Harmonic Disturbance Rejection Research Articles

Wheeled Robot Formation Control under Uncertainty Including Adaptive Rejection of Harmonic Disturbances with Arbitrary Frequencies

This work addresses an adaptive regulation problem for formation control of uncertain unicycle-like dynamical robots. The control goal is to drive a finite number of robots to a prescribed formation despite the presence of multi-sinusoidal input disturbances of unknown frequencies and despite uncertainties in the unicycle model, (mass and inertia’s are unknown). Numerical Simulations were done to illustrate the viability of the suggested strategy. The only measurements available for control are the orientation of the unicycles and the relative positions and velocities according to a given connectivity graph.

Robust Optimized Current Controller Based on a Two-Step Procedure for Grid-Connected Converters

Proportional-resonant controllers are largely used for grid-connected converters with LCL filters to ensure sinusoidal reference tracking and harmonic disturbance rejection. However, the design of such controllers becomes more difficult when it is necessary to ensure stability and suitable performance for converters operating under uncertain grid conditions, from stiff to weaker, and also when the number of resonants increases. In this more challenging scenario, available design procedures may lead to a poor tradeoff between transient and steady-state performances. To overcome this problem, this paper proposes an off-line automated control design procedure to obtain multiple robust optimized proportional-resonant controllers. The proposed procedure consists of two steps, where a particle swarm algorithm is used to obtain: i) the gains of an inner loop ensuring optimal active damping for the LCL filter resonance; ii) the gains of multiple proportional-resonant controllers by minimizing a tracking error index, taking into account uncertain grid impedance and control signal limits. The robust stability of the closed-loop system with the control gains tuned by the metaheuristics is certificated through a parameter-dependent Lyapunov function, constructed based on linear matrix inequalities. Several results from control Hardware-in-the-loop are presented for a case study, revealing that the proposal provides better performance in terms of reference tracking and disturbance rejection, when compared to similar control strategies from the literature. Experimental results from a prototype connected to the utility grid attest the practical feasibility of the proposed procedure.

Selective Periodic Disturbance Elimination Using Extended Harmonic State Observer for Smooth Speed Control in PMSM Drives

The elimination of periodic torque disturbance in permanent magnet synchronous machine (PMSM) drives is a multifrequency control task, and adding resonant parts to the controller has an impact on the robustness of the system. This article aims to address the torque-ripple reduction in PMSM drives for smooth speed control, where an extended harmonic state observer (EHSO) is designed for estimation and attenuation of the selective periodic disturbance. The defects of applying the conventional bandwidth-parameterization method to the harmonic disturbance observer are explored. To improve the disturbance-rejection capability and the relative stability, a pole-placement strategy is proposed and analyzed through sensitivity function, which can preserve the comparable dynamic performance as the conventional extended state observer at the low-frequency range. The proposed EHSO also features easy parameter tuning and a modular structure for multiple harmonic disturbance rejection. Finally, the proposed method is evaluated on a laboratory PMSM platform.

Tuning of state-feedback multi-resonant controllers based on LQR using differential evolution metaheuristic

This paper proposes a generic methodology for tuning state-feedback multi-resonant (SF-MR) controllers in power electronics applications involving L, LC, and LCL filters. The tuning of the controllers is performed using differential evolution metaheuristic in conjunction with the well-known linear-quadratic regulator (LQR) approach. This optimization algorithm avoids the empirical trial-and-error method for adjusting the weighting values of Q and R matrices while minimizing the cost function based on a weighted sum of the total harmonic distortion of the controlled variables, control loop errors, and control signals saturation. Thus, an adequate approach to adjust LQR-SF-MR controllers is achieved, proving useful for controlling active power filters (APF) since non-sinusoidal control references are involved. Furthermore, the proposed tuning method is appropriate for controlling voltage source inverters (VSI) following sinusoidal references and feeding non-linear loads since the high rejection of harmonic disturbances is reached. The effectiveness of the proposed design methodology for controllers' tuning is tested in a current-controlled 3-phase 4-wire (3P4W) shunt-APF, grid-connected through both L and LCL filters, as well as in a voltage-controlled 3P4W VSI connected to non-linear loads with LC filters. The control performances of the systems are extensively evaluated through experimental results.

