Unknown Sinusoidal Disturbances Research Articles

Adaptive Consensus Control for Linear Multi-Agent System with Unknown Sinusoidal Disturbances

This paper deals with consensus control for a multi-agent system, where agents are represented via state-space models. It is assumed that they are subjected to sinusoidal disturbances with unknown parameters in the input channel. The connections between the agents are represented by a cycle-free graph containing a spanning tree. An adaptive distributed control algorithm is proposed, guaranteeing asymptotic convergence of the agents’ states towards consensus, provided that the agent model satisfies the controllability condition. The control algorithm consists of a distributed observer, a distributed control law, and an adaptation law. The theoretical results are proven using LaSalle's invariance principle. Finally, a simulation example is presented to demonstrate the theoretical findings.

A Robust Adaptive Cancellation of Unknown Sinusoidal Disturbance

A robust adaptive controller that consists of a well-known PI controller and a robust frequency estimation in parallel was presented to cancel unknown sinusoidal disturbance in a stable linear time invariant system. The convergence of frequency estimation, the accurate cancellation of disturbance and the asymptotic stability of the overall feedback control system are analyzed by slow integral manifold and averaging method. The key advantages include asymptotically convergent cancellation for disturbance with much low frequency, the asymptotic stability of the whole error feedback system independent to the parameters of the plant and robust applicability in engineering. Simulation results validate the transient convergence performance and the steady-state anti-noise performance as well as the action of parameters of the proposed algorithm.

Rejection of sinusoidal disturbances for known LTI systems in the presence of output delay

This paper focuses on estimation and cancellation of unknown sinusoidal disturbances in a known LTI system with the presence of a known output delay. Parametrizing the disturbance and representing the delay as a transport PDE, the problem is converted to an adaptive control problem for ODE–PDE cascade. An existing state observer is used to estimate the ODE system states. The exponential stability of the equilibrium of the closed-loop and error system is proved. The perfect estimation of the disturbance and state is shown. Moreover, the convergence of the state to zero as t→∞ is achieved in the closed loop system. The effectiveness of the controller is demonstrated in a numerical simulation.

Cancellation of unmatched biased sinusoidal disturbances for unknown LTI systems in the presence of state delay

In this paper, the problem of unmatched unknown sinusoidal disturbance cancellation in the presence of delay in the virtual control input of unknown LTI systems, is solved. Firstly, the disturbance is parameterized. Secondly, the delay is represented as a transport PDE. These two steps allow us to approach the problem as an adaptive control design problem for an uncertain coupled ODE–PDE system. An infinite-dimensional backstepping procedure is employed to compensate the state delay and a finite-dimensional backstepping procedure is used to overcome unmatched disturbance condition. Finally, an adaptive controller is designed and it is proven that the equilibrium of the closed-loop system is stable, and that the state of the closed-loop system converges to zero as t→∞ while perfect disturbance estimation is achieved. The effectiveness of the controller is illustrated with a simulation example of a third-order system.

Adaptive sinusoidal disturbance cancellation for unknown LTI systems despite input delay

Solutions exist for the problems of canceling sinusoidal disturbances and compensating input delays. In this paper, two problems are considered simultaneously and an adaptive controller is designed to cancel unknown sinusoidal disturbances forcing an unknown linear time-invariant system in controllable canonical form despite input delay. The design is based on three steps, (1) parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector that depends on unknown disturbance parameters, (2) representation of the delay as a transport PDE, (3) design of the adaptive controller by using the backstepping boundary control technique for PDEs. It is proven that the equilibrium of the closed loop system is stable and the state of the considered system converges to zero as t→∞ with perfect disturbance estimation. The effectiveness of the controller is illustrated with a simulation example of a second order system.

Pitch Control Design for Tandem Lifting Body Catamaran by Aft Lifting Body Actuation

We design an adaptive controller to stabilize the pitch of the tandem lifting body catamaran with actuation of the aft lifting body for the case where the hydrodynamic and other parameters are not known a priori. We consider two scenarios: 1) we assume the pitch and the pitch rate to be available for feedback and 2) we use only the pitch rate and the pitch acceleration in the adaptive control design. Our designs are based on three steps: 1) parametrization of the unknown sinusoidal wave disturbance as the output of a known feedback system with an unknown output vector that depends on unknown disturbance parameters; 2) design of an adaptive disturbance observer for the wave disturbance; and 3) design of an adaptive controller. We demonstrate the effect of our control designs in simulations, using a time-domain seakeeping code, named AEGIR.

