Repetitive Control Design Research Articles

Spatial-based Output Feedback Adaptive Feedback Linearization Repetitive Control of Uncertain Rotational Motion Systems Subject to Spatially Periodic Disturbances

In this paper, we propose a new design of spatial-based repetitive control for rotational motion systems required to operate at varying speeds and subject to spatially periodic disturbances. The system has known model structure with uncertain parameters. To synthesize a repetitive controller in spatial domain, a linear time-invariant system is reformulated with respect to a spatial coordinate (e.g., angular displacement), which results in a nonlinear system. A nonlinear state observer is then established for the system. Adaptive feedback linearization is applied to the system with the state observer so as to minimize the tacking error. Moreover, a spatial-based repetitive controller is added and operates in parallel with the adaptively feedback linearized system, which not only further reduces the tracking error but also improves parameter adaptation. The overall output feedback adaptive feedback linearization repetitive control system is robust to structured parameter uncertainty, capable of rejecting spatially periodic disturbances under varying process speeds, and can be proved to be stable and produce bounded tracking error. Finally, feasibility and effectiveness of the proposed scheme is verified by simulation.

Design and Simulation on Improved Repetitive Controller for Inverted Power Supply

Aimed at the inverted power supply control system, an improved repetitive control method has been proposed. It combines repetitive controller with proportion and integral controllers, which improves the inverted power supply's output power performance when the load is nonlinear. Based on this control scheme, a detailed program parameters design for each part of the repetitive controller is proposed and the special Notch function is also introduced. The improved repetitive controller design method was verified by simulation and results showed that improved system has good dynamic and static characteristics, stable voltage accuracy is high; the content of output waveform harmonic dropped to 1.07%, the rate of convergence speed was greatly enhanced.

On the Settling Time in Repetitive Control Systems

Repetitive control seeks to converge to zero tracking error when a feedback control system has a periodic command or a periodic disturbance. It is of interest to examine how long one must wait until convergence is reached. Without the repetitive control loop, any feedback system has a settling time often defined as four times the longest time constant in the characteristic polynomial. When a repetitive control loop is put around such a system, there are p additional roots to the characteristic polynomial, where p is the period in time steps, which can be very large. Again one can define the settling time, which might best be measured in units of periods, representing the number of periods needed to essentially complete the convergence process. This paper studies the convergence rate for several general classes of repetitive controller design methods.

Design of noise and period-time robust high-order repetitive control, with application to optical storage

Repetitive control is useful if periodic disturbances or setpoints act on a control system. Perfect (asymptotic) disturbance rejection is achieved if the period time is exactly known. The improved disturbance rejection at the periodic frequency and its harmonics is achieved at the expense of a degraded system sensitivity at intermediate frequencies. A convex optimization problem is defined for the design of high-order repetitive controllers, where a trade-off can be made between robustness for changes in the period time and for reduction of the error spectrum in-between the harmonic frequencies. The high-order repetitive control algorithms are successfully applied in experiments with the tracking control of a CD-player system.

Repetitive control design and implementation for linear motor machine tool

The goal of this paper is to eliminate the period tracking error via the design of discrete-time domain repetitive controller. It increases the stabilizing range and enhances the robust performance by adopting the prototype repetitive controller design principle to compensate repetitive control. Furthermore, with the concept of command feedforward, it introduces the feedforward gains of speed and acceleration, which can forcefully enhance the tracking ability of the repetitive controller and improve on the errors of the system. Finally, it puts into practice the theory on a gantry type machinery platform with linear motors. The results prove that the theory can reduce period tracking error successfully.

