Asymptotic Disturbance Rejection Research Articles

Virtual feedforward control for asymptotic rejection of periodic disturbance

In this paper, a novel, simple yet effective control scheme, called virtual feedforward control (VFC), is proposed for asymptotic disturbance rejection. The VFC control is an add-on function on top of normal feedback control, and it is activated when a periodic disturbance is found to be present in the system, based on output measurements and detection of output periodic behavior. It is shown that the proposed control can reject the periodic disturbances asymptotically under the perfect plant modeling. Furthermore, the closed-loop stability is not affected by the proposed control and, thus, there is no design tradeoff between disturbance rejection and stability. The robustness of the proposed control to model mismatch is analyzed. The effectiveness of the proposed method is sustained by simulation and comparison.

Ripple-free robust output regulation and tracking for multirate sampled-data control

The problem of the robust continuous-time asymptotic tracking and disturbance rejection for a multivariable multirate sampled-data system is studied. The necessity of a continuous-time internal model of the exogenous signals (except for the constant ones, if any) for obtaining a ripple-free zero error response, is proven. The conditions are given for the existence of a hybrid control system (including, possibly, a continuous-time subcompensator) for which the exponential stability and a continuous-time convergence to zero of the tracking error are guaranteed at least in a neighbourhood of the nominal parameters. This, in particular, both for when the dead-beat convergence of the state free response and the continuous-time error response is required at the nominal parameters, and for when an exponential convergence with a prescribed rate of decay is required (including design procedures of the continuous-time and the discrete-time subcompensators); both for when the available description of the plant has a known dependence on some 'physical' parameters, and for when the only nominal description of the plant is available, and independent perturbations of the entries of (some of) the matrices characterizing the plant representation are assumed.

Asymptotic Rejection of Disturbances in Non-Minimum Phase Nonlinear Systems

We address the problem of semi-global output-feedback stabilization for a class of nonlinear non-minimum phase systems subject to sinusoidal disturbances of known frequency, but unknown amplitude and phase. To this aim, we employ, within an internal model-based control scheme, an extension of a stabilization method recently introduced by Isidori. We regard this result as a first step towards a more complete theory of output regulation in the large for non-minimum phase systems.

Asymptotic Rejection of Periodic Disturbances With Fixed or Varying Period

A constructive derivation of repetitive control is obtained, through attempting to derive a control law for asymptotic rejection of periodic disturbances. This derivation not only reveals a close relationship between iterative operator inversion and repetitive control, but also suggests a unified design method for a learning control algorithm. Also, based on the observation, digital repetitive control can be generalized to reject periodic disturbance whose period is not exactly an integer multiple of the sampling interval. This study introduces a delay filter in the digital repetitive control law, which optimally interpolates the signal between samples, thus effectively reconstructing the signal of the previous period and making the learning process of repetitive control successful. The proposed optimal delay filter can be updated easily according to different signal periods. Thus it is specifically suitable for on-line tuning when the signal period is changing. Compared with the available tuning methods, the proposed tuning method has excellent steady-state performance while maintaining fast transient and system robustness. The simulations on active noise cancellation within a duct confirm the superiority of this tuning method.

Output regulation for nonlinear systems: an overview

The problem of controlling the output of a system so as to achieve asymptotic tracking of prescribed trajectories and/or asymptotic rejection of disturbances is one of the most fundamental problems in control theory. In linear system theory, a powerful approach to the solution of this problem is the design of a controller incorporating an internal model of all exogenous inputs. The extension of this approach to nonlinear systems has been thoroughly investigated in the past 10 years. The purpose of this paper is to review the major achievements in this area as well as to outline the major problems on which the research is presently progressing. Copyright © 2000 John Wiley & Sons, Ltd.

Adaptive Sinusoidal Disturbance Rejection in Linear Discrete-Time Systems—Part I: Theory

An adaptive regulation approach against disturbances consisting of linear combinations of sinusoids with unknown and/or time varying amplitudes, frequencies, and phases for SISO LTI discrete-time systems is considered. The new regulation approach proposed is based on constructing a set of stabilizing controllers using the Youla parametrization of stabilizing controllers and adjusting the Youla parameter to achieve asymptotic disturbance rejection. Three adaptive regulator design algorithms are presented and their convergence properties analyzed. Conditions under which the on-line algorithms yield an asymptotic controller that achieves regulation are presented. Conditions both for the case where the disturbance input properties are constant but unknown and for the case where they are unknown and time varying are given. In the case of error feedback, the on-line controller construction amounts to an adaptive implementation of the Internal Model Principle. The performance of the adaptation algorithms is illustrated through a simulation example. A companion paper [4] describes the implementation and evaluation of the algorithms for the problem of noise cancellation in an acoustic duct.