Retrospective cost adaptive harmonic disturbance rejection using dereverberated target models

This paper focuses on adaptive feedback disturbance rejection for lightly damped structures using retrospective cost adaptive control (RCAC). RCAC uses a target model of the closed-loop dynamics in order to enable controller adaptation. The target model captures specific features of the dynamics of the structure; in the SISO case, this information consists of the sign of the leading numerator coefficient, relative degree, and nonminimum-phase zeros of the discretized dynamics. The present paper investigates the feasibility of using a dereverberated transfer function (DTF) as the target model for harmonic disturbance rejection with unknown disturbances. In particular, the dereverberated target model (DTM) obtained by magnitude and phase averaging captures the magnitude and phase trend of the structure but ignores resonances and anti-resonances, thus providing a low-order target model for controller adaptation. The robustness of RCAC is investigated with the target model given by a DTF based on a nominal model with erroneous damping ratio. The technique is implemented experimentally on an acoustic noise control setup.

A discrete repetitive sliding mode multicontrol for non-linear systems

The identification and the design of an accurate control are still an active researches of nonlinear systems subject to harmonic disturbances. In this paper, we propose two techniques to deal with nonlinear system identification and control problems. First, a new identification scheme based only on input/output measurements is proposed. In this scheme, an adaptive filter is used to extract the periodic disturbance and the non-perturbed system dynamics from the real output. Then, a multimodel approach is adopted to obtain the models base of the real non-perturbed system. Secondly,the models base is used to develop a multi-model sliding mode control (MM-SMC). Thereafter, the structure of plug-in repetitive control is incorporated into the MM-SMC to ensure good closed loop performances in terms of harmonic disturbance rejection and tracking in the case of nonlinear systems. Simulation results of two numerical examples shows the effectiveness of the proposed identification and control strategies in spite the presence of nonlinearities and harmonic disturbances.

State Feedback Regulation Problem to the Reaction-Diffusion Equation

In this work, we explore the state feedback regulator problem (SFRP) in order to achieve the goal for trajectory tracking with harmonic disturbance rejection to one-dimensional (1-D) reaction-diffusion (R-D) equation, namely, a partial differential equation of parabolic type, while taking into account bounded input, output, and disturbance operators, a finite-dimensional exosystem (exogenous system), and the state of the exosystem as the state to the feedback law. As is well-known, the SFRP can be solved only if the so-called Francis (regulator) equations have solution. In our work, we try with the solution of the Francis equations from the 1-D R-D equation following given criteria to the eigenvalues from the exosystem and transfer function of the system, but the state operator is here defined in terms of the Sturm–Liouville differential operator (SLDO). Within this framework, the SFRP is then solved for the 1-D R-D equation. The numerical simulation results validate the performance of the regulator.

Frequency-adaptive cancellation of harmonic disturbances at non-measurable positions of steel strips

The active rejection of harmonic disturbances is of great importance in many industrial applications. For instance, transverse vibrations of steel strips in hot-dip galvanizing lines entail an inhomogeneous zinc coating of the final product. Controlling the vibrations of these steel strips is particularly complicated because their direct measurement at the relevant location is not available. More specifically, the disturbance input, the displacement measurement, the electromagnetic actuator which acts as control input, and the system output to be controlled are all located at different positions along the steel strip. The control scheme proposed in this work minimizes the harmonic steady-state response of the system output to be controlled. In contrast to a state–space approach, the method does not utilize a high-dimensional state observer, and requires only modest computational resources during online operation. Furthermore, negative effects in the closed-loop system due to observation or control spillover are effectively avoided. The developed harmonic disturbance rejection scheme is validated by experiments conducted on a test rig that mimics the conditions from an industrial hot-dip galvanizing line.

