Repetitive Control Design Research Articles

Tracking and disturbance attenuation control for stochastic switched systems with input delay

This work precisely deals with the phenomena of state tracking, attenuation of external disturbance and compensation of input delay for switched stochastic dynamical systems via improved-equivalent-input-disturbance (IEID) estimator and Smith predictor based modified repetitive control design. By hosting the stochastic state observer and combining it with the IEID estimator and modified repetitive control design, a new closed-loop form of control system is formulated. To be specific, for the resultant closed-loop augmented configuration, a novel criterion which ensures the exponential stability of the considered system is derived in the form of linear-matrix-inequalities in accordance with the Lyapunov theory. Simultaneously, an IEID estimator and Smith predictor based modified repetitive control is designed in such a way that the states of the considered system track the specific reference input signals perfectly. Finally, as an example F-18 aircraft model is provided for describing the competence of the designed controller strategy and to explain the dominance of the obtained proposed controller over the existing results.

Design of Repetitive Control Systems Using a Delayed Control Input and a State Error

This paper presents a modified repetitive control scheme comprising of a state error and a control input via delayed feedback to track periodic reference trajectories and/or attenuate disturbances. The closed-loop state error dynamics can be represented using a typical neutral delay system with an exogenous input to be attenuated. The sufficient conditions to achieve overall stability and H∞ performance to minimize state error are derived by applying a Lyapunov-Krasovskii functional and a Hamiltonian, which are expressed as an algebraic Riccati inequality (ARI) and a linear matrix inequality (LMI). Based on the derived conditions, it is shown that the repetitive controller design problem can be reformulated as an optimization problem with an LMI constraint to determine the state error feedback gain. Finally, a numerical example is presented to demonstrate the feasibility of the proposed method.

Passivity-Based Design of Repetitive Controller for $LCL$-Type Grid-Connected Inverters Suitable for Microgrid Applications

A repetitive controller (RC) is one of the most promising candidates for harmonic compensation when designing the current controller of grid-connected inverters. The discrete-time closed-loop transfer function based frequency response method can be used to shape RC, which is applicable for a single inverter connecting to well-known inductive-impedance grids, but cannot guarantee the stability in the case of capacitive-impedance grids or complex systems, such as microgrids. To address this issue, this article presents a new passivity-based design method for an RC for LCL-type grid-connected inverters with either inverter-side or grid-side current control. With the proposed design guidelines, the output admittance of the RC-controlled inverter is tuned to be passive in all frequencies, so that it can be plug and play connected to a grid regardless of grid impedance. Meanwhile, thanks to infinite gains of an RC at the fundamental frequency and its multiples as the high-quality grid injected current in accordance with IEC 61000-3-4 standard is ensured even in the presence of distorted grid conditions. Finally, experimental results with an established lab prototype are provided to verify the effectiveness of the proposed approach.

Repetitive control design for vehicle lateral dynamics with state‐delay

In this work, the authors precisely concentrate on the subject of enhanced vehicle handling performance of the bicycle model with two-degrees-of-freedom via improved-equivalent-input-disturbance and repetitive control technique. To be specific, improved-equivalent-input-disturbance estimator is inserted into the controller design for attenuating the effect of the crosswind in the considered vehicle system with state-delay. A modified two-dimensional repetitive control design is implemented for improving the accurate tracking performance of the considered model. In particular, by combining an improved-equivalent-input-disturbance approach together with two-dimensional modified repetitive control design, steering angles of front and rear wheels of the considered vehicle have been controlled in order to achieve the accurate tracking performance of the vehicle states. The criteria for the robust asymptotic stability on the basis of Lyapunov stability theory is developed by means of the sufficient conditions which are obtained in the form of linear-matrix-inequalities. Simultaneously, through these inequality conditions, the parameters of proposed improved-equivalent-input-disturbance based repetitive control strategy are designed for improving the accurate tracking performance against the crosswind effect. Finally, simulation results are presented to show that the proposed control design is more effective when aperiodic disturbances occur.

Position Control of Robotic Manipulator Using Repetitive Control Basedon Inverse Frequency Response Design

It is very common nowadays to see robotic manipulators performing repetitious work during the assembly process. One of their general tasks is to assemble electronic components which requires high position accuracy along the desired path. Conventional implementation with classical control schemes have proved capable of only limited performance. This paper demonstrates the efficiency achieved by using a repetitive control (RC) structure with the ability to learn from experience to reduce positioning errors from robotic manipulators in performing repetitive tasks. Firstly, the performance of the classical control method is illustrated to show the occurrence of nearly repeated patterns in tracking errors from each period. A simple RC design was then developed, with the aim of eliminating the tracking error in each repetition. However, some tracking errors were still noticeable and could even increase when using an inappropriate gain. An inverse frequency response from the RC design is therefore proposed by taking into consideration stability in the design criteria. The stability and robustness of the RC approach is verified by the experiments. The results show that the proposed method can reduce the tracking error by 99:22% for joint T and 95:03% for joint Z compared to the classical control method. In addition, the tracking error was reduced by 80% for both joints compared to the simple RC design.

