Asymptotic Disturbance Rejection Research Articles

Robust Consensus Tracking Control of Uncertain Multi-Agent Systems With Local Disturbance Rejection

In this paper, a new distributed consensus tracking protocol incorporating local disturbance rejection is devised for a multi-agent system with heterogeneous dynamic uncertainties and disturbances over a directed graph. It is of two-degree-of-freedom nature. Specifically, a robust distributed controller is designed for consensus tracking, while a local disturbance estimator is designed for each agent without requiring the input channel information of disturbances. The condition for asymptotic disturbance rejection is derived. Moreover, even when the disturbance model is not exactly known, the developed method also provides good disturbance-rejection performance. Then, a robust stabilization condition with less conservativeness is derived for the whole multi-agent system. Further, a design algorithm is given. Finally, comparisons with the conventional one-degree-of-freedom-based distributed disturbance-rejection method for mismatched disturbances and the distributed extended-state observer for matched disturbances validate the developed method. Manuscript received May 13, 2022; accepted June 12, 2022. This work was supported by the National Natural Science Foundation of China (62003010, 61873006, 61673053), the Beijing Postdoctoral Research Foundation (Q6041001202001), the Postdoctoral Research Foundation of Chaoyang District (Q1041001202101), and the National Key Research and Development Project (2018YFC1602704, 2018YFB1702704). Recommended by Associate Editor Xiaohua Ge. (Corresponding author: Pan Yu.)

Adaptive Fuzzy Backstepping Asymptotic Disturbance Rejection of Multiagent Systems With Unknown Model Dynamics

This article presentsan adaptive fuzzy asymptotic disturbance rejection scheme for multiagent mechanical systems with unknown model dynamics and unknown frequency disturbances. The mechanical motion equations are expressed as the parameterized equations and the disturbances are described by unknown parametric exogenous system. The unknown parametric exogenous system is transformed into the canonical model with unknown disturbances as the inputs. The disturbance filter provides estimations of the state vector in the canonical model such that disturbances are represented as parameterized forms with exponentially decaying errors. The disturbance rejection can be converted into the adaptive control. Based on the adaptive vectorial fuzzy backstepping, the disturbance rejection formation controller is designed with the fuzzy logic systems approximating the model unknown dynamics. The adaptive robust control term attenuates fuzzy approximation errors. In contrast to the existing results, the adaptive fuzzy disturbance rejection formation control realizes the estimation and rejection for unknown frequency disturbances without requiring the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> knowledge of model dynamics. Based on the Barbalat’s lemma, it is shown that the adaptive disturbance rejection controller achieves the asymptotic formation tracking. Application on the surface vessel formation confirms the availability.

Uncertainty and disturbance rejections of complex dynamical networks via truncated predictive control

This study investigates the combined problems of uncertainty and disturbance rejections and synchronization of a class of complex dynamical networks with input delay. Specifically, a new uncertainty and disturbance estimator (UDE)-based truncated predictive control approach is used to simultaneously compensate the effects of unknown bounded disturbance and known input delay. The proposed approach relies on the conventional state prediction model to estimate the current state for the feedback by using the delayed state information and the estimation error is treated as an additional disturbance. Then, the effects of uncertainty and disturbance in the system model are robustly canceled with an appropriate filter based on the UDE approach. In addition, a set of sufficient conditions that guarantees the synchronization of the concerned system, the input delay compensation and the asymptotic disturbance rejection is derived with the aid of Lyapunov stability theory. In numerical examples, the proposed control method shows the better state estimation and robust synchronization performance by suppressing the effects of uncertainty and disturbance without any prior knowledge about them.

Stability analysis of single area power system considering parameter uncertainties

ABSTRACT In this work, the stability of a single area power system AVR loop is analysed in terms of specified gain and phase margin standpoint, by utilising an extended reduced-order observer (EROO). The design approach utilises a full-state feedback as well as an estimated signal for external disturbance (parametric uncertainties and disturbances due to change in load demands) to form the control law. Symmetric root locus (SRL) technique is used to assign the closed-loop poles (CLPs) of the system at desired locations by considering the stability margins. Parametric model uncertainty has been considered to demonstrate the robustness of control achieved by assigning a bound on the deviations in plant parameters. The proposed observer provides the estimates of unavailable states and state of the disturbance model in order to compensate system in the presence of external disturbances. The control scheme achieves performances satisfying the specified stability margins with asymptotic tracking and disturbance rejection property. The methodology provides control over peak values of the terminal voltage (with guaranteed zero steady-state errors) and control signal deviations which may be utilised to meet hardware constraints. Step by step design procedures with illustrative examples have been provided using MATLAB commands.