A Stable Adaptive Gradient Descent Harmonic-Disturbance Rejection for Improving Phase-Tracking Accuracy

This paper proposes a stable adaptive gradient descent for harmonic-disturbance rejection as a tool for grid-power signal processing, magnetic rotary encoders, and permanent-magnet synchronous motors. The method can be widely applied to increase the accuracy of phase or position estimation in various systems in which harmonic disturbances exist. The proposed technique is based on learning the harmonic amplitudes by means of gradient descent on the feedback phase error. To compensate for the disadvantages of existing gradient-descent methods, the derivative expansion is fully developed with system transfer function integration for stable weighting update. In addition, an adaptive learning rate is also proposed based on discrete Lyapunov standard to achieve stability, and theoretical analysis is discussed. The performance of the method is evaluated by numerical simulation in MATLAB with various scenarios, and by the experiment with the rotary magnetic encoders. The results show that the proposed method achieves stability and high performance in harmonic rejection.

Unbalance and Harmonic disturbance attenuation of a flexible shaft with active magnetic bearings

Abstract Active magnetic bearings (AMB)s are attractive replacement of hydrostatic bearings mainly due to the absence of mechanical frictions, high-precision and low maintenance costs in high-speed and high-precision applications. However, they are inherently open-loop unstable and hence feedback controllers are essential for stabilisation of AMB equipped systems. This paper studies the robust stabilization and harmonic disturbance rejection of a flexible shaft and an AMB system. Firstly, a H ∞ loop-shaping method is utilized to stabilize the flexible shaft while the system is stationary. Then, an inner-loop is introduced to the feedback loop to minimize vibration performance measures while the shaft is in rotation at various rotational speeds. The inner-loop aims to combine the features of the common disturbance observer-based controllers and the repetitive controllers. The performance of the developed algorithm is experimentally verified on a multi-input-multi-output active magnetic bearing system. The experimental results demonstrate that the combination of the feedback H ∞ - controller and the inner-loop repetitive disturbance observer-based controller (RDOBC) not only robustly stabilizes the AMB system and greatly reduces the gain amplification of harmonic disturbances at fundamental frequencies, but it also reduces the gain amplification of the non-repetitive frequencies substantially.

Small signal modelling and control of high gain coupled inductor boost inverter for solid oxide fuel cell based power generation system

Small signal model of high gain coupled inductor boost inverter is established in presented work. Developed small signal model is then integrated with the model of planar solid oxide fuel cell and simulation of complete system is realized using MATLAB/Simulink environment and compared with the already developed fuel cell-based power converters. Coupled inductor boost converter was chosen to achieve higher gain in dc link voltage by selecting the appropriate turn ratio. Small signal model for dc-dc and dc-ac stages is derived separately and accordingly control system is designed. Dual loop with feed forward control scheme for coupled inductor boost inverter resulted in good performance like stable dc link, fast transient response, low total harmonic distortion (THD) and input disturbance rejection. Mathematical analysis, simulation and hardware results prove the stability and reliability of the complete system.

Finite Control Set–Model Predictive Control with Modulation to Mitigate Harmonic Component in Output Current for a Grid-Connected Inverter under Distorted Grid Conditions

This paper presents an improved current control strategy for a three-phase grid-connected inverter under distorted grid conditions. In terms of performance, it is important for a grid-connected inverter to maintain the harmonic contents of inverter output currents below the specified limit even when the grid is subject to harmonic distortion. To address this problem, this paper proposes a modulated finite control set–model predictive control (FCS-MPC) scheme, which effectively mitigates the harmonic components in output current of a grid-connected inverter. In the proposed scheme, the system behavior in the future is predicted from the system model in the discrete-time domain. Then, the cost function is selected based on the control objective of system. This cost function is minimized during the optimization process to determine the control signals that minimize the cost function. In addition, since the proposed scheme requires pure sinusoidal reference currents in the stationary frame to work successfully, the moving average filter (MAF) is employed to enhance the performance of the traditional phase lock loop (PLL). Due to the control performance of the FCS-MPC scheme as well as the harmonic disturbance rejection capability of the MAF-PLL, the proposed scheme is able to suppress the harmonic distortion even in the presence of distorted grid condition, while retaining fast transient response. Comparative simulation results of different controllers verify the effectiveness of the proposed control scheme in compensating the harmonic disturbance. To validate the practical feasibility of the proposed scheme, the whole control algorithm is implemented on a 32-bit floating-point digital signal processor (DSP) TMS320F28335 to control a 2 kW three-phase grid-connected inverter. As a result, the proposed scheme is a promising approach toward improving the current quality of a grid-connected inverter under distorted grid conditions.