Design of fractional delay repetitive control with a dead-beat compensator for a grid-tied converter under distorted grid voltage conditions

The paper presents the design of a current control system of a grid-tied converter which provides high dynamic in transients states and symmetrical sinusoidal currents under distorted and asymmetrical grid voltage conditions. The current control loop contains a dead-beat compensator and a plug-in fractional delay repetitive controller. The whole control system is designed with regard to signal processing delay present in the control loop. The tuning procedure of the repetitive control uses particle swarm optimization to determine the optimal gain, phase lead and filter parameter. The resulting control system with optimal parameters is applied on the digital signal controller and verified experimentally on the laboratory test bench, which is the main contribution of the paper.

Modified Repetitive Control Design for Nonlinear Systems With Time Delay Based on T–S Fuzzy Model

In this paper, based on the Takagi-Sugeno fuzzy model approach, a novel output feedback control strategy is developed for a class of continuous-time nonlinear time delay systems via modified repetitive control scheme. The main objective of this paper is to design a fuzzy rule-based modified repetitive controller such that the system output can track any given periodic reference signal even in the presence of periodic disturbances. For this purpose, by employing fuzzy-dependent Lyapunov-Krasovskii functional together with the free-weighting matrix technique, a new set of sufficient conditions is presented in terms of linear matrix inequalities to guarantee the robust stability of the resulting closed-loop system. Based on these conditions and using internal model principle, it is shown that the system output tracks the given reference input within the desired error. Finally, two application-oriented examples are presented to validate the obtained theoretical results in which the proposed control design scheme gives better performance over the existing control scheme.

Sequential Multiperiod Repetitive Control Design With Application to Industrial Wide-Format Printing

Repetitive control (RC) enables high control performance for systems subject to periodic disturbances. Many disturbances in mechatronic applications involve the sum of multiple periodic signals, which is not necessarily periodic over a small time interval. The contribution of this article is a design procedure for multiple repetitive controllers, each addressing a single periodic component that achieves high performance with fast convergence in the presence of multiple periodic disturbances. The developed approach involves sequential design of the controllers, and systematically addresses modeling errors and coupling between controllers. An experimental case study on an industrial roll-to-roll printer confirms the benefits of the proposed approach, including superior performance compared to preexisting RC designs.

Dissipativity-Based Asynchronous Repetitive Control for Networked Markovian Jump Systems: 2-D System Approach

This article addresses the dissipativity-based asynchronous repetitive control problem for networked Markovian jump systems subject to time delays and partly accessible mode detection probabilities. A hidden Markov model is introduced to describe the asynchronous phenomenon between the system modes and controller modes. Based on this, an asynchronous repetitive controller is proposed. By utilizing the lifting technique, the 1-D delayed Markovian jump system and controller governing equations are converted into a stochastic and closed-loop 2-D delayed model to describe the control and learning actions. Utilizing a stochastic Lyapunov functional, sufficient conditions in terms of matrix inequalities are derived such that the closed-loop system is mean-square stable and achieves the specified $(\mathscr {W}_1,\mathscr {W}_2,\mathscr {W}_3)$ - $\gamma$ -dissipative performance. Under the assumption that the input matrix is full column rank in all modes of operation, a set of feasible sufficient conditions described by linear matrix inequalities is established by making use of the Schur complement. A procedure for synthesizing the controller parameters is also provided. A detailed numerical example with simulation results is presented to validate the proposed dissipativity-based asynchronous repetitive control design scheme.

Design of Robust Higher-Order Repetitive Controller Using Phase Lead Compensator

The performance of conventional repetitive controller (RC) deteriorates under frequency variations and system uncertainties. Due to limited bandwidth, it is also a trivial task to stabilize the conventional RC. This paper proposes a higher-order repetitive controller (HORC) with linear phase lead as a stabilizing compensator and zero-phase tracking error (ZPTE) compensator. The periodic signal generator, used by the HORC, offers relatively high gains in the neighborhood of tuned frequency and its harmonics. Stability conditions for higher-order repetitive (HOR) control system, including the phase lead compensator, are presented. The proposed solution is applied to repetitive current control of a two-level grid-connected inverter. Simulation and experimental results show that the HORC designed using the phase lead compensation is robust to frequency variation in reference/disturbance and system uncertainties.