Multiobjective output-feedback control via LMI optimization

This paper presents an overview of a linear matrix inequality (LMI) approach to the multiobjective synthesis of linear output-feedback controllers. The design objectives can be a mix of H/sub /spl infin// performance, H/sub 2/ performance, passivity, asymptotic disturbance rejection, time-domain constraints, and constraints on the closed-loop pole location. In addition, these objectives can be specified on different channels of the closed-loop system. When all objectives are formulated in terms of a common Lyapunov function, controller design amounts to solving a system of linear matrix inequalities. The validity of this approach is illustrated by a realistic design example.

A New Approach for Designing Robust Controllers for the Servomechanism Problem

In this paper, we provide an alternative method for solving the more general servomechanism problem. The new approach based on designing a simple structure of a dynamic output feedback controller to achieve asymptotic tracking, disturbance rejection and pole assignment in linear time-invariant multivariable control systems. In addition, the resulting dynamic compensator is robust in the sense that asymptotic regulation take place for some or all disturbances and reference signals independent of any nondestabilizing perturbations in the system parameters. The main results of this paper are illustrated by an example.

A comparison of two adaptive algorithms for disturbance cancellation

The objective of this paper is to compare two approaches to the adaptive rejection of disturbance inputs represented by a finite sum of sinusoids. The first approach is based on adapting the parameters of a finite impulse response (FIR) feedback controller using a least mean square (LMS) type algorithm to achieve asymptotic disturbance rejection. The second approach is based on using the recursive least squares (RLS) algorithm to search within the set of parametrized stabilizing controllers for a controller that leads to asymptotic disturbance rejection. The two approaches are compared in terms of thier basic characteristics, as well as their performance in a simulation example.

Robust ripple-free regulation and tracking for parameter-dependent sampled-data systems

The robust ripple-free asymptotic tracking and disturbance rejection problem is studied for sampled-data systems whose matrices are assumed to depend on some "physical" parameters, each of which possibly affects all the elements of the matrices describing the system, and for the case when only a subset of the scalar outputs must track corresponding exogenous reference signals; ripple-free dead-beat regulation and tracking is also required at the nominal parameters. The necessary and sufficient conditions are given for the existence of a solution which may exist even when no solution exists for wholly independent variations of the entries of the matrices describing the system. A design procedure of both the continuous-time internal model and the discrete-time controller is also outlined.

A Comparison of Two Adaptive Algorithms for Disturbance Cancellation

The objective of this paper is to compare two approaches to the adaptive rejection of disturbance inputs represented by a finite sum of sinusoids. The first approach is based on adapting the parameters of a finite impulse response (FIR) feedback controller using a least mean square (LMS) type algorithm to achieve asymptotic disturbance rejection. The second approach is based on using the recursive least squares (RLS) algorithm to search within the set of parametrized stabilizing controllers for a controller that leads to asymptotic disturbance rejection. The two approaches are compared in terms of their basic characteristics, as well as their performance in a simulation example.

The Design of an Adaptive Control System for Linear Discrete-Time Systems with Disturbance Input

The problem of output dead-beat control with asymptotic disturbance rejection for linear discrete-time systems with disturbance input is considered. The system considered is composed of the plant to be controlled and the disturbance generator whose state vector is the disturbance input to the plant. We propose a design method of the controller which is organized by the feedback gain to stabilize the closed-loop of the plant and the compensator for the disturbance. It is shown that the proposed controller can force the output of the plant to zero and keep it zero by using the measurement output of the augmented system and the estimate of the disturbance which is obtained from the adaptive estimation process composed of an unbiased linear functional observer and an adaptive state observer. Some numerical examples show the validity of the proposed controller.

Optimal asymptotic robust performance via nonlinear controllers

In this paper we introduce a novel measure of asymptotic disturbance rejection for a feedback system. This notion of asymptotic performance is particularly well suited to the robust control of systems that exhibit both parametric and dynamic modelling uncertainty. We then derive a switching-type controller that provides optimal asymptotic disturbance rejection properties. The particular notion of disturbance rejection we consider is rejection of persistent bounded disturbances (i.e. l 1-optimal control). While asymptotic performance is guaranteed, we also provide bounds that quantify the transient response behaviour of this particular control scheme.

