Adaptive compensation strategy for the tracking/rejection of signals with time-varying frequency in digital repetitive control systems (original) (raw)
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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.
Stability analysis of digital repetitive control systems under time-varying sampling period
IET Control Theory & Applications, 2011
Repetitive control is an internal model principle-based technique for tracking periodic references and/or rejecting periodic disturbances. Digital repetitive controllers are usually designed assuming a fixed frequency for signals to be tracked/rejected, its main drawback being a dramatic performance decay when this frequency varies. A common approach to overcome this problem consists of an adaptive change of the sampling time according to the reference/disturbance period variation. Such a structural change may indeed compromise closed-loop stability. Nevertheless, no formal stability proofs are reported in the literature. This study addresses the stability analysis of a digital repetitive control system operating under time-varying sampling period. The procedure adapts the robust control approach introduced by Fujioka and Suh, which treats the time-varying parts of the system description as norm-bounded uncertainties, to the special features of digital repetitive control systems. This results in a conservatism reduction leading to an improvement in the obtained stability intervals. The proposed technique is also applicable to a more general class of systems incorporating a discrete-time dynamic controller. The article is completed with the application of the method to two standard examples in the repetitive control literature. Experimental results confirm the theoretical predictions.
Iet Control Theory and Applications, 2011
Repetitive control is an internal model principle-based technique for tracking periodic references and/or rejecting periodic disturbances. Digital repetitive controllers are usually designed assuming a fixed frequency for signals to be tracked/rejected, its main drawback being a dramatic performance decay when this frequency varies. A common approach to overcome this problem consists of an adaptive change of the sampling time according to the reference/disturbance period variation. Such a structural change may indeed compromise closed-loop stability. Nevertheless, no formal stability proofs are reported in the literature. This study addresses the stability analysis of a digital repetitive control system operating under time-varying sampling period. The procedure adapts the robust control approach introduced by Fujioka and Suh, which treats the time-varying parts of the system description as norm-bounded uncertainties, to the special features of digital repetitive control systems. This results in a conservatism reduction leading to an improvement in the obtained stability intervals. The proposed technique is also applicable to a more general class of systems incorporating a discrete-time dynamic controller. The article is completed with the application of the method to two standard examples in the repetitive control literature. Experimental results confirm the theoretical predictions.
Non-uniform sampling in digital repetitive control systems: an LMI stability analysis
2009
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. This report presents a stability analysis of a digital repetitive controller working under time-varying sampling period by means of an LMI gridding approach. Theoretical developments are illustrated with experimental results.
Digital Repetitive Control under Nonuniform Sampling: An LMI Stability Analysis
Mathematical Problems in Engineering, 2011
Digital repetitive control is a technique which allows tracking periodic references and/or rejecting periodic disturbances. Repetitive controllers are usually designed assuming a fixed fundamental frequency for the signals to be tracked/rejected and 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 period according to the reference/disturbance period variation. This paper presents a stability analysis of a digital repetitive controller working under time-varying sampling period by means of an LMI gridding approach. Theoretical developments are illustrated with experimental results, which are preceded by a detailed description of fundamental issues related to the implementation procedure.
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.
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.
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.
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.
Repetitive Control Design for the Possible Digital Feedback Control Configurations
Advances in the Astronautical Sciences, 2018
Digital repetitive control (RC) seeks to make a feedback control system converge to zero tracking error at each sample time following a periodic command. Many spacecraft sensors perform repeated periodic scanning maneuvers. Zero tracking error might best be accomplished by observing previous period error and computing the needed correction from the system inverse. Unfortunately, discrete time equivalents of continuous time models usually have zeros introduced outside the unit circle, making the inverse model unstable. The asymptot-ic pattern of zero locations is known in general for each pole excess. One can cancel all dynamics inside the unit circle, but one cannot cancel the zeros outside. The authors and co-workers have developed several RC methods to design FIR filters that compensate these zeros, each making its own pattern of additional zeros outside. Previous literature considers many pole excesses, but normally only considers a continuous time feedback system converted to discrete time. More general applications need to handle general digital feedback control systems , with digital controller, but continuous time plant, possible anti-aliasing filter , possible sensor noise filter, etc. It is the purpose of this paper to examine what the possible patterns of zero locations can be for these different situations. New situations occur with repeated original zero pattern outside the unit circle, or neighboring zeros outside, or the union of zero patters for two different pole excesses. Each RC approach addresses these situations differently. Generally, the RC based on inverse frequency response tends to produce the best result, but the other approaches develop understanding of the source of observed compen-sator zero patterns.