Adaptive rejection of harmonic disturbance anticollocated with control in 1D wave equation

In this paper, we consider the output regulation problem for a one dimensional wave equation with harmonic disturbance anti-collocated with control. We first design an adaptive observer by the measured output to estimate unknown parameters of the disturbance and recover the system state. Then by using the observer system and estimator of unknown harmonic disturbance, we construct an auxiliary system in which the control and the anti-collocated disturbance become collocated. By applying the Backstepping method for infinite dimensional system, we design an output feedback adaptive controller which regulates the output to zero and keeps all the states bounded.

Comparison between LCL Passive Damping Filters and Parallel Active Filter in a Solar Conversion Chain Connected to the Electrical Network with Nonlinear Loads

This article is focused on the production of electricity from a solar photovoltaic panel. Here the harmonics problem is treated as one of the issues of photovoltaic panel integration into the network. This work focuses on the rejection of harmonic disturbances caused by the presence of non-linear loads and static converters in the solar conversion chain connected to the network using: parallel active filters compared to traditional and modern solutions of passive filters (L, LC, LCL), damping LCL filters with series and parallel resistors. A simulation with Matlab/Simulink environment of the photovoltaic system is used considering: the DC-DC converter (boost), the parallel active filter, the passive filters, the network, a nonlinear load and a solar inverter performed for PWM control strategy. Conventional techniques (Fast Fourier Transform (FFT)) and instantaneous power methods ('p-q' Theory) are used to calculate and identify the harmonic current.

Harmonic disturbance attenuation in a three-pole active magnetic bearing test rig using a modified notch filter

This study is concerned with the problem of harmonic disturbance rejection in active magnetic bearing systems. A modified notch filter is presented to identify both constant and harmonic disturbances caused by sensor runout and mass unbalance. The proposed method can attenuate harmonic displacement and currents at the synchronous frequency and its integer multiples. The reduction of stability is a common problem in adaptive techniques because they alter the original closed-loop system. The main advantage of the proposed method is that it is possible to determine the stability margins of the system by few parameters. The negative phase shift of the modified notch filter can be tuned to achieve a desired phase margin, while the gain margin can also be adjusted separately. It is shown that the modified notch filter can be designed to suppress multiple harmonics at the same time. It is implemented on a three-pole magnetic bearing test rig to evaluate its performance. Simulation and experimental results indicate that the presented method can be successfully applied to compensate the periodic disturbances such as sensor runout and mass unbalance in active magnetic bearing systems.

A systematic approach for robust repetitive controller design

In this paper, a methodology for the synthesis of repetitive controllers to ensure periodic reference tracking and harmonic disturbance rejection is cast in a robust control framework. Specifically, the Lyapunov–Krasovskii theory is applied to derive LMI-based conditions for designing a state feedback control law with guaranteed stability and performance properties for system parameter variations. Practical experiments in commercial uninterruptible power supplies – UPS are considered to illustrate and discuss some practical implementation aspects of the proposed method.

Active Rejection of Harmonic Disturbances with Nonstationary Harmonically Related Frequencies Using Varying-Sampling-Time LPV Control

This paper presents a method for the active noise and vibration control (ANC/AVC) of harmonically related nonstationary disturbances using varying-sampling-time linear parameter-varying (LPV) controller. The frequencies are assumed to be known and varying within given ranges and they are multiples of one fundamental frequency.

