Repetitive Control Design Research Articles

A multirate fractional-order repetitive control for laser-based additive manufacturing

This paper discusses fractional-order repetitive control (RC) to advance the quality of periodic energy deposition in laser-based additive manufacturing (AM). It addresses an intrinsic RC limitation when the exogenous signal frequency cannot divide the sampling frequency of the sensor, e.g., in imaging-based control of fast laser-material interaction in AM. Three RC designs are proposed to address such fractional-order repetitive processes. In particular, a new multirate RC provides superior performance gains by generating high-gain control exactly at the fundamental and harmonic frequencies of exogenous signals. Experimentation on a galvo laser scanner in AM validates effectiveness of the designs.

A Modified Feedback Scheme Suitable for Repetitive Control of Inverter With Nonlinear Load

It is mandatory to keep the total harmonic distortion in the output of most inverters below the limits prescribed by different international standards. The harmonic distortions caused due to nonlinear loads may not get corrected by typical magnitude controller, like PID controller. Repetitive controller is more effective in such situations. Often, repetitive controller is used as add-on block to the conventional magnitude controller. Design of repetitive controller can be easily implemented on digital platform. Rapid change in phase and magnitude of inverter-filter's transfer function near corner frequency causes instability problems in repetitive controller. Various techniques have been proposed by researchers to overcome this problem. Most of the reported techniques rely on digital compensation. However, it is hard to find a digital compensator, which simultaneously meets the phase and gain requirements at moderate computational effort. Here, a new output voltage feedback scheme has been proposed, which simplifies the requirement of digital compensation. The proposed scheme requires an extra hardware but at negligible added cost. In spite of this extra hardware, the proposed circuit turns out to be more energy efficient in comparison to few popular schemes, reported in literature, where some resistance is introduced in the inverter's filter for better stability of controller. In addition to the proposed modification the paper presents a simplified explanation of the various factors affecting stability of repetitive controller. The paper also discusses a novel experimental method for verifying the efficacy of repetitive controller in suppressing distortion of any particular harmonic order.

Robust design of high order repetitive controllers under control saturation

Abstract This paper presents a methodology to simultaneously design a high order repetitive controller (HORC) and an anti-windup compensator for systems subject to control saturation and parametric uncertainties. With the proposed structure it is possible to ensure a certain level of steady-state tracking and/or rejection performance when dealing with uncertain periodic signals. Based on a modified state-feedback formulation of the HORC and an static anti-windup structure, linear matrix inequality (LMI) conditions are proposed to guarantee closed-loop stability provided that the state trajectory and the reference/disturbance signals are inside admissible sets. A systematic procedure to determine upper bounds for the system initial conditions and maximum reference/disturbance values is also proposed. A numerical example illustrates the method.

Dual IM‐based ILC scheme for linear discrete‐time systems with iteration‐varying reference

A novel iterative learning control (ILC) scheme is proposed to improve the convergence rate of ILC by ensuring the convergence in both the time and iteration domains simultaneously. First, an iteration-varying reference is generated by a high-order IM (HOIM) along the iteration axis, and is approximated by an HOIM along the time axis. Then, the HOIM-based repetitive control (RC) and ILC design methods are introduced, which can update the input along the time and iteration axes, respectively. Motivated by the separately tracking abilities of the HOIM-based RC and ILC in the time and iteration domains, a new ILC scheme is proposed by incorporating both the time-domain and iteration-domain HOIMs of the reference. The new ILC scheme is the combination of the HOIM-based RC and ILC, which can update the input along both the time and iteration axes. The new ILC scheme consists of two loops: (i) the HOIM-based ILC loop can learn the control input from previous iterations and (ii) the HOIM-based RC loop can learn the control input from previous times at the current iteration. Moreover, the new ILC scheme is established on a dual-HOIM (DHOIM) that is the assembly of the two HOIMs of the reference. In consequence, the new ILC scheme is named as DHOIM-based repetitive ILC (RILC). On rthe basis of the two-dimensional H ∞ theory, a DHOIM-based RILC design criterion is presented. Meanwhile, it is shown that the convergence rate of the proposed DHOIM-based RILC scheme outperforms that of traditional ILC schemes. Finally, a microscale robotic deposition system is given to illustrate the efficiency of the proposed RILC scheme.

