Robust H∞ control of uncertain singular systems based on equivalent‐input‐disturbance approach

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 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

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.

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.

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 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.

Robust disturbance rejection for uncertain fractional-order systems

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.

Sliding mode control (SMC) has been considered as a powerful method for disturbances rejection. On the other hand, we have presented an equivalent-input disturbance (EID) approach to reject disturbances. This paper takes a dual-stage feed drive as an example to compare these two methods. The example shows that, while the EID approach obtains almost the same disturbance rejection performance for matched disturbances as that of the SMC does, it can reject unmatched disturbances. This shows the superiority of the EID approach over SMC method.

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.

This study investigates the challenge of repetitive control in a type of linear uncertain system with exogenous disturbances. The uncertain systems with state and state derivative uncertainties. To preserve the uncertain properties of these systems, this class is not directly transformed into a general linear uncertain system. Therefore, it is challenging and complicated to study the control issues of these systems. In this study, a novel approach that combines the system and differential states into a new state is presented; this approach transforms an uncertain system into a linear singular system and is effective for handling uncertainty. The repetitive control problem of the linear singular system with disturbances is addressed from two perspectives. First, the traditional modified repetitive control system is enhanced by introducing an error compensator to improve system tracking performance. Second, to enhance disturbance rejection, a novel modified equivalent‐input‐disturbance (EID) approach is introduced for the first time. Unlike the traditional EID method, the modified method directly compensates for the disturbance estimation error to enhance the accuracy of disturbance estimation and achieve optimal disturbance‐rejection performance in the system. The required and sufficient requirements for the stability of a closed‐loop system are provided. And the controller design algorithm is presented based on these conditions. Finally, the presented method is compared with other control methods, demonstrating its effectiveness and superiority.

This paper focuses on the issues of tracking controller enhancement, input delay rectification, and disturbance elimination for dynamical systems characterized as fractional-order semi-Markovian jump processes. In particular, the design of the modified repetitive control technique integrated with the filtered Smith predictor scheme based on the Majhi–Atherton approach guarantees exact tracking performance and disturbance elimination. To be more specific, the active rectification of both external disturbances and delays is safeguarded by the construction of a modified proportional derivative-based active disturbance estimator along with the traditional Smith predictor framework. Also, the modified repetitive control in this framework is able to track the reference signals with multiple periodicities. In accordance with the Lyapunov stability criterion, a group of applicable principles is produced in the structure of matrix inequality constraints. Furthermore, the parameters of the controller block are designed concurrently by way of elucidating the stated matrix inequality constraints. Finally, the simulation results and the comparison analysis between the developed control technique and existing works such as equivalent input disturbance and the truncated predictor feedback control method validate the advantage of the recommended control framework.