Performance improvement of a three‐phase phase‐locked‐loop algorithm under utility voltage disturbances using non‐autonomous adaptive filters

This study proposes phase-locked-loop (PLL) algorithms, which are employed to improve the performance related to the estimation of the phase angle, as well as the frequency, in three-phase systems under utility voltage disturbances. The proposed PLL schemes are based on the three-phase instantaneous active power (3pPLL), which is composed of non-autonomous adaptive filters (AFs) operating in conjunction with a positive-sequence detectors (PSDs), yielding the AF-PSD-3pPLL algorithms operating in both three-phase (abc-axis) and two-phase (αβ-axis) stationary reference frames. The AFs are used to extract the fundamental components of the utility voltages, allowing an adequate rejection of harmonic disturbances, whereas the PSDs at fundamental utility frequency are employed for rejecting the power quality problem related to the utility unbalances. A complete stability analysis of the PLL systems is carried out. In addition, to validate the theoretical development, the dynamic response and the robustness of the proposed AF-PSD-3pPLL schemes are evaluated by means of simulation and experimental tests, taking into account utility disturbances, such as voltage harmonics and unbalances, voltage sags, phase-angle jumps and frequency variations. The effectiveness of the proposed PLL schemes are emphasised by means of a comparative analysis with the conventional 3pPLL algorithm.

Robust Single-Loop Direct Current Control of LCL-Filtered Converter-Based DG Units in Grid-Connected and Autonomous Microgrid Modes

This paper presents a robust direct single-loop current control scheme based on structured singular value (μ) minimization approach for induced-capacitor-inductor (LCL)-filtered distributed generation converters in grid-connected and isolated microgrid modes. Unlike the conventional H∞ -based approach, the proposed interface maintains perturbed system stability, under wide range of grid (or microgrid) impedance variation, without the application of any additional damping loops. Moreover, the performance of the perturbed system in terms of grid-voltage and harmonic disturbance rejection can be improved significantly by the adopted method. This is due to the less conservative nature of the μ-synthesis-based solution as it takes advantage of the additional structure introduced to the uncertainty block by the performance criteria. The salient features of the proposed controller are 1) single-loop direct current control of LCL -filtered converters with inherent damping of the LCL filter resonance without any need for additional damping loops; 2) robust stability and active damping performances by mitigating the LCL resonance under wide range of grid (or microgrid) impedance variation; 3) improving the performance of the current controller by removing its dependency on the grid-voltage feed-forward loop by providing high disturbance rejection feature against fundamental and harmonic voltage disturbances; 4) computationally efficient fixed-order structure with minimum sensor requirements (only grid-side currents are needed for feedback control). A comparative theoretical analysis, time-domain simulation results, and experimental test results are presented to show the effectiveness of the proposed control scheme.

REJECTION OF HARMONIC AND TRANSIENT DISTURBANCES OF A SMART STRUCTURE WITH PIEZOELECTRIC ACTUATORS

Light flexible structures are easily prone to vibrate due to external forces or due to forces generated in the inner structure. This situation is common in machinery or mechanical structures with rotational devices. The unwanted vibration of such structures can be compensated with the addition of piezoelectric actuators for active vibration control (AVC). The rejection of harmonic disturbances is frequently done with controllers based on the internal model principle. The goal of this research is to reduce the effect of harmonic disturbances with known (measured) time-varying frequencies acting on a system as well as to increase the damping of the system for the transient response (first mode of vibration). The experimental setup is made up of a slender aluminium flexible beam, a pair of piezoelectric actuators, an accelerometer and two DC motors, as well as the data acquisition and signal conditioning equipment. The harmonic disturbance is generated by DC motors. The control design utilizes an augmented description of the plant. The plant including the disturbance is modelled as a polytopic linear parameter-varying (pLPV) system. An observer-based gain-scheduling controller is calculated based on quadratic stability and the stability is guaranteed for the specified range of variation of the scheduling parameters, also restriction in the performance is introduced in the sense of the H 2 -norm. Experimental results show very good disturbance cancellation.