Robust Decentralized Secondary Frequency Control in Power Systems: Merits and Tradeoffs

Frequency restoration in power systems is conventionally performed by broadcasting a centralized signal to local controllers. As a result of energy transition, technological advances, and scientific interest in distributed control and optimization methods, a plethora of distributed frequency control strategies have been proposed recently, which rely on communication amongst local controllers. In this paper, we propose a fully decentralized leaky integral controller for frequency restoration, which is derived from a classic lag element. We study steady-state, asymptotic optimality, nominal stability, input-to-state stability, noise rejection, transient performance, and robustness properties of this controller in closed loop with a nonlinear and multivariable power system model. We demonstrate that the leaky integral controller can strike an acceptable tradeoff between performance and robustness as well as between asymptotic disturbance rejection and transient convergence rate by tuning its dc gain and time constant. We compare our findings to conventional decentralized integral control and distributed-averaging-based integral control in theory and simulations.

Output feedback anti-disturbance control of input-delayed systems with time-varying uncertainties

For input-delayed systems with time-varying uncertainties in industrial applications, a robust predictor-based anti-disturbance control design is proposed in this paper based on only output measurement, which can be applied to improve system performance in the presence of constant, asymptotically stable, step, ramp, or harmonic type disturbances, typically encountered in engineering practice. A novel predictor, named state & disturbance observer–predictor (SDOP), is firstly introduced to estimate the ‘delay-free’ system state and disturbance dynamics simultaneously, with no need to store the control history as required in the existing predictor-based control methods. To allow for long input delay, another design of sequential SDOPs (SSDOPs) is proposed such that each SSDOP only needs to estimate the future system state and disturbance in terms of a specified step size for implementation. Moreover, a recursive sub-optimal H∞ design of SSDOPs is given such that the computation burden is independent of the number of SSDOPs and thus could be significantly reduced. Consequently, two anti-disturbance control schemes are developed based on an SDOP or SSDOPs to improve system performance. For the nominal system, the input delay is allowed to be arbitrarily long by increasing the number of SSDOPs. For the presence of time-varying plant uncertainties, asymptotic disturbance rejection performance can be achieved. A sufficient condition for robust stability of the closed-loop system is established in terms of matrix inequality, which can be effectively solved to determine the controller parameters. An illustrative example from the literature is used to demonstrate the effectiveness and merit of the proposed method. ,

Attitude manoeuvre control and asymptotic disturbance rejection of flexible spacecraft

This paper presents a novel approach to tackle the issues of attitude manoeuvre control and asymptotic disturbance rejection for a flexible spacecraft. The resulting attitude controller employs an internal model-based compensator to reject a class of persistent disturbances and a modal estimator for dynamic compensation of the rigid-flex coupling effect. The convergence of the modal variables can be guaranteed without the measures of them. The stability of the system is proved via the Lyapunov technique rigorously. Numerical results illustrate that improved attitude control performance and asymptotic disturbance rejection can both be achieved.

Asymptotic Reference Tracking and Disturbance Rejection of UDE-Based Robust Control

The uncertainty and disturbance estimation (UDE)-based robust control strategy is able to achieve good robust performance by estimating and compensating the uncertainty and disturbance in a system with a filter having the appropriate frequency characteristics. However, how to systematically design the filter and the reference system in a UDE-based control system to achieve asymptotic reference tracking and disturbance rejection is still missing in the literature. In this paper, this is solved by applying the well-known internal model principle. The conditions to guarantee the closed-loop system stability and to achieve asymptotic disturbance rejection and reference tracking are derived. Experimental results on a servo system are presented as an example to demonstrate its excellent performance, which can actually reach the hardware resolution limit, with comparisons to the disturbance-observer-based control and the active disturbance rejection control.

The leader-following rendezvous with connectivity preservation via a self-tuning adaptive distributed observer

ABSTRACTThis paper studies the leader-following rendezvous with connectivity preservation problem for multiple double-integrator systems subject to external disturbances via a self-tuning adaptive distributed observer approach. This approach offers two advantages over the existing approach. First, it removes the existing assumption that all the followers know the system matrix of the leader system. Second, the difficult task of calculating the observer gain is avoided by the employment of the dynamic observer gain. A rigorous analysis shows that our control law is capable of maintaining the connectivity of any initial connected communication network, and achieving the asymptotic tracking and disturbance rejection for a class of leader's signals and external disturbances, which can be the algebraic sum or multiplication of any polynomial functions with any unknown coefficients and sinusoidal functions with arbitrary unknown amplitudes, initial phases, and any frequencies.

