Design and analysis strategies for digital repetitive control systems with time-varying reference/disturbance period (original) (raw)
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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.
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.
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.
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.
Robust design of repetitive control system
Repetitive controller is usually designed by assuming constant period of reference/disturbance signal, which leads to the selection of fixed sampling period. However, in practical, reference signal and disturbance are varying in period. Therefore, sampling period is carefully adjusted to overcome period variation, which makes characteristic of the plant is also changing. Robust design is employed to obtain pre-compensator which stabilizes closed loop repetitive system for all values of sampling period in the known interval. The design consists of two steps; constructing a nominal pre-compensator and designing robust pre-compensator which works well for large range of sampling period variation. In the design, time-varying plant parameters due to sampling period variation are treated as parametric uncertainties. The new form of pre-compensator which works with this robust design is also proposed.
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.
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.
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.