Repetitive Control Design Research Articles

Robust and quantized repetitive tracking control for fractional‐order fuzzy large‐scale systems

SummaryIn this article, the decentralized repetitive tracking controller design for fractional‐order large‐scale Takagi–Sugeno fuzzy system with time delays is developed. We mainly focus on the design of a decentralized repetitive tracking controller based on the Lyapunov stability theory, by which the addressed large‐scale system asymptotically stabilized with performance index. Further, the repetitive control with quantized signal is developed to ensure the good tracking performance with the presence of interconnected model and external disturbances. Specifically, a logarithmic quantizer is used to quantify the control signal which can reduce the data transmission rate in the network. Finally, a numerical example is presented to verify the effectiveness of the proposed controller design technique.

A Performance Evaluation of Repetitive and Iterative Learning Algorithms for Periodic Tracking Control of Functional Electrical Stimulation System

Functional electrical stimulation (FES) is a medical device that delivers electrical pulses to the muscle, allowing patients with spinal cord injuries to perform activities such as walking, cycling, and grasping. It is critical for the FES to generate stimuli with the appropriate controller so that the desired movements can be precisely tracked. By considering the repetitive nature of the movements, the learning-based control algorithms are utilized for regulating the FES. Iterative learning control (ILC) and repetitive control (RC) are two learning algorithms that can be used to accomplish accurate repetitive motions. This study investigates a variety of ILC and RC designs with distinct learning functions; this constitutes our contribution to the field. The FES model of ankle angle, which is in a class of discrete-time linear systems is considered in this study. Two learning functions, i.e., proportional, and zero-phase learning functions, are simulated for the second-order FES model running at a sampling time of 0.1 s. The results indicate the superior performance of the ILC and RC in terms of convergence rate using the zero-phase learning function. ILC and RC with a zero-phase learning function can reach a zero root-mean-square error in two iterations if the model of the plant is correct. This is faster than proportional-based ILC and RC, which takes about 40 iterations. This indicates that the zero-phase learning function requires two iterations to ensure that the patient's ankle angle precisely tracks the intended trajectory. However, the tracking performance is degraded for both control methods, especially when the model is subject to uncertainties. This specific problem can lead to future research directions.

Frequency Adaptive Discrete Repetitive Controller Design for Electric Vehicle Charger

Frequency Adaptive Discrete Repetitive Controller Design for Electric Vehicle Charger

Robust Design of a Fractional-Delay Repetitive Controller for Uncertain Feedback Control Systems and Its Validation on a Magnetic Bearing Test Rig

This article presents a robust design of a fractional-delay repetitive controller in the frequency domain. The control goal is to accurately suppress the control error caused by a disturbance whose period may be a non-integer multiple of the sampling period. Coefficients of the repetitive controller finite impulse response (FIR) filters are calculated by solving a convex optimization problem that includes constraints limiting both the sensitivity function and the control sensitivity function. The proposed new design algorithm is verified by experiments on a test rig to efficiently damp shaft vibrations of an active magnetic bearing (AMB).

Artificial neural network–based modelling of pacemaker and its pace tracking using discrete wavelet transform–based finite dimension repetitive controller

Efficient control of cardiac pacing is a very important aspect as it provides lifesaving regulated cardiac rhythm in this dynamic hostile environment. The foremost control objective is set to design a highly reliable and advanced control strategy to ensure the utmost accuracy in the control effort. A modified artificial neural network (ANN)–based modelling and pace tracking using finite dimension repetitive controller (FDRC) design based on internal model principle (IMP) has been presented here. This controller will not only provide accurate tracking but also minimize the control action time due to less amount of data handling through the deployment of discrete wavelet transform (DWT) in the loop of repetitive controller (RC). Finally, a case study has been propounded considering ANN model using available data sets and software to validate the control strategy and justify the control objective for optimizing the pace tracking in a pacemaker. Result of the experiment showed good accuracy as well as very low error in terms of mean-squared error (MSE), integral absolute error (IAE), integral time absolute error (ITAE) and integral time square error (ITSE). Along with that, it is observed that DWT not only benefits the handling of very less memory but also acts as an additional filter while reconstructing the signal, which serves as an added advantage of this model.

