An adaptive “quasi” repetitive controller for the fundamental frequency estimation of periodic signals (original) (raw)
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Adaptive repetitive control of system subject to periodic disturbance with time-varying frequency
Repetitive Control (RC) has been widely used to track/reject periodic signal. However, RC alone fails to track any non-periodic reference signal. Another control scheme such as Model Reference Control (MRC) or Model Reference Adaptive Control (MRAC) is required to do such task. MRC is employed when the plant parameters are known, while MRAC is used when the plant parameters are unknown. Therefore, MRC/MRAC needs to be combined with RC in order to simultaneously track any reference signal (not necessarily periodic) and reject the periodic disturbance. The design of RC mostly assumes the constant frequency of disturbance which leads to the selection of a fixed sampling period. In practical, disturbance is possibly time-varying in frequency. The sampling period has to be carefully adjusted in order to keep the number of samples per period remains constant. This sampling period adjustments change the plant parameters. This paper proposes the design of MRAC combined with RC for system subject to periodic disturbance with time-varying frequency. As a preliminary, the design of MRC combined with RC is also discussed here.
Periodic signal frequency tracking via a shifted second-order generalized integrator
2013 Africon, 2013
Second-order generalized integrators have been extensively used for the frequency estimation of periodic input signal. In this paper a novel structure is proposed by considering two additional parameters into the estimation scheme. This results in frequency tracking processes that sensibly attenuate overshooting phenomena affecting the classical approaches. Moreover an opportune choice of such parameters makes the scheme more robust in presence of unaccounted noises. The convergence in case of generic periodic input signal is discussed.
IEEE Transactions on Circuits and Systems Ii-express Briefs, 2005
A feedforward modification for both positive-and negative-feedback schemes of repetitive control is described. It was shown that repetitive controllers can be a useful tool for tracking of periodic reference signals and compensation of periodic disturbances, in other words, for harmonic compensation. It was shown that the feedforward modification considerably improves the frequency response and performance, providing higher gains with enhanced selectivity. Simple analog circuits are presented to implement both positive-and negative-feedback repetitive schemes. A description of the circuits and their corresponding experimental frequency responses are also given.
Adaptive Repetitive Control for Periodic Disturbance Rejection with Unknown Period
International Journal of Industrial Electronics, Control and Optimization (IECO), 2020
In this paper, an adaptive repetitive controller (ARC) is proposed to reject periodic disturbance with an unknown period. First, a repetitive controller is designed when the disturbance period is known. In this case, the RC time delay is equal to the period of disturbance. Then, the closed-loop system with the RC controller is analyzed and the effect of RC gain, k, is studied analytically. It is shown that by increasing k, the steady-state error is reduced. It is dependent on the speed of the response convergence. Secondly, an adaptive fast Fourier transform (AFFT) algorithm is proposed to extract the accurate period of disturbance adaptively. Simulation results show that the period is converged to its true value even though varying the period. Also, simulation results about the effect of controller gain are in good agreement with analytical results. Finally, it is shown that the proposed method can decrease the amplitude and energy of output signal significantly.
Journal of Process Control, 2010
Digital repetitive control is a technique which allows to track periodic references and/or reject periodic disturbances. Repetitive controllers are usually designed assuming a fixed frequency for the signals to be tracked/rejected, its main drawback being a dramatic performance decay when this frequency varies. A usual approach to overcome the problem consists of an adaptive change of the sampling time according to the reference/disturbance period variation. However, this sampling period adaptation implies parametric changes affecting the closed-loop system behavior, that may compromise the system stability. This article presents a design strategy which allows to compensate for the parametric changes caused by sampling period adjustment. Stability of the digital repetitive controller working under timevarying sampling period is analyzed. Theoretical developments are illustrated with experimental results.
Adaptive asymptotic tracking of repetitive signals-a frequency domain approach
IEEE Transactions on Automatic Control, 1993
The problem of designing an adaptive tracking controller for repetitive reference signals is considered. It is assumed that the controlled plant is linear time invariant whose steady state behavior can be described by its frequency response. The proposed controller, being able to identify the gain and phase of a plant at selected frequencies, adjusts the I / 0 map at frequencies contained in the reference signal so as to achieve zero steady state errors. Hence, no structural knowledge of the plant has to be known in the proposed approach. However, the proposed controller does not alter the transient property of the plant, e.g., locations of poles. The transient property can be improved by adding feedback control action. In this note, a combination of the adaptive controller and a feedback LTI controller is studied.
IET Control Theory & Applications, 2014
The repetitive control is well known for rejecting the periodic disturbances. However, most of the existing repetitive control algorithms assume that either the plant is known or the disturbance period is fixed. This study proposes the digital design of adaptive repetitive control for a class of linear systems subject to time-varying periodic disturbances, whose periods are assumed to be identifiable. The proposed control is based on the direct adaptive control scheme and the internal model principle. A comparative study is conducted and the effectiveness of the approach is verified in simulations and experiments on a servo motor system.
Design of Robust Repetitive Control With Time-Varying Sampling Periods
IEEE Transactions on Industrial Electronics, 2014
This paper proposes the design of robust repetitive control with time-varying sampling periods. First, it develops a new frequency domain method to design a low-order, stable, robust, and causal IIR repetitive compensator using an optimization method to achieve fast convergence and high tracking accuracy. As such, a new stable and causal repetitive controller can be implemented independently to reduce the design complexity. The comprehensive analysis and comparison study are presented. Then, this paper extends the method to design a robust repetitive controller, which compensates time-varying periodic signals in a known range. A complete series of experiments is successfully carried out to demonstrate the effectiveness of the proposed algorithms.
An Adaptive Periodic-Disturbance Observer for Periodic-Disturbance Suppression
IEEE Transactions on Industrial Informatics
Repetitive operations are widely conducted by automatic machines in industry. Periodic disturbances induced by the repetitive operations must be compensated to achieve precise functioning. In this paper, a periodic-disturbance observer (PDOB) based on the disturbance observer (DOB) structure is proposed. The PDOB compensates a periodic disturbance including the fundamental wave and harmonics by using a time delay element. Furthermore, an adaptive PDOB is proposed for the compensation of frequency-varying periodic disturbances. An adaptive notch filter (ANF) is used in the adaptive PDOB to estimate the fundamental frequency of the periodic disturbance. Simulations compare the proposed methods with a repetitive controller (RC) and the DOB. Practical performances are validated in experiments using a multi-axis manipulator. The proposal provides a new framework based on the DOB structure to design controllers using a time delay element.
IEEE Transactions on Automatic Control, 2000
Repetitive controllers are generally applied to reject periodic disturbances and to track periodic reference signals with a known period. Their design is based on The Internal Model Principle, proposed by Francis and Wonham. This paper describes a new finite-dimensional SISO repetitive controller for two different classes of nonlinear plants. Simulation results show asymptotic tracking of the periodic reference signal by the proposed repetitive controller in closed loop up to the th harmonic frequency. A proof of robustness of the repetitive control system to small nonlinearities, like actuator nonlinearities, is provided.