Simple approximate phase cancellation for repetitive control of CVCF PWM inverters

SummaryIn this paper, a simple approximate phase cancellation repetitive controller is proposed for a constant‐voltage constant‐frequency pulse‐width modulation inverter. The compensator is a linear combination of linear phase compensators, which can better fit the inverse of a plant model phase curve compared with the conventional linear phase compensator. Repetitive controllers with the proposed phase compensator can improve pulse‐width modulation inverter system's stability, tracking accuracy, and error convergence rate. An optimization method is applied to design the parameters of the proposed phase compensation repetitive controller. Analysis and design of the proposed repetitive controller are presented. Furthermore, simulations and experiments are provided to demonstrate the advantages of the approximate phase cancellation repetitive controller design.

Observer‐based tracking control for switched stochastic systems based on a hybrid 2‐D model

SummaryThis paper is concerned with the observer‐based output tracking problem for a class of linear switched stochastic systems with time delay and disturbance by using repetitive control approach. More precisely, a two‐dimensional hybrid model is incorporated to obtain and optimize the repetitive controller. In particular, the repetitive controller is used to improve the tracking performance through its continuous learning actions. In addition, an equivalent‐input‐disturbance estimator is incorporated into the repetitive control design approach to reduce the effect of the external disturbances. The main aim of the control design is to track the periodic reference signal with the measured output of the system under consideration even in the presence of an unknown bounded disturbance. By constructing a suitable Lyapunov‐Krasovskii functional and using average dwell time approach and Jensen inequality, sufficient conditions are obtained in terms of linear matrix inequalities to guarantee the mean‐square exponential stability of the considered system. Eventually, a numerical example is provided to demonstrate the effectiveness of the developed method.

Development and Repetitive Learning Control of Lower Limb Exoskeleton Driven by Electrohydraulic Actuators

This paper presents a novel development of lower limb exoskeleton, which is named as CASWELL, and its repetitive learning control design for movement assistance. CASWELL has five degrees of freedom per leg, two of which are driven by linear single-rod electrohydraulic actuators. First, the mechanical structure and embedded electronic system are constructed, respectively. Second, by incorporating the systems of rigid body and electrohydraulic actuators, the complete dynamics of CASWELL are analyzed and modeled. Third, under the framework of backstepping design, a repetitive learning control scheme is presented to address the periodic tracking control of lower limbs of exoskeleton, where the learning convergence of the closed-loop system is proved rigorously in a Lyapunov way. Finally, the proposed controller is implemented in the embedded electronic system via a 32-bit microcontroller, and tested on the developed CASWELL. The experimental results are given to demonstrate the performance of the whole exoskeleton system.

EID estimator-based modified repetitive control for singular systems with time-varying delay

This paper investigates the disturbance rejection for a modified repetitive control system (MRCS) that is described by a class of linear singular systems in the presence of external disturbances and time-varying delay. In particular, an equivalent-input-disturbance (EID)-based estimator is included in the MRCS to compensate both periodic and aperiodic disturbances which yields an EID-based MRCS. More precisely, the incorporation of the EID-based estimator into the control input enables rejection of all types of disturbances in MRCS and tracking of a periodic reference input is archived via a repetitive controller. Attention is focused on the state-feedback repetitive controller design which not only guarantees the regular, impulse free, and asymptotic stability of the closed-loop singular MRCS, but also provides an optimized upper bound of the time-varying delay. Based on Lyapunov stability theory and utilizing some advanced mathematical techniques, a new set of delay-dependent sufficient conditions is presented in terms of linear matrix inequalities for obtaining the required result. Then, an explicit expression for the desired state-feedback repetitive control law is developed. Further, the obtained results are validated through two numerical examples in the simulation section.