Design of discrete-time adaptive repetitive controllers and application to feed drive systems

Although repetitive control is well known to be useful for controlling systems required to perform periodic motions with high accuracy, the repetitive control system is generally a high-order system and has undesirable high-frequency characteristics. Hence, there has been much research on the robustness improvement of repetitive controllers. Although adaptive control is useful when the plant dynamics is unknown, little effort has been made to apply adaptive control to the repetitive control system. Since the repetitive control system is generally a high-order system, many controller parameters need to be estimated online, especially if adaptive pole-placement control, which enables arbitrary pole placement of the control system, is applied. This paper presents a discrete-time design of adaptive poleplacement repetitive controllers for plants with unknown transfer function coefficients (orders of the plants are assumed to be known) and disturbances by assuming that a non-minimum phase continuous-time plant is controlled with a small sampling period. From this assumption, plant unstable zeros appearing by discretization can be approximated by known ones (limiting zeros). By employing the idea of limiting zeros, the repetitive controller can be realized as a feedforward controller without knowing the plant transfer function coefficients. Since the repetitive controller is placed out of the feedback loop by this design, the adaptive pollplacement controller can be realized without updating a large number of controller parameters. Experimental results with the application of a feed drive system, which is often used in computer numerical control (CNC) machine tool systems with repetitive motion, demonstrate the effectiveness of the proposed method. Design methods with and without the limiting zeros are compared in the experiment. It is then shown that using the limiting zeros reduces the control input variance and improves the control performance.

Design of a repetitive controller: an application to the track-following servo system of optical disk drives

In an optical disk drive servo system, disturbances with significant periodic components cause tracking errors of a periodic nature. As an effective control scheme for improving periodic disturbance attenuation performance, repetitive control has been applied successfully to the track-following servo system of optical disk drives. The increase in disk rotational speed to achieve a better data throughput leads to the increase in the frequency of periodic disturbance, which needs a high loop gain in a wider control bandwidth. However, this requirement is not easily accomplished because plant uncertainty hinders selecting the bandwidth of a filter in the repetitive controller. The problem of add-on type repetitive controller design for a track-following servo with norm-bounded uncertainties in optical disk drives with high rotational speed is examined. Using the Lyapunov functional for time-delay systems, a sufficient condition for robust stability of the repetitive control system is derived in terms of an algebraic Ricatti inequality or a linear matrix inequality (LMI). On the basis of the derived condition, it is shown that the repetitive controller design problem can be reformulated as an optimisation problem with an LMI constraint on the free parameter. The validity of the proposed method is verified through experiments using a DVD-ROM drive.

Repetitive controller design for minimum track misregistration in hard disk drives

Repetitive control is a widely used technique for the compensation of repeatable error in systems that contain rotating mechanisms or repeat a trajectory. Generally, it includes delay chains and a low-pass filter in the positive feedback loop, which generate a periodic signal. The controller has typically been implemented in a plug-in fashion and designed heuristically with the simplest form of the filter. However, this design approach is somewhat ambiguous in the selection of controller parameters because of its influence over nonharmonic frequencies. Also, it leaves the possibility for further improvement. This paper presents an improved design method for the repetitive controller that provides minimum track misregistration (TMR) in a hard disk drive (HDD). For TMR prediction, the method identifies disturbances acting on an HDD and estimates servo performance, using the identification result. We have confirmed the identification and estimation procedure through experiments. In our method, first the basic tracking controller is designed and later the repetitive controller is designed in conjunction with a Q filter. A cost function based on Parseval's theorem, reflecting the servo performance as TMR, is defined. Then the servo performance is estimated from the identified disturbance, and the plant and designed controller's frequency response are modified as necessary by changing the parameters of the controller, whose optimization is carried out with a commercial nonlinear optimization tool. The design strategy facilitates the controller design by providing an accurate estimation for the attainable servo performance and design criteria under the optimization framework.

Robust Repetitive Controller Design in Parameter Space

A new and simple robust repetitive controller design procedure in controller parameter space is presented here. The structure of the repetitive controller filters are fixed, thus, simplifying the design procedure to tuning of the fixed structure filters’ parameters. This approach results in simple and physically meaningful robust controllers that are easily implementable. The design method is based on mapping frequency domain performance specifications into a chosen controller parameter plane. Weighted sensitivity (nominal performance) and weighted complementary sensitivity (robust stability) function magnitude bounds are chosen as the frequency domain specifications to be mapped into controller parameter space here. The design method is illustrated numerically in the context of a servohydraulic material testing machine application available in the literature.

