Rejection Of Sinusoidal Disturbances Research Articles

Rejection of Sinusoidal Disturbances With Unknown Slowly Time-Varying Frequencies for Linear Time-Varying Systems

Abstract Recently, a class of adaptive schemes has been developed for rejecting sinusoidal output disturbances with unknown frequencies, phases, and amplitudes. These adaptive schemes require an accurate model of the affected system's dynamics to function, and the controller performance degrades as the modeling error increases. While linear time-invariant (LTI) dynamics can adequately model the dynamics of some systems, a time-varying model of the system dynamics is more appropriate in certain scenarios. This paper proposes a robust adaptive scheme for rejecting disturbances that affect the output of a system described by a known linear time-varying model. The disturbances are described by an unknown number of sinusoidal terms with unknown time-varying frequencies. Analysis is done in ideal case where the disturbance frequencies are perfectly known to provide conditions guaranteeing the existence of a controller and a corresponding set of parameters which reject the disturbance. Analysis is then done in the more realistic adaptive scenario where the disturbance frequencies are unknown, and a robust adaptive scheme for selecting controller parameters which reject the disturbance is proposed. Performance of the controller with respect to the speed of variation in the plant model parameters is assessed via simulation.

Rejection of Sinusoidal Disturbances with Unknown Slowly Time-Varying Frequencies For Linear Time-Invariant Systems

Rejection of Sinusoidal Disturbances with Unknown Slowly Time-Varying Frequencies For Linear Time-Invariant Systems

Enhanced Voltage Regulation for PV Power Conversion Using Quasi-Proportional Resonant Extended State Observer

Extended state observer (ESO) is a promising control technology thanks to its robustness against model inaccuracy. This article expands the application of an ESO-based control scheme to digitally regulate a grid-tied photovoltaic (PV) power converter. It focuses on mitigating the steady-state disturbance resulting from the dc to single-phase ac conversion and dynamic disturbances caused by solar irradiance and voltage reference changes. The development is based on an in-depth analysis of PV power systems regarding the nonlinear and time-variant features. Thanks to the disturbance rejection loop, the active damping function is naturally offered, which boosts the system damping without extra sensors or complex model-based tuning. A new ESO scheme, namely quasi-proportional resonant ESO, is developed by the frequency-domain analysis, which enables the precise tracking and rejection of fast-varying sinusoidal disturbance at the targeted frequency. The advantages include simple and intuitive tuning, easy implementation, and enhanced transient and steady-state control performance. A 1.5-kW laboratory platform is built to verify the effectiveness and practicality of the proposed control scheme.

Adaptive Rejection of a Sinusoidal Disturbance with Unknown Frequency in a Flexible Rotor with Lubricated Journal Bearings

Frequency-dependent adaptive noise cancellation-based tracking controller (ANC-TC) is a known technique for the stabilization of several nonlinear dynamical systems. In recent years, this control strategy has been introduced and applied for the stabilization of a flexible rotor supported on full-lubricated journal bearings. This paper proposes a theoretical investigation, based on robust immersion and invariance (I&I) theory, of a novel ANC-frequency estimation (FE) technique designed to stabilize a flexible rotor shaft affected by self-generated sinusoidal disturbances, generalized to the case of unknown frequency. A structural proof, under assumptions on closed-loop output signals, shows that the sinusoidal disturbance rejection is exponential. Numerical simulations are presented to validate the mathematical results in silico. The iterative Inexact Newton method is applied to the disturbance frequency and phase estimation error point series. The data fitting confirms that the phase estimation succession has an exponential convergence behavior and that the asymptotical frequency estimation is a warm-up phase of the overall close-loop disturbance estimation process. In two different operating conditions, the orders of convergence obtained by phase and frequency estimate timeseries are pφ=1, pω,unc=0.9983 and pω,cav=1.005. Rejection of the rotor dynamic disturbance occurs approximately 76% before in the cavitated than in the uncavitated condition, 2 (s) and 8.5 (s), respectively.

Centralized and decentralized adaptive harmonic control for sinusoidal disturbance rejection

This paper presents two new algorithms for rejection of known-frequency sinusoidal disturbances that act on a completely unknown, multi-input multi-output, asymptotically stable, linear time-invariant system. The first algorithm is centralized adaptive harmonic control (AHC), which does not impose any structural constraints on the input–output channels of the controller. The second algorithm is decentralized AHC, which imposes the constraint that each local control is computed using only local sensor measurements. These new control methods are data-driven, adaptive algorithms that do not rely on any information regarding the system. It is also worth noting that all control computations are performed using discrete Fourier transform data. The stability and closed-loop performance with each algorithm are analyzed. The main analytic results show that each algorithm asymptotically rejects sinusoidal disturbances. Illustrative numerical simulations and active noise control experiments demonstrate the effectiveness of centralized and decentralized AHC.