Repetitive control design for variable instantaneous frequencies signals

Vibration disturbances with variable instantaneous frequencies can be found in many industrial applications. Therefore, rejecting vibration disturbances is a key point for accuracy machining. This paper presents a new method for synthesizing repetitive controllers capable of rejecting variable instantaneous frequencies disturbance. The instantaneous frequencies of the disturbance signal are always consisted of multiple-periods characteristics. Therefore, multiple-periodic repetitive control scheme is obtained and multiple-periods are estimated by Hilbert-Huang transform (HHT). HHT is a way to decompose a signal into so-called intrinsic mode functions, and obtain instantaneous frequency data. It is designed to work well for data that is non-stationary and non-linear. Control performance and stability of the proposed repetitive controller with a multi-periodic disturbance are analyzed and its control scheme can be obtained. The decay rate of the rejecting error due to the multiple-periodic disturbance inputs is related to the peak value of a defined regeneration spectrum function. The control performance of the present method is evaluated in an experimental disturbance rejecting control system. Both computer simulation and experimental results are presented to illustrate the effectiveness of the proposed repetitive controller design.

High-order repetitive control for discrete-time linear switched systems

ABSTRACTThis paper is concerned with the design of a high-order repetitive control (RC) law for a class of discrete-time linear switched systems with repetition-varying reference trajectories. First, a high-order RC law, which embeds the characteristic of known variation of the reference trajectories, is proposed to the system, and a two-dimensional (2D) model is presented to describe the control and learning actions of the repetitive control system by using the lifting technique. By choosing appropriate multiple Lyapunov–Krasovskii functions, sufficient conditions for asymptotic stability of the 2D system are derived in the form of a set of linear matrix inequalities. Finally, an example is given to illustrate the effectiveness of the proposed results.

On the Design of Discrete Time Repetitive Controllers in Closed Loop Configuration

This paper deals with a discrete time repetitive control synthesis for non minimum phase plants. Two parts can be distinguished. The main design features of the repetitive controllers are discussed in the first part. More precisely one shows that one can realize two objectives; tracking with zero error and tracking with nonzero error. In the second part, a suitable plant model identification procedure for the repetitive control is proposed. An adequate input-output identification filter is designed such that the difference between the nominal and the actual repetitive control convergence conditions is minimized. Some illustrative examples are given to highlight the main features of the proposed approach.

A systematic approach for robust repetitive controller design

In this paper, a methodology for the synthesis of repetitive controllers to ensure periodic reference tracking and harmonic disturbance rejection is cast in a robust control framework. Specifically, the Lyapunov–Krasovskii theory is applied to derive LMI-based conditions for designing a state feedback control law with guaranteed stability and performance properties for system parameter variations. Practical experiments in commercial uninterruptible power supplies – UPS are considered to illustrate and discuss some practical implementation aspects of the proposed method.

Dynamic Stiffness Analysis of Repetitive Control System

For dynamic stiffness enhancement, this paper presents a new method for synthesizing repetitive controllers capable of rejecting periodic vibration disturbance. Dynamic stiffness of the control system is analyzed. Direct and quadrature dynamic stiffness are defined for the repetitive controllers’ design. A trade-off method between the determinations of the controller’s parameters is necessary such that both the rejecting performance and stability can be achieved simultaneously. An illustrated example of a twin linear drive system is given to verify the performance of the proposed control design. The control performance of the present method is evaluated in the experimental disturbance rejecting control system, where the real-time control algorithms are implemented using a floating-point digital signal processor. Both computer simulation and experimental results are presented to illustrate the effectiveness of the proposed repetitive controller design.

MIMO Repetitive Control of an Active Magnetic Bearing Spindle

Abstract: We present the identification and control of an open loop unstable MIMO Active Magnetic Bearing Spindle (AMBS) for machining applications. A 20th order model is obtained from reducing a higher order model identified by the ARX method. For verification purposes, the model is compared to the system’s frequency responses obtained by the frequency sweep method. The model is used to design a linear quadratic optimal controller, where the weighting gains are tuned by simulation and experiment. A plug-in repetitive controller for asymptotic regulation and tracking of signals synchronous to the spindle rotation is designed by formulating the control design as a model matching filter design problem. The model matching’s optimal solutions for the non-minimum phase MIMO stabilized system are obtained respectively for H ∞ and H 2 norm minimizations. Simulation and experimental results are presented to compare the proposed MIMO repetitive control design methods and demonstrate the control performance.

