, show that the consideration of quasi-renewal time-delay fault-removal assumption improves the descriptive properties of the model, which means that the length of time delay is getting decreased since testers and programmers adapt themselves to the working environment as testing and debugging activities are in progress.

This article presents an improved equivalent-input-disturbance (EID) approach to handle unknown disturbances and plant uncertainties. The disturbances and uncertainties are treated as a lumped disturbance in an EID-based control system. The effect of the lumped disturbance is compensated by an EID estimator. A constraint between design parameters and uncertainties is imposed on the design of the estimator. In addition, there are insufficient analyses of the influence of uncertainties on the control performance and the stability of the system. A new filter is devised for an improved EID estimator in this article to remove the constraint. This ensures that the sensitivity of the system to disturbances at low frequencies can be freely decreased. An analysis of the system reveals that uncertainties not only influence disturbance-rejection and reference-tracking performance but also affect system stability. A sufficient stability criterion is derived with consideration of uncertainties. The validity of the presented method is demonstrated by simulation and experimental results.

The techniques of an efficient 3-D sound system based on the psychoacoustics of spatial hearing with multimedia or virtual reality have been developed by many researchers. In this paper, we propose an idea for an improved 3-D sound system using conventional stereo headphones to obtain a better sound diffusion from the mono-sound recorded in an anechoic chamber. We use the HRTF (Head Related Transfer Function) for the sound localization and the wavelet filter bank with time delay for the sound diffusion. We investigate the effects of the 3-D sound depending on the length of time delay at the lowest frequency band. Also the correlation coefficient of the signals between the left channel and the right channel is measured to identify the sound diffusion.

Robust disturbance rejection for uncertain fractional-order systems

In this paper a robust dynamic controller design algorithm for nonlinear systems with unmatched uncertainties and an input time delay is provided. For many practical systems, the existence of time delay is common in control practice. Therefore the problem of controlling such systems becomes more complex and sometimes degrades the control performance. We will propose a feasible method to deal with the problem of unmatched uncertainties and an input time delay. Based on the Lyapunov theory and the concept of functional analysis, the conditions of the robust stability of the overall closed-loop system with unmatched uncertainties and an input time delay will be derived. Finally, some examples and simulation results are provided to illustrate the versatility and performance of the proposed method.

The recent decades have witnessed active studies in fault detection and isolation (FDD) of the small satellites subject to actuator failures and attitude coordination control of spacecraft formation flying (SFF) which plays a significant role in missions such as synthetic-aperture radar imaging. However, because of the time delay in communication links, the performance of coordination control is not always satisfactory. In this paper we propose a method to estimate the actuator fault as well as the input time delay at the same time. First of all, the model of the altitude control system of the small satellite with actuator fault and the model of the altitude control system with actuator fault and the input time delay are presented respectively. Based on the Two-Stage Kalman Filter algorithm, the fault and input time delay of the altitude control system of the small satellite can be estimated. At last, the simulation of the algorithm in a satellite attitude control system with actuator fault and input time delay will illustrate the effectiveness of the proposed approach.