Estimation and rejection of sinusoidal disturbance with unknown frequency using cascade disturbance observer

A disturbance rejection approach is presented for a class of uncertain systems subject to sinusoidal disturbance with unknown frequency. The proposed disturbance estimation method includes two types of observers that are connected in cascade form. The disturbance property is excited through an auxiliary filter, and then a frequency factor observer is constructed to generate the information required by full-order state observer. Thus, with the disturbance and system state estimation values, the composite control structure including a cascade disturbance observer (CDO) and a robust feedback controller is designed. As a result, the uncertain system with unknown-frequency sinusoidal component can be controlled within the disturbance observer-based control (DOBC) framework, where the asymptotic stability performance can be guaranteed.

Time-Domain Adaptive Higher Harmonic Control for Rejection of Sinusoidal Disturbances

Abstract This paper presents two new time-domain feedback controllers that reject sinusoidal disturbances with known frequencies acting on an asymptotically stable linear time-invariant (LTI) system. The first controller is time-domain higher harmonic control (TD-HHC), which is effective for uncertain LTI systems. The second controller is time-domain adaptive higher harmonic control (TD-AHHC), which is effective for completely unknown LTI systems. TD-HHC requires an estimate of the control-to-performance transfer function evaluated at the disturbance frequencies. In contrast, TD-AHHC does not require any information regarding the LTI system. We analyze the stability and closed-loop performance of TD-HHC and TD-AHHC. For both TD-HHC and TD-AHHC, we show that the controller asymptotically rejects the disturbance. We present numerical simulations comparing TD-HHC and TD-AHHC with frequency-domain higher harmonic control (FD-HHC), which is an existing frequency-domain controller for rejection of sinusoidal disturbances. We also present results from acoustic disturbance rejection experiments, which demonstrate the practical effectiveness of both TD-HHC and TD-AHHC.

Robust adaptive motion tracking of piezoelectric actuated stages using online neural-network-based sliding mode control

Robust and precise motion tracking for micro-electro-mechanical systems in the presence of inherent nonlinearity and external disturbance is of great importance in many applications. Due to high sensitivity to environmental variations, the entire model or some parameters of the system tend to change unexpectedly. Existing offline nonlinearity models are computationally intensive and may be not suitable under system perturbations. In this work, for a class of piezoelectric actuated (PEA) system, a new online neural-network-based sliding mode control (OLNN-SMC) scheme is developed to obtain robust adaptive precision motions. The nonlinearity of the PEA system is identified online and compensated using singularity-free neural networks (NNs). To alleviate the residual NN approximation errors and meanwhile maintain robust stability under external disturbance, a feedback sliding-mode is synthesized into the control law. Considering unknown and varying disturbances, an adaptive mechanism is designed to achieve robust adaptive motion tracking. The controller is implemented and evaluated through experiments on a PEA platform. Results show that the proposed OLNN-SMC is superior to existing proportional-integral-derivative control with disturbance observer (PID+DOB) and adaptive sliding mode control (ASMC) in terms of sinusoidal tracking and disturbance rejection. In particular, the root-mean-square (RMS) errors for sinusoidal tracking at 0.1–10 Hz using the proposed OLNN-SMC are reduced by 83.5% compared with the cases using PID+DOB or ASMC.

Adaptive Harmonic Control for Rejection of Sinusoidal Disturbances Acting on an Unknown System

We present a sampled-data adaptive harmonic control algorithm that rejects sinusoids with known frequencies that act on a completely unknown asymptotically stable linear time-invariant system. We analyze the stability and closed-loop performance for systems with at least as many controls as performance measurements. We show that the closed-loop system is uniformly Lyapunov stable and the adaptive controller asymptotically rejects the disturbances. We present numerical simulations comparing the new sampled-data adaptive controller with an existing sinusoidal disturbance rejection approach (i.e., higher harmonic control). We also present results from an active disturbance rejection experiment in an acoustic environment. These experimental results demonstrate the practical effectiveness of the adaptive harmonic controller.

Rejection of time-varying frequency sinusoidal disturbance using refined observer for a class of uncertain systems

The time-varying frequency disturbance rejection problem is addressed for a class of nonlinear uncertain system. A novel refined disturbance observer (RDO) is developed composed of auxiliary observer and calibration observer. At first, the disturbance is redescribed using auxiliary observer after coordinate transformation, which contains a parametric form about frequency and a decay term. The derivative of frequency and system uncertain are absorbed in the decay term, furthermore, the correlation between disturbance frequency and disturbance can be derived. Then the key parameter, i.e. frequency factor is estimated by calibration observer characteristic with two-degree-freedom, the decay term associated with derivative of frequency can be attenuated in feedback control loop. Thus, the composite controller including a refined disturbance observer (RDO) and a robust feedback controller is designed, which inherits the elegant feature of disturbance observer based control (DOBC). The H∞ index performance can be guaranteed to attenuate the estimation error driven by disturbance time-varying frequency together with system uncertainty.

Dynamic Friction Characterization of a Linear Servo Motor Using an Optimal Sinusoidal Reference Tracking Controller

This letter presents the design of an optimal sinusoidal tracking and disturbance rejection controller for a linear voice-coil motor. The optimal tracking and disturbance rejection system is used to characterize the nonlinear dynamic friction of the servo motor. The control scheme allows investigating the hysteresis characteristics of friction as a function of frequency. Experimental results indicate the effectiveness of the proposed identification procedure for the dynamic friction estimation.