Adaptive band‐limited disturbance rejection in linear discrete‐time systems

The problem of adaptively rejecting a disturbance consisting of a linear combination of sinusoids with unknown and/or time varying frequencies for SISO LTI discrete‐time systems is considered. The rejection of the disturbance input is achieved by constructing the set of stabilizing controllers using the Youla parametrization and adjusting the Youla parameter to achieve asymptotic disturbance rejection. The first main result in this paper concerns off-line controller design where a controller that achieves regulation is numerically designed off‐line based on the assumption that only the sequence of discrete disturbance input values (as opposed to a model of the disturbance) is available. A least squares based optimization algorithm is used in the controller design. As expected, it is shown, under some mild assumptions, that if the off‐line designed controller achieves regulation, then it must include a model of the disturbance input. The second main result concerns on-line controller design where recursive versions of the off‐line algorithm used above for controller design are presented and their convergence properties analyzed. Conditions under which the on‐line algorithms yield an asymptotic controller that achieves regulation are presented. Conditions both for the case where the disturbance input properties are constant but unknown and for the case where they are unknown and time‐varying are given. The on‐line controller construction amounts to an adaptive implementation of the Internal Model Principle. The performance robustness of the off‐line designed controller in the face of plant model uncertainties is investigated. It is shown, under some mild assumptions, that performance robustness is realized provided internal stability is maintained. The performance of the adaptation algorithms is illustrated through a simulation example.

Synthesis of discrete‐time nonlinear feedforward/feedback controllers

AbstractThis work concerns the synthesis of discrete‐time feedforward/feedback control systems for general nonlinear processes with stable zero dynamics. Depending on the process under consideration, the derived feedforward/feedback controllers can completely eliminate the effect of measurable disturbances and produce a prespecified linear response with respect to a reference input, or provide integral‐square error optimal response to step changes in the disturbances and a prespecified linear response with respect to a reference input. In either case, the developed feedforward/feedback controllers allow for the asymptotic rejection of unmeasurable disturbances. These controllers are derived within the globally linearizing control frame‐work, first under full state information and then in the absence of state measurements. The internal stability of the closed‐loop system is addressed. The derived controllers are interpreted from a model‐predictive point of view, and their connections with the feedforward internal model control and the model algorithmic control are established. The theoretical results are illustrated through a continuous stirred‐tank reactor example.

On the Output Dead-Beat Controller with Asymptotic Disturbance Rejection

On the Output Dead-Beat Controller with Asymptotic Disturbance Rejection

Robust H-infinity control synthesis method and its application to benchmark problems

This paper presents a robust H-infinity control synthesis method for structured parameter uncertainty. The robust H-infinity control design methodology is also incorporated with the so-called internal model principle for persistent-disturbance rejection. A noncollocated control problem of flexible space structures subject to parameter variations is used to illustrate the design methodology. It is shown that the proposed design method invariably makes use of nonminimum-phase compensation and that it achieves the desired asymptotic disturbance rejection by having a disturbance rejection 'dipole'.

Asymptotic disturbance rejection for momentum bias spacecraft

short duration is such that a right switch following closely on an initial left break by E ceases to be effective. The pursuer of course initially runs directly toward the evader, and in this case E breaks to one side or the other when the separation is only slightly more than L. The subsequent composite motions end with E at E2, where his heading makes only about 10 deg with the sideline. E has gained about 10 yd compared with the final position E}. The diagram here indicates that the players are in contact at the tackle range over the majority of the time, as shown by the curved dashed lines.

Robust tracking and regulation of linear periodic discrete-time systems

In this paper the robust asymptotic tracking and disturbance rejection problem is studied for linear periodic discrete-time systems, and for general classes of disturbance functions and reference signals, consisting in free responses of periodic processes. The necessary and sufficient conditions for the existence of a solution, which involve the periodic notion of invariant zero, are found. A constructive design procedure of the periodic compensator is given; it is based on the internal model principle.

Design of Multivariable Control Systems for Linear Periodic Processes *

Abstract In this paper the asymptotic tracking and disturbance rejection problem is studied for linear periodic discrete-time systems under parameter uncertainties, and for general classes of disturbance functions and reference signals, consisting in free responses of periodic processes. The necessary and sufficient conditions for the existence of a solution, which involve the periodic notion of invariant zero, are found, assuming that some measurements are available in addition to the controlled outputs. A constructive design procedure of the periodic compensator is contained in the sufficiency proof