Position Regulation of an EGR Valve Using Reset Control With Adaptive Feedforward

We propose a hybrid control system performing set-point regulation of an exhaust gas recirculation valve of a Diesel engine. The control technique is based on a first-order reset element (FORE) embedded with an adaptive feedforward action whose aim is to provide asymptotic rejection of disturbances acting at the plant input. The feedforward action is adapted by suitable resetting laws occurring whenever the FORE is reset to zero. We first provide a formal analysis of the effectiveness of the adaptive reset system to guarantee asymptotic set-point regulation, and then, we illustrate how the adaptive feedforward can be parameterized for improved transient performance. We experimentally illustrate the proposed solution on a Diesel engine testbench, which reveals substantial position accuracy improvement during a standard driving cycle, as compared with the production standard solution.

Asymptotic rejection of sinusoidal disturbances based voltage balance control in back-to-back power converters

SUMMARY This paper addresses the imbalance problem of the dc-link capacitor voltages in the three-level diode-clamped back-to-back power converter. In order to cope with it, a mathematical analysis of the capacitor voltage difference dynamics, based on a continuous model of the converter, is first carried out. It leads to an approximated model that contains explicitly several sinusoidal functions of time. In view of this result, the voltage imbalance phenomenon can be addressed as an output regulation problem, considering the sinusoidal functions of time as exogenous disturbances. Thus, a novel approach to deal with the mentioned problem in the back-to-back converter is presented. Then, the particular features of the disturbances are used to design several controllers. They all follow an asymptotic disturbance rejection approach. In this way, the estimates of the disturbances are used to apply a control law that cancels them while regulating the capacitor voltage balance as well. Finally, the performance of the proposed control laws is evaluated, presenting the simulation results obtained when the different controllers are implemented. Copyright © 2013 John Wiley & Sons, Ltd.

Asymptotic rejection of unmatched general periodic disturbances with nonlinear Lipschitz internal models

This article deals with asymptotic rejection of general periodic disturbances in a class of nonlinear systems by exploiting observer design with Lipschitz output nonlinearities for the internal model design. It is shown that a class of general periodic distances can be modelled as outputs of linear systems with nonlinear output functions. Based on this observation, a nonlinear observer design with output Lipschitz nonlinearities is investigated and integrated for the internal model design to estimate the phase and amplitude of the desired feedforward input for asymptotic disturbance rejection in a class of nonlinear systems with input-to-state stable zero dynamics. A number of problems on disturbance rejection can be formulated in the disturbance rejection form shown in this article to which the proposed nonlinear Lipschitz internal model can be applied. Two examples are included to demonstrate the proposed design strategies.

Asymptotic rejection of nonvanishing disturbances despite plant-model mismatch

A direct adaptive control methodology for the rejection of unmeasured non-vanishing disturbances is proposed. The approach uses the framework of polynomial RST controllers and relies on the internal model principle with additional degrees of freedom provided by the Q parametrization. The parameters of the Q polynomial are adapted using minimization of the closed-loop output error. Asymptotic disturbance rejection of unmeasured non-vanishing disturbances can be guaranteed despite plant-model mismatch, provided the closed-loop system remains stable. A simulation example illustrates the theoretical developments.

Adaptive Asymptotic Rejection of Unmatched General Periodic Disturbances in Output-Feedback Nonlinear Systems

This note deals with asymptotic rejection of periodic disturbances in a class of nonlinear systems via output feedback. The disturbance undertaken is unmatched but the period of the disturbance is known. A novel method for estimating periodic disturbances is proposed, which ensures convergence of the estimation error to zero. By applying such estimation, a controller is constructed such that all the signals in the closed loop are bounded and the output converges to zero. A numerical example is presented to show the utility of the results presented in the note.