Demonstration of the Internal Model Principle by Digital Repetitive Control of an Educational Laboratory Plant

A key topic in classical control theory is the Internal Model Principle (IMP). A particular case of the IMP for tracking periodic references or attenuating periodic disturbances in closed-loop control systems is a technique called repetitive control. This work proposes and describes an educational laboratory plant to show the students the advantages of repetitive controllers in systems with periodic references or disturbances. The plant has been designed to be low cost, easy to build, and subject to periodic disturbances with a clear physical explanation. More specifically, it consists of a pulsewidth modulation (PWM) electronic amplifier, a small dc motor, and a magnetic setup that generates a periodic load torque under constant mechanical speed operation. The control objective for the closed-loop control system is to regulate the mechanical speed to a constant value in spite of the periodic load torque disturbance. In order to accomplish this performance specification, a detailed design of a digital repetitive controller is presented, and some basic experimental results are provided to prove its good behavior. The paper also includes some repetitive control concepts and facts that teaching experience shows as essential to understand the design process.

THE PARAMETRIZATION OF ALL ROBUST STABILIZING REPETITIVE CONTROLLERS

In this paper, we investigate the parameterization of all robust stabilizing repetitive controllers for single-input/single-output continuous time non-minimum phase systems. The repetitive control system is a type of servo mechanism designed for a periodic reference input. When repetitive control design methods are applied to real systems, the influence of uncertainties in the plant must be considered. In some cases, the uncertainties in the plant make the repetitive control system unstable, even though the controller was designed to stabilize the nominal plant. The stability problem with uncertainty is known as the robust stability problem. Several papers to design robust stabilizing repetitive control systems have been published. However the parametrization of all robust stabilizing repetitive controllers has not been considered. In this paper, we propose the parametrization of all robust stabilizing repetitive controllers for non-minimum phase systems. Finally, a numerical example is illustrated to show the effectiveness of the proposed parametrization.

시변 불확실성을 가지는 선형 시스템을 위한 반복 제어 시스템의 설계

This paper considers a design problem of the repetitive control system for linear systems with time-varying norm bounded uncertainties. Using the Lyapunov functional for time-delay systems, a sufficient condition ensuring robust stability of the repetitive control system is derived in terms of an algebraic Riccati inequality (ARI) or a linear matrix inequality (LMI). Based on the derived condition, we show that the repetitive controller design problem can be reformulated as an optimization problem with an LMI constraint on the free parameter.

Two-Parameter Robust Repetitive Control With Application to a Novel Dual-Stage Actuator for Noncircular Machining

This work presents a robust repetitive controller design for a novel dual-stage actuator system. The dual-stage actuator, which consists of an electrohydraulic actuator for 25-mm-gross motion and a piezoelectric actuator for 40-/spl mu/m fine motion, is designed for noncircular machining application. The controller is designed through a sequence of two single-input-single-output (SISO) designs by exploiting the triangular structure of the two by two actuator system dynamics. The tracking error from the first stage electrohydraulic actuator is used as reference for the second stage piezoelectric actuator. In this master-slave control arrangement, the overall sensitivity function is the product of two sensitivity functions from each actuator's servo loop. Thus, performance is improved at the frequencies where the sensitivity values are already well less than one. In the real-time control implementation, the effects of finite word length are analyzed and addressed via controller order reduction and realization. In an experiment of tracking an automotive cam profile at the rate of 10 cycles per second (600 rpm), the proposed dual-stage servo system generated tracking error of 4-/spl mu/m peak-to-valley and 0.80-/spl mu/m root-mean-square (RMS) value, showing a substantial improvement over the 16 micron peak-to-valley and 2.64-/spl mu/m RMS errors generated by the electrohydraulic servo system alone.

Repetitive learning of backstepping controlled nonlinear electrohydraulic material testing system

This paper develops repetitive control design and analysis for back stepping-controlled non-linear systems. To precisely track periodic trajectories for nonlinear systems, back stepping control is first designed to render closed-loop stability and, in theory, asymptotic tracking performance. However, due to the sensitivity to the unmodelled dynamics and plant variations, asymptotic tracking performance is usually not feasible. Thus, repetitive control is applied over the back stepping-controlled system to restore asymptotic tracking performance. This approach is applied to an electrohydraulic material testing system, in which the material specimen present substantial nonlinear force and displacement relationship. The back stepping control employs both feedback and feedforward actions to render linearized I/O plant and thus the outer loop repetitive control design can be based on the compensated linear system. Experimental results are presented to demonstrate the effectiveness of the proposed approach.

