An adaptive “quasi” repetitive controller for the fundamental frequency estimation of periodic signals (original) (raw)
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.
Journal of Sound and Vibration, 1998
An alternative feedback structure, inspired from a speech coding structure, is introduced for the adaptive active control of periodic and time-varying periodic disturbances. The new structure is an Internal Model Control (IMC) structure. It separates the information and the processing pertaining to the plant from the information and the processing pertaining to the disturbance signal. A non-causal filter modelling the inverse of the secondary path is used, and the future samples of the disturbance signal are estimated by linear prediction (using an LMS algorithm). No filtering of a reference signal with the model of the secondary path is required to compute a filtered reference signal. In consequence, for the cases presented in the paper, the new feedback structure has a much faster convergence behavior and a better transient response than the classical FX-LMS algorithm with a feedback IMC structure, or the more recent and usually faster ANC-LMS algorithm with the same IMC structure. Simulation results with experimentally measured primary and secondary paths of a beam are presented, showing that either for multi-harmonic disturbance signals or sweeping sine wave disturbances, the structure presented in this paper greatly improves the convergence behavior of an adaptive feedback controller.
Real-Time Estimate of Velocity and Acceleration of Quasi-Periodic Signals Using Adaptive Oscillators
IEEE Transactions on Robotics, 2000
Estimation of the temporal derivatives of a noisy position signal is a ubiquitous problem in industrial and robotics engineering. Here, we propose a new approach to get velocity and acceleration estimates of cyclical/periodic signals near to steady-state regime, by using adaptive oscillators. Our method combines the advantages of introducing no delay, and filtering out the high-frequency noise. We expect this method to be useful in control applications requiring undelayed but smooth estimates of velocity and acceleration (e.g., velocity control and inverse dynamics) of quasi-periodic tasks (e.g., active vibration compensation, robot locomotion, and lower-limb movement assistance).
MIMO multi-periodic repetitive control system: universal adaptive control schemes
International Journal of Adaptive Control and Signal Processing, 2006
This paper presents a simple adaptive multi-periodic repetitive control scheme when the MIMO LTI plant is not necessarily positive real (PR), however it is strictly minimum-phase, the spectrum of high-frequency gain matrix CB is symmetric and lies in the open right/left half complex plane(sign/spectrum definite). The non-identifier-based direct adaptive control technique, which does not need plant parameter information, is used to construct adaptive schemes and the system stability is analysed by Lyapunov second method. The extension to plant under certain non-linear perturbations and an exponential stability scheme are also discussed. Finally, an adaptive proportional plus multi-periodic repetitive control scheme is proposed. The theoretical findings are supported with simulations.
A new viewpoint on the internal model principle and its application to periodic signal tracking
2010
Periodic signal tracking is certainly easier than general signal tracking. This has been manifested for linear time-invariant systems by applying theories of repetitive control. However, because of the lack of corresponding theories, the difficulties in designing repetitive controllers for both periodic signal tracking and general signal tracking in nonlinear systems are similar or the same. In view of this, this paper proposes a new viewpoint on the internal model principle which is used to explain how the internal models work in the time domain when the desired signals are step signals, sine signals and general periodic signals, respectively. Guided by this viewpoint, the periodic signal tracking problem is considered as a stability problem for nonlinear systems. To demonstrate the effectiveness of this new viewpoint, a new method of designing repetitive controllers is proposed for periodic signal tracking of nonminimum phase nonlinear systems, where the internal dynamics are subject to a periodic disturbance. A simulation example illustrates the effectiveness of the new method.
International Journal of Control, 2011
This article introduces and analyzes the performance features of different design schemes for digital repetitive control systems subject to references/disturbances that exhibit non-uniform frequency. Aiming for the maintenance of a constant value for the ratio T p /T s , where T p is the period of the reference/disturbance signal and T s is the sampling period, two approaches are proposed. The first one deals with the realtime adaptation of T s to the actual changes of T p ; the stability issue is studied by means of an LMI gridding method and also using robust control techniques. The second one propounds the introduction of an additional compensator that annihilates the effect of the time-varying sampling in the closed-loop system and forces its behavior to coincide with the one corresponding to an a priori selected nominal sampling period; the procedure needs the internal stability of the compensator-plant subsystem, which is checked by means of LMI gridding. The theoretical results are experimentally tested and compared through a mechatronic plant model.