Digital repetitive controller design via sampled-data delayed signal reconstruction (original) (raw)
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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.
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.
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.
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.
Discrete-Time Design of Dual Internal Model-Based Repetitive Control Systems
Applied Sciences
This paper presents a novel design of discrete-time dual internal model-based repetitive control systems. The design strategy is accomplished by combining general and high-order modified repetitive control schemes for simultaneous tracking repetitive tasks and rejection of uncertain periodic disturbances. The proposed controller is constructed from two different discrete-time internal models, rendering a dual internal model-based repetitive controller (DIMRC). The first internal model is intended to track repetitive commands with a fixed fundamental frequency. Meanwhile, the second internal model is coupled to compensate for an exogenous periodic disturbance with an uncertain frequency. The controller structure, stability conditions, and convergence analysis are discussed in this paper. The performance of the proposed controller is validated through simulation studies showing accurate tracking and excellent disturbance rejection simultaneously.
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.
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.
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.