Repetitive Control for Lur’e-Type Systems: Application to Mechanical Ventilation

Repetitive control (RC) has shown to achieve superior rejection of periodic disturbances. Many nonlinear systems are subject to repeating disturbances. The aim of this article is to develop a continuous-time RC design with stability guarantees for nonlinear Lur’e-type systems. Approximate output tracking is achieved by combining an internal model, consisting of a finite number of linear oscillators with frequencies at the reference frequency and at its multiples, with a stabilizer that guarantees a convergence property of the closed-loop system. The developed RC approach is applied to a nonlinear mechanical ventilation system for intensive care units (ICUs), which can be modeled as a Lur’e-type system. The experimental study confirms that the RC scheme is able to successfully follow the desired target pressure profile to properly support the ventilation needs of an adult patient.

Design, analysis and experiment of robust adaptive repetitive angle tracking control for a one-DOF manipulator driven by pneumatic artificial muscles

There exist nonlinearities, uncertainties and time-varying characteristics in the system dynamics of manipulators driven by pneumatic artificial muscles (PAMs), which makes the accurate dynamic modeling and controller design challenging. In this paper, a robust adaptive repetitive control scheme is proposed to solve the periodic-trajectory tracking problem for a one-degree of freedom (one-DOF) manipulator driven by two PAMs. First, the system model of the one-DOF PAM-driven manipulator is analyzed and derived. Next, during output constraint design by using a barrier Lyapunov function, a sliding mode surface is reasonably constructed to compensate for the differential term of time-varying constraint parameter. Then, with the help of Lipchitz condition, signal replacement technique and reparameterization are implemented to deal with nonparametric uncertainties in the manipulator system for the subsequent uncertainty compensation by using difference learning method and robust feedback strategy. Moreover, the stability of closed-loop PAM-driven manipulator is proven theoretically by using Lyapunov synthesis. In the end, comparative experiments are provided on a self-built PAM testbed to demonstrated the effectiveness of the proposed robust adaptive repetitive control scheme.

Repetitive control design for switched neutral systems with input time‐delay

SummaryThe design of tracking control problem and compensation of disturbance for switched neutral systems with multiple time‐delays and external disturbances are addressed in this paper. In this regard, a modified repetitive control technique based on the Matausek‐Micic modified Smith predictor approach is being implemented, which assures the exact tracking performance and disturbance attenuation with high precision in the considered system. To be specific, the integration of transfer function with modified Smith predictor block not only provides the accurate compensation of input time‐delays but also ensures the exact estimation and attenuation of external disturbances effectually. Furthermore, according to Lyapunov stability approach combined with average‐dwell‐time technique, a group of adequate conditions is derived in the form of matrix inequalities. Simultaneously, by solving the established matrix inequalities using available software the controller gain matrices are calculated. Ultimately, the simulation results of three numerical examples are presented to validate the efficiency and dominance of the suggested control procedure.

Design of a Repetitive Control for a Three-Phase Grid-Tied Converter under Distorted Grid Voltage Conditions

The paper presents a design of repetitive control (RC) in the current control system of a three-phase grid-tied converter. The goal of the control system is to provide sinusoidal input filter currents under the conditions of distorted and asymmetrical grid voltage. A novel design of the RC is presented, in which the repetitive part is not excited by sharp and non-periodic changes of the reference signal, but it enables high-quality performance under periodic disturbance conditions. In the proposed system. RC cooperates with a discrete state feedback controller. An innovative approach to tuning is proposed in which parameters of the repetitive, as well as the state feedback controller, are selected as a result of the optimization process with the use of a particle swarm algorithm. The proposed control system is verified experimentally on a laboratory test bench. The achieved results confirm the high-quality system performance.

Design of a preview repetitive control with equivalent-input-disturbance system based on a continuous-discrete 2D model

This paper deals with the problem of two-dimensional (2D) system-based preview repetitive control (PRC) with equivalent-input-disturbance (EID) for uncertain continuous-time systems. First, to use the available values of the reference signal, we construct an equality constraint which includes the output of a basic repetitive controller, preview compensation and tracking error. Next, to compensate the unknown external disturbances, we incorporate an EID estimator into the PRC controller. Then, by employing the 2D system theory together with the linear matrix inequality (LMI) approach, we derive a sufficient condition to ensure the robust stability of the closed-loop system. By solving an LMI, the gains of the controller and state observer can be obtained. The results obtained in this paper generalize and include some results in the existings. literature. Finally, a numerical simulation demonstrates the effectiveness and superiority of the proposed method.