Multivariable Repetitive Sliding Mode Control with Frequency Estimator: Rejection of Sinusoidal Disturbances with Time Varying Frequency

In this paper a repetitive sliding mode control (RSMC) with frequency estimator for discrete multivariable systems to reject unknown sinusoidal disturbances is proposed. The RSMC can reject only the harmonic disturbances with known frequency. When, this frequency is unknown or varying in time, we use a new strategy based on the combination between the multivariable RSMC and an on-line frequency estimator. The simulation results are satisfactory and show a good performances in terms of tracking reference trajectories in spite of the presence of sinusoidal disturbances with time varying frequency.

Rotor Vibration Control of Active Magnetic Bearing System Using Adaptive Forced Balancing Method

The adaptive forced balancing (AFB) method was used to estimate and eliminate the rotor vibration with unknown amplitudes and frequencies in active magnetic bearing (AMB) feedback control systems. Firstly, the rotor vibration producing mechanisms of AMB were analyzed. Then, the AFB under the assumption of unknown rotational frequency and amplitude are designed. Finally the simulation results show that the AFB method proposed in this paper makes it possible to completely reject unknown sinusoidal disturbance in a closed loop control system

Adaptive Cancellation of Matched Unknown Sinusoidal Disturbances for LTI Systems by State Derivative Feedback

Solutions already exist for the problem of canceling sinusoidal disturbances by measurement of state or an output for linear and nonlinear systems. In this paper, we design an adaptive controller to cancel matched sinusoidal disturbances forcing a linear time-invariant system by using only measurement of state-derivatives. Our design is based on three steps; (1) parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector, (2) design of an adaptive disturbance observer and, (3) design of an adaptive controller. We prove that the equilibrium of the closed-loop adaptive system is globally uniformly asymptotically stable and locally exponentially stable. The effectiveness of the controller is illustrated with a simulation example of a second-order system.

An iterative algorithm of adaptive output control with complete compensation for unknown sinusoidal disturbance

The problem is considered for the output control of a linear, parametrically indeterminate object subjected to the effect of an external unknown, sinusoidal disturbing influence. The solution of this problem is found in the class of iterative adaptive algorithms involving the channels of stabilization and identification of the frequency of a disturbing influence.

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.

Asymptotic attenuation of a class of nonlinear systems with unknown sinusoidal disturbances

In this paper, nonlinear observers are incorporated into the adaptive control to synthesize controllers for a class of uncertain nonlinear systems with unknown sinusoidal disturbances which are presented in matched and unmatched forms. In addition to magnitudes and phases, frequencies of the sinusoidal disturbances need not be known as well, so long as the overall order is known. Nonlinear observers are constructed to eliminate the effect of unknown sinusoidal disturbances to improve the steady-state output tracking performance-asymptotic output tracking is achieved. The adaptation law is used to obtain the estimate of all unknown parameters. The presented disturbance decoupling algorithms can deal with matched and unmatched unknown sinusoidal disturbances.

Adaptive observer of an unknown sinusoidal output disturbance for linear plants

A new algorithm is proposed to the design of an adaptive observer for an unknown sinusoidal disturbance that affects the output of a non-minimum phase linear control plant.

Compensation of unknown sinusoidal disturbances in linear plants of arbitrary relative degree

A new algorithm is proposed for compensating parametrically uncertain harmonic disturbances. In contrast to the known results, the compensation is carried out in the situation where only the output variable and the control signal are measured, and the relative degree of the plant is arbitrary.

Asymptotic rejection of unknown sinusoidal disturbances in nonlinear systems

This paper deals with global disturbance rejection of nonlinear systems. The disturbance is assumed to be sinusoidal with completely unknown phases, amplitude, and frequencies, but the number of distinct frequencies or the order of the corresponding unknown linear exosystem is known. Different from the common structural assumptions of nonlinear systems needed in literature for disturbance rejection of nonlinear systems, the proposed method only requires the information of control design with a known Lyapunov function when the system is disturbance-free, and a mild assumption needed for internal model design. The proposed disturbance rejection algorithm extends complete global rejection of unknown sinusoidal disturbances for nonlinear dynamic systems beyond the common nonlinear models such as the strict feedback forms and the output feedback forms.