Digital repetitive controller design via sampled-data delayed signal reconstruction

In this paper, we propose a design method of digital repetitive controllers to track continuous-time periodic references based on sampled-data H∞ delayed signal reconstruction. It is well known that perfect tracking is not possible for arbitrary periodic signals with a fixed period if the plant to be controlled is strictly proper.For this reason, we adopt the internal model control (IMC), with which the repetitive control is cast into the framework of sampled-data H∞ delayed signal reconstruction problem. We also extend this formulation to multi-rate and robust control. Design examples show the effectiveness of our method.

Low-order continuous-time robust repetitive control: Application in nanopositioning

A low-order repetitive control (RC) design in continuous-time for nanopositioning applications is presented. It focuses on achieving high performance and sufficient robustness to uncertainties. The design is mainly applicable to analog implementation, but due to the exceptionally low order, it also results in a fast and efficient digital implementation. Experimental results for an analog implementation using a bucket brigade device (BBD), as well as a digital implementation, is presented. RC can provide fast and accurate tracking of periodic reference signals, which is useful in many scanning probe microscopy and nanofabrication applications.

Repetitive control for TORA benchmark: An additive-state-decomposition-based approach

The repetitive control (RC) or repetitive controller problem for nonminimum phase nonlinear systems is both challenging and practical. In this paper, we consider an RC problem for the translational oscillator with a rotational actuator (TORA), which is a nonminimum phase nonlinear system. The major difficulty is to handle both a nonminimum phase RC problem and a nonlinear problem simultaneously. For such purpose, a new RC design, namely the additive-state-decomposition-based approach, is proposed, by which the nonminimum phase RC problem and the nonlinear problem are separated. This makes RC for the TORA benchmark tractable. To demonstrate the effectiveness of the proposed approach, a numerical simulation is given.

Repetitive Learning Control Design for LED Light Tracking

A lighting system composed of three color light-emitting diode (LED) strings is considered. On the basis of a simplified dynamic model (with uncertainties) for the aforementioned system, the tracking of (possibly complex) periodic reference signals (with known period) for both the light color and intensity is achieved by designing, for each LED string, a decentralized repetitive learning control. Experimental results illustrate the effectiveness of the proposed approach in a practical user-friendly scenario: the color coordinates are obtained by an external low-cost red, green, blue sensor which allows for measuring the overall lighting effects (including external disturbances) while increasing the overall energy saving. A detailed theoretical analysis of the learning control design for first-order linear systems with zero relative degree under suitable assumptions is also included.

Robust µ control and repetitive control for precision motion control of a pneumatic actuating table

Because of uncertain and time-varying parameters influenced by air pressure and thermal parameters, applying H∞ robust control techniques to a pneumatic servo design has proven to be an efficient control strategy over the past few decades. However, because this method is a worst-case design that must yield robustness under given uncertainties, the inevitable trade-off may be too conservative and thus deteriorates its motion control performance. This study presents a robust µ control and repetitive control method for attaining precise dynamic tracking control of a pneumatic actuating table. The applied hybrid control structure consists of two feedback controllers. The first is a repetitive controller used to improve periodic tracking performance, and the second is a µ controller used to manage the dominant nonlinearities and uncertainties in pneumatic servo systems. This study presents an independent design of two controllers and takes advantage of the synergetic effect that results in an enhanced robust repetitive control design. In this study, a weighted average method is applied to determine optimal performance weights between these two control actions without violating robust stability. The experimental results on tracking dynamic motion profiles at perturbed operating regions for a heavy-duty pneumatic actuating table demonstrate the effectiveness of the proposed control method.

Adaptive Repetitive Control Design With Online Secondary Path Modeling and Application to Bit-Patterned Media Recording

This paper presents an adaptive repetitive controller for active tracking (rejecting) of unknown periodic trajectories (disturbances). The proposed control law is based on a modified filtered-x least mean squares (MFX-LMS) algorithm with a novel variable step size that improves the convergence rate and fades the steady state excess error in a stochastic environment. A novel secondary path modeling scheme is also proposed to adaptively compensate for the dynamic mismatches between the internal model of the MFX-LMS and the real dynamic system in an online fashion. We further discuss the application of this adaptive controller in servo mechanisms for hard disk drives (HDDs) that use bit patterned media recording in which full spectrum tracking of a periodic trajectory is crucial. Finally, comprehensive numerical simulations and experimental implementations are presented for an HDD servo system that is subjected to periodic disturbances known as repeatable run-out.