The optimal design of repetitive controllers based on inverse frequency response

AbstractThis article presents a complete design of non‐causal finite impulse response (FIR) and infinite impulse response (IIR) compensators for repetitive control. The concept of repetitive controllers involves imitating the inverse frequency response of the feedback control system by minimizing the amplitude of error propagation from one period to the next in the frequency domain. The FIR compensator design has already been presented in our previous work. However, it was not complete since some parameters, such as the number of causal gains and total number of gains were still left open for the designers to select. This work provides a reasonable suggestion on how to choose parameters based on the steepest descent method. In addition, an IIR compensator is further developed based on the designed FIR design. The gains of the IIR compensator are adjusted by aiming to minimize the cost function using the steepest descent. As can be observed from the results, the IIR compensator developed from the FIR compensator cannot overcome the original FIR compensator since its learning performance is relatively slow and the extra gains added to the denominator increase memory usage when executing.

A Fractional Order Fast Repetitive Control Paradigm of Vienna Rectifier for Power Quality Improvement

Due to attractive features, including high efficiency, low device stress, and ability to boost voltage, a Vienna rectifier is commonly employed as a battery charger in an electric vehicle (EV). However, the 6k ± 1 harmonics in the acside current of the Vienna rectifier deteriorate the THD of the ac current, thus lowering the power factor. Therefore, the current closed-loop for suppressing 6k ± 1 harmonics is essential to meet the desired total harmonic distortion (THD). Fast repetitive control (FRC) is generally adopted; however, the deviation of power grid frequency causes delay link in the six frequency fast repetitive control to become non-integer and the tracking performance to deteriorate. This paper presents the detailed parameter design and calculation of fractional order fast repetitive controller (FOFRC) for the non-integer delay link. The finite polynomial approximates the non-integer delay link through the Lagrange interpolation method. By comparing the frequency characteristics of traditional repetitive control, the effectiveness of the FOFRC strategy is verified. Finally, simulation and experiment validate the steadystate performance and harmonics suppression ability of FOFRC.

Design of Fractional Order Odd-Harmonics Repetitive Controller for Discrete-Time Linear Systems with Experimental Validations.

This paper presents a simple and straightforward design of a discrete-time fractional-order odd-harmonics repetitive controller (RC). Unlike general RC designs, the proposed method utilizes an internal model with a half-period delay and a stabilizing controller with a fractional phase lead compensator. First, the odd-harmonics internal model representing odd-harmonics frequencies is constructed by using the information of the reference's basis period and the preferred tracking bandwidth. Secondly, an optimization problem synthesized from the stability condition of the RC closed-loop system is solved to obtain the fractional phase lead compensator. Finally, the fractional term of the stabilizing controller is realized by using a causal and stable infinite impulse response (IIR) filter, where the filter coefficients are computed by applying the Thiran formula. Simulation and experimental validation on a servomotor system are conducted to verify the effectiveness of the proposed design.

Learning-Based Repetitive Control of a Bowden-Cable-Actuated Exoskeleton with Frictional Hysteresis.

Bowden-cable-actuated soft exoskeleton robots are known for their light weight and flexibility of power transmission during rehabilitation training or movement assistance for humans. However, friction-induced nonlinearity of the Bowden transmission cable and gearbox backlash pose great challenges forprecise tracking control of the exoskeleton robot. In this paper, we proposed the design of a learning-based repetitive controller which could compensate for the non-linearcable friction and gearbox backlash in an iterative manner. Unlike most of the previous control schemes, the presented controller does not require apriori knowledge or intensive modeling of the friction and backlash inside the exoskeleton transmission system. Instead, it uses the iterative learning control (ILC)to adaptively update the reference trajectory so that the output hysteresis caused by friction and backlashis minimized. In particular, a digital phase-lead compensator was designed and integrated with the ILC to address the issue of backlash delay and improve the stability and tracking performance. Experimental results showed an average of seven iterations for the convergence of learning and a 91.1% reduction in the RMS tracking error (~1.37 deg) compared with the conventional PD control. The proposed controller design offers promising options for the realization of lightweight, wearable exoskeletons with high tracking accuracies.