Adaptive disturbance rejection of nonlinear systems in an extended output feedback form

The author deals with asymptotic rejection of unknown sinusoidal disturbances for uncertain nonlinear systems in an extended output feedback form, which allows the vector field coupled with the system input to have different nonlinear functions of the system output as its elements. A new internal model design is proposed to deal with nonlinear functions of the system output that are coupled with the input and the unknown disturbance. Adaptive control techniques are then used to deal with the uncertainty in the system. The proposed adaptive disturbance rejection algorithm with the new internal model design ensures the asymptotic rejection of the unknown sinusoidal disturbance and the boundedness of all the variables.

Adaptive estimation and rejection of unknown sinusoidal disturbances in a class of non-minimum-phase nonlinear systems

The author deals with adaptive estimation of unknown disturbances in a class of non-minimum phase nonlinear systems, and the stabilisation and disturbance rejection based on the estimated disturbances. The unknown disturbances are the combination of sinusoidal disturbances with unknown frequencies, unknown phases and amplitudes. The only information of the unknown disturbances is the number of distinctive frequencies inside. The class of nonlinear systems considered by the author consists of nonlinear systems in the output feedback form and the systems may be non-minimum phase, that is with unstable zero dynamics. An adaptive estimation algorithm is developed to give exponentially convergent estimates of the unknown disturbance and the system states. The asymptotic convergent estimates of unknown frequencies are also obtained. The proposed estimation algorithm works for both minimum phase and non-minimum phase nonlinear systems in output feedback form. Disturbance rejection with stabilisation is achieved by combining the control designed for the stabilisation of the disturbance-free system and the exponentially convergent estimate of the disturbance. Under the conditions specified for the control design of the system with no disturbance, the overall stability and complete rejection of the unknown disturbance are guaranteed by the proposed control algorithm.

Nonlinear control of systems with multiple equilibria and unknown sinusoidal disturbance

In this paper, nonlinear systems having multiple equilibrium points and low order dynamics are investigated. Roll motions of ships are studied by means of modern nonlinear techniques to exemplify the behavior of such nonlinear systems in the case when they are under the influence of external sinusoidal disturbances with unknown amplitudes. The main objective is to analyze the performance of this system at different operating conditions, including those giving rise to chaos, and to design a controller with an overparameterized structure to stabilize the system at the origin. A nonlinear recursive backstepping controller is proposed and the transient performance is investigated. Lyapunov-based techniques are used to force systematic following of a reference model while introducing a nonlinear parameter estimator to guarantee adaptivity. Robustness problems as well as ways to tune the controller parameters are examined. Simulation results are submitted for the uncontrolled and controlled cases, verifying the effectiveness of the proposed controller. Finally, a discussion and conclusions are given with possible future extensions.

Adaptive estimation and rejection of unknown sinusoidal disturbances through measurement feedback for a class of non‐minimum phase non‐linear MIMO systems

AbstractThis paper develops an adaptive estimation method to estimate unknown disturbances in a class of non‐minimum phase non‐linear MIMO systems. The unknown disturbances are generated by an unknown linear exosystem. The frequencies, phases and amplitudes of the disturbances are unknown, the only available information of the disturbances is the number of distinctive frequencies. The system considered in this paper is a class of MIMO non‐linear systems in the output feedback form which can be non‐minimum phase. The proposed estimation algorithm provides exponentially convergent estimates of system states, unknown disturbances in the system and frequencies of the disturbances characterized by the eigenvalues of the exosystem. Moreover, based on the stabilization controller for the disturbance free system, the estimates of the disturbances are used to solve the disturbance rejection problem. The unknown disturbances are compensated completely with the stability of the whole closed‐loop system. Copyright © 2006 John Wiley & Sons, Ltd.

Global compensation of unknown sinusoidal disturbances for a class of nonlinear nonminimum phase systems

A class of output feedback stabilizable nonlinear systems with known output dependent nonlinearities and affected by unknown sinusoidal disturbances is considered: Nonminimum phase systems are also allowed. The problem of designing a global output feedback compensator which drives the state of the system exponentially to zero is solved when the disturbance consists of a known number of biased sinusoids with any unknown bias, magnitudes, phases, and frequencies.