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

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.

This paper considers the problem of tracking a periodic signal for a plant with an input dead zone in the actuator. The nonlinearity greatly degrades control performance. To solve this problem, we incorporate an equivalent-input-disturbance (EID) compensator into a repetitive control system (RCS), resulting in a new system configuration. We combine the linear-matrixinequality technique with singular-value decomposition to analyze the stability of the system and to devise a design method. Unlike other methods, this one does not require any information about the dead zone. Simulation results demonstrate its effectiveness.

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 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 paper presents a reduced order discrete extended state observer (RODESO) based repetitive controller (RC) with application to a piezoelectric actuator (PEA) based nano-positioning system. The RODESO-based RC proposed in this paper is capable of rejecting both periodic and aperiodic disturbances. Moreover, RODESO can be tuned using only two parameters and the model free approach of RODESO-based RC makes it an ideal solution to overcome the challenges of piezoelectric actuator control. Various types of periodic and aperiodic disturbances are used in the simulation to demonstrate the disturbance rejection capability of the proposed algorithm. The comparison studies demonstrate that the RODESO-based RC has superior performance over the phase lead RC.

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.

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 presents an extended state observer (ESO) based repetitive control (RC) to compensate periodic signals, aperiodic disturbances, and uncertainties of the plant with relative degree equal to or greater than zero. Since linear ESO has only two tuning parameters, the proposed controller provides a simple and user friendly solution to complex engineering problems in practice. Moreover, due to the model free approach of a ESO-based control, it can be applied to a wide variety of plants. The design procedures are proposed to ensure a stable system. Various types of disturbances are used in simulations and experiments which show that the ESO-based RC cannot only reject periodic and aperiodic disturbances but also handle the plant parameter uncertainty. The comparison studies demonstrate that the ESO-based RC has superb performance.

The modified repetitive control system is a type of servomechanism for periodic reference inputs. That is, the modified repetitive control system follows the periodic reference input with a small steady state error, even if a periodic disturbance or uncertainty exists in the plant. Using previously proposed modified repetitive controllers, even if the plant does not include time-delay, transfer functions from the periodic reference input to the output and from the disturbance to the output have infmite numbers of poles. To specify the input-output and the disturbance attenuation characteristic easily, Yamada et al. proposed the concept of a simple repetitive control system such that the controller works as a modified repetitive controller and transfer functions from the periodic reference input to the output and from the disturbance to the output have fmite numbers of poles. In addition, Yamada et al. clarified the parameterization of all stabilizing simple repetitive controllers. Recently, the p...

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.

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.

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.

In this paper, the adaptive neural controllers of subsystems are proposed for a class of discrete-time switched nonlinear systems with dead zone inputs under arbitrary switching signals. Due to the complicated framework of the discrete-time switched nonlinear systems and the existence of the dead zone, it brings about difficulties for controlling such a class of systems. In addition, the radial basis function neural networks are employed to approximate the unknown terms of each subsystem. Switched update laws are designed while the parameter estimation is invariable until its corresponding subsystem is active. Then, the closed-loop system is stable and all the signals are bounded. Finally, to illustrate the effectiveness of the proposed method, an example is employed.

Sliding-mode repetitive learning control with integral sliding-mode perturbation compensation