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.

Optimised active disturbance rejection motion control with resonant extended state observer

ABSTRACTTracking sinusoidal references with high precision and rejection of sinusoidal disturbances is a challenging task in the motion control practice. In order to deal with this control problem, a new resonant extended state observer is proposed and introduced in the active disturbance rejection control concept. The frequency analysis shows that an appropriate selection of resonant frequency provides complete rejection of sinusoidal disturbance and ideal reference tracking in the steady state. Further, it is shown that the proposed structure achieves better performances than generalised extended state observer based system in the wide frequency range. Moreover, in order to improve the system performances in transient period, the optimal parameter tuning method is developed. The results demonstrate that the optimally tuned system achieves better performances than the conventionally tuned one by about 25%, with the same robustness and noise sensitivity. The experimental validation of the new controller is carried out on the laboratory model of the didactic three-axis radar platform in fast sinusoidal reference tracking mode.

Adaptive harmonic steady‐state control for rejection of sinusoidal disturbances acting on a completely unknown system

SummaryThis paper presents an adaptive harmonic steady‐state (AHSS) controller that addresses the problem of rejecting sinusoids with known frequencies that act on a completely unknown asymptotically stable linear time‐invariant system. We analyze the stability and closed‐loop performance of AHSS for multi‐input multi‐output systems that are square (ie, the number of controls equals the number of performance measurements). In this case, we show that AHSS asymptotically rejects disturbances, that is, the performance measurement tends to 0. We also present a numerical study of the steady‐state and transient performance of AHSS for square and nonsquare systems.

Multivariable filtered Smith predictor for systems with sinusoidal disturbances

ABSTRACTThis paper presents a new design condition for the multivariable filtered Smith predictor (MFSP) in order to achieve sinusoidal disturbance rejection in steady state. The proposed MFSP strategy is based on a transfer matrix description with multiple delays. A suitable prediction error filter is presented to deal with this new design condition. The proposed design requirement can be used in model predictive controllers with inactive constraints in steady state. Two case studies are used to illustrate the main benefits of the proposed framework.

Multimodel repetitive–predictive control of nonlinear systems: rejection of unknown non-stationary sinusoidal disturbances

ABSTRACTIn the present work, we propose a supervised multimodel repetitive–predictive control scheme for discrete-time nonlinear systems in order to reject unknown non-stationary sinusoidal disturbances and to track reference trajectory. The nonlinear system is described by the decoupled state multimodel. Also, a non-stationary sinusoidal unknown input multi-observer is used to estimate the state and the unknown non-stationary sinusoidal disturbances simultaneously. The estimate of the disturbances is exploited by the magnitude–phase-locked loop (MPLL) approach to reconstruct the accurate disturbance period used to develop a robust supervised multi-rejector. The proposed control strategy provides good closed-loop performance despite the changes of the disturbance characteristics. A simulation example is provided to illustrate the significance of the proposed multi-rejector.

Adaptive Add-On Output Regulator for Rejection of Sinusoidal Disturbances and Application to Optical Disc Drives

In this paper, we revisit an add-on output feedback controller that achieves output regulation and disturbance rejection. By add-on controller, we mean an additional controller, which runs harmonically with a preinstalled controller that has been in operation for the plant. When the disturbance attenuation performance of the preinstalled controller is not satisfactory, the add-on controller can be used to eliminate the disturbance. Some advantages of the proposed add-on controller include that it can be designed without much information about the preinstalled controller and it can be plugged in the feedback loop any time in operation without causing unnecessary transient response. In particular, we propose an adaptive add-on controller, which can eliminate sinusoidal disturbances of unknown frequencies. Both simulation and experimental results of the track-following control for optical disc drive systems confirm the effectiveness of the proposed method.

Research on Modeling and Control Strategy for Two-Stage Photovoltaic Grid-Connected System

This paper has built the mathematic model of the single-phase two-stage photovoltaic(PV) grid-connected system. The model consists of a boost DC/DC converter and a DC/AC inverter with LCL filter. On the basis of the variable step perturbation and observation method(P&O), the boost converter changes the output voltage of the PV array by adjusting the duty cycle to realize the PV maximum power point tracking(MPPT). The inverter system restrains the voltage fluctuation effectively by using feed-forward of the grid voltage and current tracking control technology, which has the high performance in both sinusoidal reference tracking and disturbance rejection. LCL filter improves the dynamic performance and restrains the high harmonics efficiently. The simulation with Matlab soft confirms the effectiveness of the model and control strategy.

Biased Sinusoidal Disturbance Compensation With Unknown Frequency

This note combines an adaptive frequency estimation scheme with a fractional-order controller for unknown biased sinusoidal disturbance rejection. The disturbance is estimated via an adaptive orthogonal signals generator based on a third-order generalized integrator. A fractional-order controller is designed which guarantees the closed-loop stability of the system if the location of the plant frequency response, at the estimated frequencies, lies in an half-plane passing through the origin of the complex plane.

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.