A Modified Functional Observer-Based EID Estimator for Unknown Continuous-Time Singular Systems

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.

Sintering plays a key role in generating blast furnace burden in metallurgical processes. The continuous production and stable quality of sintering significantly depends on the stable and precise control of sintering ignition, which, however, is achieved through an input time delay system, and suffers from different and unknown disturbances. To reject disturbances and enhance the control precision of ignition temperature, this paper introduces a modified equivalent input disturbance (EID)‐based disturbance compensation that is suitable for controlling sintering ignition. First, the periodic properties of disturbances induced by gas pressure fluctuations are obtained based on spectral density decomposition. Second, to obtain the dynamics of sintering ignition, an iterative subspace modeling method is developed, which estimates not only the model parameters but also the length of time delay. By considering the periodic property, a control structure of sintering ignition based on the modified EID‐based compensation is proposed, in which an additional time‐delay element is designed to make the phase difference between EID estimation and real disturbance close to zero. Finally, the validity of the proposed method is verified by a simulation.

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.

The designs of optimal linear quadratic estimator and tracker for the linear continuous-time systems with unknown disturbances have been improved in this paper. Compared with the advanced robust control design methodologies developed in the literature, the proposed method significantly improves both the unknown input estimation and the servo performance for the systems subject to the unknown disturbances. The aforementioned design objective can be achieved due to the fact that the proposed approach ensures the relative stability in both the unknown input estimation and the servo performance from the theoretical point of view. Besides, based on the equivalent input disturbance principle developed in the literature, the proposed approach is applicable to the system with a class of mismatched input disturbances. Furthermore, the newly proposed unknown input estimation technique is able to extend the recently developed generalized optimal linear quadratic tracker for continuous-time systems with known disturbances to those with unknown disturbances.

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.

Robust disturbance rejection for uncertain fractional-order systems

This paper concerns the problem of designing a modified repetitive-control (RC) system for a class of servo system with nonintegral-chain form and unknown nonlinear dynamics, whose relative degree may be less than the system order. Our solution focuses on the unique features of equivalent input disturbance (EID) and extended state observer (ESO) approaches. An improved ESO is designed to estimate the EID together with the states by exploiting the known information of the plant model and the incorporation of the EID estimate into an RC law compensates for the influences of the actual disturbances. Both the stability criteria and optimization algorithm for controller parameters are provided. Finally, an application to speed control of a brushless DC motor system demonstrates the validity of the method.

This work is focused on the active vibration control of piezoelectric cantilever beam, where an adaptive feedforward controller (AFC) is utilized to reject the vibration with unknown multiple frequencies. First, the experiment setup and its mathematical model are introduced. Due to that the channel between the disturbance and the vibration output is unknown in practice, a concept of equivalent input disturbance (EID) is employed to put an equivalent disturbance into the input channel. In this situation, the vibration control can be achieved by setting the control input be the identified EID. Then, for the EID with known multiple frequencies, the AFC is introduced to perfectly reject the vibration but is sensitive to the frequencies. In order to accurately identify the unknown frequencies of EID in presence of the random disturbances and un-modeled nonlinear dynamics, the time–frequency-analysis (TFA) method is employed to precisely identify the unknown frequencies. Consequently, a TFA-based AFC algorithm is proposed to the active vibration control with unknown frequencies. Finally, four cases are given to illustrate the efficiency of the proposed TFA-based AFC algorithm by experiment.

ABSTRACTMany practical systems are described as unknown multi-input-multi-output (MIMO) time-delay systems with unknown disturbances. The properties and performance of multi-time-delay MIMO systems are quite different compared to delay-free systems, in particular if the time-delay is long. In addition, for practical implementation digital controllers are often required instead of analog controllers. This paper presents: (i) an overview of the mathematical modelling based on the observer/Kalman filter identification (OKID) method, with some insight on known/unknown MIMO systems; (ii) a study of the pole-zero maps of the identified delay-free system and the known/unknown time-delay system for various sampling periods; (iii) a development of the explicit pole-zero map of the sampled-data MIMO neutral system with multiple discrete and disturbed time delays; (iv) an utilisation of the OKID method for known/unknown time-delay sampled-data MIMO systems with unknown disturbances; (v) an extension of the existing equivalent-input-disturbance (EID) estimator, to determine a robust tracker for the unknown time-delay system with unknown disturbances; and (vi) an investigation on the unknown time-delay system with stable or unstable zeros to determine which traditional or customised tracker can be applied. In addition, simulation studies are performed on the relationship between pole-zero maps and delay times.

Aiming at the problem of performance degradation of flue gas acid‐making control system caused by system uncertainty and external interference, this paper presents a model predictive control scheme based on an equivalent input disturbance (MPC‐EID) for the temperature tracking control of flue gas acid production systems. First, a nonlinear Wiener model is established for the process, which can well character the nonlinear change of process temperature. Second, design the overall control strategy and complete the design of MPC and EID, the observer estimates the equivalent input disturbance, and compensates the estimated value in a feed‐forward manner to obtain the final composite control rate to achieve the rapidity, accuracy and robustness to the disturbance of the reference temperature tracking. Third, a rigorous stability analysis shows that the closed‐loop system is stable. Finally, simulation and experimental results demonstrate that the MPC combined with EID method is more efficient compared with MPC and MPC‐PID approaches.

Disturbance rejection of offshore drilling platforms: An equivalent-input-disturbance-based dynamic positioning control method