Repetitive control design for linear systems with time-varying uncertainties

The design of a repetitive control system for linear systems with time-varying norm-bounded uncertainties is presented. Using a Lyapunov functional for the time-delay systems, a sufficient condition is derived in terms of either an algebraic Ricatti inequality or a linear matrix inequality (LMI), which ensures robust stability of the repetitive control system. Based on the derived condition, we show that the repetitive controller design problem can be reformulated as an optimisation problem with an LMI constraint of the free parameter.

Repetitive Controller Design in Parameter Space

A new and simple repetitive controller design procedure in controller parameter space, where the structure of the filters in the repetitive controller are fixed from the start and parameters within these filters are tuned, is presented here. This approach results in simple and physically meaningful controllers that are easily implementable. The design method is based on mapping frequency domain performance specifications into a chosen plane of controller parameters. Sensitivity function magnitude bounds and a relative stability measure are chosen as the frequency domain specifications to be mapped into controller parameter space here. The design method is illustrated numerically in the context of a servohydraulic material testing machine application available in the literature.

Digital repetitive controlled three-phase PWM rectifier

In this paper, a digital repetitive control (RC) strategy is proposed to achieve zero tracking error for constant-voltage constant-frequency (CVCF) pulse width modulation (PWM) converters. The proposed control scheme is of structure: a plug-in digital repetitive controller plus a conventional controller (e.g., PD controller). The design of the plug-in repetitive learning controller is systematically developed. The stability analysis of overall system is discussed. A repetitive controlled three-phase reversible PWM rectifier is given as an application example. Near unity power factor and constant output DC voltage are ensured under parameter uncertainties and load disturbances. Simulation and experimental results are provided to testify the effectiveness of the proposed control scheme.

Repetitive Learning of Back Stepping Controlled Nonlinear Electrohydraulic Material Testing System

This paper develops repetitive and iterative learning control design and analysis for back stepping controlled nonlinear systems. To precisely track periodic or finite duration trajectories for nonlinear systems, back stepping control is first designed to render closed loop stability and, in theory, asymptotic tracking performance. However, due to the sensitivity to the unmodelled dynamics plant variations, asymptotic tracking performance is usually not feasible. Thus, repetitive or learning control is applied over the back stepping controlled system to restore asymptotic tracking performance. This approach is applied to an electrohydraulic material testing system, in which the material specimen present substantial nonlinear force and displacement relationship. It will be shown that the back stepping control employs both feedback and feedforward actions to render linearized I/O plant and thus the outer loop repetitive and learning control design can be based on the compensated linear system. Experimental results will be given to demonstrate the effectiveness of the proposed approach.

Design of a plug-in type repetitive controller for periodic inputs

This paper presents some practical design criteria for a plug-in type repetitive controller to achieve good tracking performance within a specified frequency range. Upper and lower bounds of the repetitive controller parameters that ensure the stability and the desired performance are derived. It has been found that the decay rate of the tracking error due to periodic 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 software cam system, which needs periodic linear motions, where the real-time control algorithms are implemented using a floating-point digital signal processor (DSP). Both computer simulation and experimental results are presented to illustrate the effectiveness of the proposed repetitive controller design.

Handling Non-Periodic Disturbances In Repetitive Control Systems With Applications To Robot Manipulators

Abstract Repetitive control is used in programmable mechanisrns to iteratively improve the tracking of periodic control signals. While a repetitive controller can effectively compensate for periodic disturbances, its ability to learn can cause non-periodic disturbances to degrade performance for many cycles while the controller “forgets” about the disturbance. For example, aone-time jolt to a disk drive can cause a repetitive controller to actually introduce a disturbance by attempting to reject the jolt in later cycles. This paper discusses two methods for reducing the effects of such onetime disturbances. The fast is an “adaptive error saturation” element that is used in conjunction with a new frequency-based repetitive controller design to suppress one-time disturbances with little effect on the learning rate. The second method reduces the disturbance sensitivity of the feedback loop with a “disturbance observer” that can be added to an existing linear feedback controller to directly identify and rejec...