Phase Compensation Strategies for Modulated-Demodulated Control With Application to Pulsed Jet Injection

Modulated-demodulated control is an effective method for asymptotic disturbance rejection and reference tracking of periodic signals, however, conventional static phase compensation often limits the loop gain in order to avoid sensitivity function peaking in a neighborhood of the frequencies targeted for rejection or tracking. This paper introduces dynamic phase compensation for modulated-demodulated control which improves disturbance rejection characteristics by inverting the plant phase in a neighborhood of the control frequency. Dynamic phase compensation is implemented at baseband which enables the use of low-bandwidth compensators to invert high frequency dynamics. Both static and dynamic phase compensation methods are used to demonstrate a novel application of repetitive control for pulsed jet injection. In this application pulsing an injectant has been shown to produce advantageous effects such as increased mixing in many energy generation and aerospace systems. The sharpness of the pulse can have a large impact on the effectiveness of control. Modulated-demodulated control is used to maximize the sharpness of a pulsed jet of air using active forcing by tracking a square wave in the jet’s temporal velocity profile.

Delay-varying repetitive control with application to a walking piezo actuator

The performance of systems that exhibit repetitive disturbances can be significantly improved using repetitive control. If the repetitive disturbance is periodic with respect to time, perfect asymptotic disturbance rejection can be achieved by well-known methods. However, many systems have a repetitive nature with respect to a variable other than time. For this type of systems, we propose a delay-varying repetitive control (DVRC) method, which employs a time-varying delay in the repetitive controller that is continuously adjusted based on the repetitive variable. An H ∞ norm-based criterion is derived that guarantees stability of the time-varying delay system for a given range of variations of the repetitive delay. The strengths of this new repetitive control scheme are shown by applying it to a nanomotion stage driven by a walking piezo actuator.

Observer Design of Lipschitz Output Nonlinearity with Application to Asymptotic Rejection of General Periodic Disturbances

AbstractIn this paper, observer design for systems with nonlinear outputs is investigated, and a sufficient condition is provided for the convergence of the estimates. The proposed observer design is then applied to estimate general periodic disturbances which can be modelled as nonlinear outputs of harmonic oscillators. The proposed observers for general periodic disturbances are then exploited for internal model design for asymptotic rejection of nonlinear systems with ISS zero dynamics. A number of problems on disturbance rejection and output regulation can be formulated in a disturbance rejection form shown in the paper to which the proposed nonlinear Lipschitz internal model can be applied. An example is included to demonstrate the proposed design strategies.

Asymptotic rejection of unknown sinusoidal disturbances in non-linear dynamic systems with delay

The authors deal with asymptotic rejection of unknown disturbances in non-linear dynamic systems with delay. The disturbances are generated from an unknown linear exosystem whose order is known. The non-linear dynamic system contains non-linear terms in the system state variables with delay. There is no restriction on the non-linear functions, as long as they have continuous first-order derivatives. Here, a state feedback stabilisation control strategy is proposed for the system without the disturbances. An adaptive internal model is then designed and incorporated with the state feedback control design to asymptotically reject the unknown disturbances. A simulation example is included to demonstrate the proposed control design.

Adaptive Tracking and Disturbance Rejection for a Class of Distributed Systems

In this paper,direct adaptive-state feedback control schemes are developed to solve the problem of asymptotic tracking and disturbance rejection for a class of distributed large-scale systems with faulty and perturbed interconnection links.In terms of the special distributed architectures,the adaptation laws are proposed to update controller parameters on-line when all interconnected fault factors,the upper bounds of perturbations in interconnection links,and external disturbances on subsystems are unknown. Then,a class of distributed state feedback controllers is constructed to automatically compensate the fault and perturbation effects, and reject the disturbances simultaneously based on the information from adaptive schemes.The proposed adaptive robust tracking controllers can guarantee that the resulting adaptive closed-loop distributed system is stable and each subsystem can asymptotic-output track the corresponding reference signal in the presence of faults and perturbations in interconnection links,and external disturbances.The proposed design technique is finally evaluated in the light of a simulation example.

Asymptotic rejection of unmatched general periodic disturbances in a class of non-minimum-phase non-linear systems

This article deals with asymptotic rejection of unmatched general periodic disturbances in nonminimum phase non-linear output feedback systems. The steady state responses are defined for unstable systems subject to general periodic disturbances, and the generalised gain and phase are defined for stable systems subject to general periodic disturbances. Based on the new definitions, new results are obtained for the equivalent input disturbance and disturbance estimation. An L p -convergent estimate of the equivalent input disturbance is incorporated in the control design to ensure the asymptotic rejection of unmatched general periodic disturbances while maintaining the stability of the non-linear system.