Correction to: A Systematic Method for Repetitive Controller Design Based on the Process Frequency Response

Correction to: A Systematic Method for Repetitive Controller Design Based on the Process Frequency Response

Adaptive odd repetitive control for magnetically suspended rotor harmonic currents suppression

Magnetic levitation rotating machinery has been widely used in industrial applications. Odd harmonic currents in the active magnetic bearing coils, which are caused by rotor mass unbalance and sensor runout, increase the power consumption and the base vibration. Repetitive control has recently been used to suppress harmonic currents in magnetic bearing systems. However, repetitive control needs the rotor rotational speed information and has some limitations without a speed sensor. In this paper, an adaptive odd repetitive control which does not need the speed sensors is proposed to suppress the active magnetic bearing odd harmonic currents. Compared to the conventional repetitive control, the second-order generalized integral frequency-locked loop is applied in adaptive odd repetitive control to estimate the rotor speed in real time without additional speed sensors. The magnetically suspended rotor with harmonic disturbances is modeled. The work principle, structure, and design of the adaptive odd repetitive control are addressed. The simulation and experiments are carried out on a rotor active magnetic bearing test rig to validate the effectiveness of the proposed adaptive odd repetitive control, and the results show that the active magnetic bearing odd harmonic currents are well suppressed.

Model-free repetitive control design and implementation for dynamical galvanometer-based raster scanning

Data-driven repetitive control (RC) is proposed in this work to track online, dynamical raster trajectories in galvanometer-based scanning. To remove the requirement of a plant model in conventional model-based RC, we use model-free iterative learning control (ILC) to synthesize the data-driven repetitive controllers. Specifically, the frequency-domain plant-inversion and loop-shaping methods are both converted into time-domain trajectory tracking problems. The ILC is then applied to solve the trajectory tracking problems and subsequently derive the repetitive controllers from data. The stability conditions of both methods are analyzed and used to guide the data-driven control design. Experimental results on a commercially available galvanometer scanner demonstrate that the proposed methods improve the tracking error of a predefined raster scan by more than 30 times, as the conventional ILC does. Moreover, after applying data-driven RC, users can online assign various center positions and magnitudes of the raster trajectory. Once assigning a new reference in this continuous mode, the tracking error rapidly converges to the steady-state within ten periods.

A Systematic Method for Repetitive Controller Design Based on The Process Frequency Response

A Systematic Method for Repetitive Controller Design Based on The Process Frequency Response

Modified repetitive control design for two stage off board Electric Vehicle charger

In this paper, a three-phase, two stage, bidirectional off board plug-in Electric Vehicle (PEV) charger controller has been designed and implemented in real time. The proposed PEV charger is able to work in all four quadrants in active–reactivepower plane. Generally, power electronics converters are controlled by PI regulators in d-q reference frame, where the signals to be regulated are inherently DC in nature. These controllers are implemented in two loops i.e., Slow (outer) control loop and fast (inner) control loop. Setting the gains of outer loops are little bit easier in comparison to fast acting inner loops besides the involvement of decoupling terms to have independent operation of active and reactive current components. Therefore, a repetitive controller (RC) is designed to regulate the inner sinusoidal reference current having both active–reactive​ components as per the control requirement without involving any decoupling terms. The RC is well known for their ability to track periodic signal and inherently based on internal model control theory. However, the major problem with RC is its sensitivity due to which it provides high gains at all frequencies levels. Therefore, in proposed controller the sensitivity of RC is modified by squaring it. This results the deep notches at higher frequency levels This approach is found to be very much suitable for the compensation of reactive power and load current harmonics. This also helps to exclude unwanted frequencies which results reduction in THD level. Therefore, the main contribution of this paper is adapting such robust EV charger controller for harmonic compensation. Moreover, from the implementation, it is found that the conventional RC is capable to compensate load current harmonic to some extent but it takes around 140 μs computational time. However, the proposed RC takes around 100 μs computational time, this results the grid current purely sinusoidal. The MATLAB/Simulink environment has been used to simulate proposed PEV charger controller, further it has been verified on scaled down experimental prototype.

Repetitive control design based on forwarding for nonlinear minimum-phase systems

We propose a new design for a repetitive control scheme for nonlinear minimum-phase systems with arbitrary relative degree and globally Lipschitz nonlinearities. We represent the delay of the repetitive control scheme as a transport equation and we propose a new forwarding-based (partial) state-feedback design that uses not only the boundary information of the delay, but the entire state of the transport equation representing the delay. Through a rigorous mathematical analysis, we show that, from a theoretical point of view, asymptotic convergence of the desired regulated output can be achieved with the proposed control design.