Analysis and Design of PI Plus Repetitive Control for Grid-Side Converters of Direct-Drive Wind Power Systems Considering the Effect of Hardware Sampling Circuits

In inverters based on a single proportional-integral (PI) or deadbeat (DB) controller, an inherent resonance peak may emerge near their current loop cut-off frequency, which results in harmonic amplification or even resonance. Additionally, inappropriate filter circuits implemented in sampling circuits may result in the expansion of the resonance peak. Thus, this paper further investigates the influence of the sampling circuits on a PI- or DB-based control loop. Then, the RC filter in the sampling circuit is designed to reduce the inherent resonance peak. Moreover, a compound control strategy based on an improved repetitive controller (IRC) plus a PI controller is adopted for the grid-side converter of a direct-drive wind system. This strategy enhances the harmonic and reactive compensation performance by reconstructing the internal model of the classic repetitive controller (CRC) and limiting the bandwidth of the PI-based loop to a low level. The parameters of the presented IRC-plus-PI control are designed for the purpose of resonance peak elimination and system stability. Furthermore, the non-integer delay problem is solved with an inserted fraction compensator (FC), which plays the role of a low-pass filter in the IRC. Finally, the feasibility and effectiveness of the presented control method is verified by the experimental results.

Perfect tracking of ZMP trajectory for humanoid locomotion using repetitive control

In this paper, the tracking of the zero moment point (ZMP) trajectory for humanoid locomotion is addressed. For that, a combination of a repetitive controller (RC) and a linear quadratic regulator (LQR) is proposed. The RC controller achieves a zero steady state tracking error for any periodic desired output with a fixed period. Here, the robot model is simplified as a cart table model. In the first stage, a walking pattern with constant gait is considered to allow the use of a repetitive controller. The results are then compared to a classical PD control. In the second part, the proposed controller is applied to track a desired ZMP profile generated using a central pattern generator (CPG). Here, the speed of the oscillator is adjusted via a proper selection of the parameters of the CPG and the RC design is simultaneously updated to assure the perfect tracking of the ZMP.

Three-dimensional impact angle guidance law based on robust repetitive control

This paper presents a robust repetitive control (RC) design applied to three-dimensional homing guidance of missiles with impact angle constraint. The proposed guidance law is substantially a composite control method, which is constructed through a combination of RC and sliding mode control. More specifically, the RC exerts advantages to drive the state tracking error converge to zero, then sliding mode control is triggered, making the system be robust in terms of noise and disturbance. The effectiveness of the proposed guidance law is validated through simulation.

Tracking of Periodic Trajectories for Switched Systems Under Time-Varying Asynchronous Switching

In this technical brief, we provide an asynchronous modified repetitive controller design to address the periodic trajectory tracking problem for switched systems with time-varying switching delays between plant modes and controllers. In the feedback channel, a dynamic output feedback mechanism is adopted. By utilizing the lifting technique, the dynamic output feedback-based switched repetitive control system is transformed into a continuous-discrete two-dimensional (2D) model to differentiate the control and learning actions involved in the repetitive controller. For the transformed 2D model, by constructing a piecewise Lyapunov functional and utilizing a matrix decomposition approach, sufficient conditions in terms of linear matrix inequalities (LMIs) and the average dwell time are developed to guarantee closed-loop exponential stability. The performance of the proposed approach is illustrated via a switched RLC series circuit example and numerical simulations are provided.

Analysis and Design of Repetitive Controllers for Applications in Distorted Distribution Grids

This paper proposes a generalized design procedure for repetitive current controllers in distorted distribution grids to obtain good disturbance rejection properties and well behaved and robust system dynamics. Different implementation options for repetitive controllers (RCs) are discussed based on an accurate discrete time model. A simple control design is derived, which allows any desirable dynamics to be adjusted by one single parameter. Even a deadbeat design is possible. The impact of model inaccuracies and numerical errors on the dynamic and stability of the system is investigated. It is shown that the RC leads to low damping or even instability at high switching frequencies caused by modeling errors or numerical inaccuracies. Based on the stability analysis, it is discussed how to handle these design challenges, which exist especially for RCs of high order. The proposed control structure and control design concept is verified by simulations and experiments.

Design and Analysis of a Repetitive Current Controller for a Single-Phase Bridgeless SEPIC PFC Converter

This paper studies a repetitive controller design scheme for a bridgeless single-ended primary inductor converter (SEPIC) power factor correction (PFC) converter to mitigate input current distortions. A small signal modeling of the converter is performed by a fifth-order model. Since the fifth-order model is complex to be applied in designing a current controller, the model is approximated to a third-order model. Using the third-order model, the repetitive controller is designed to reduce the input current distortion. Then, the stability of the repetitive controller is verified with an error transfer function. The proposed controller performance is validated by simulation, and the experiment results show that the input current total harmonic distortion (THD) is improved by applying the proposed controller for an 800 W bridgeless SEPIC PFC converter prototype.

Design of a Robust Discrete-time Phase Lead Repetitive Control in Frequency Domain for a Linear Actuator with Multiple Phase Uncertainties

This paper presents a simple and effective design of a discrete-time repetitive control (RC) in frequency domain. Unlike existing phase lead RC designs, the proposed approach provides flexible phase lag compensation at multiple frequencies, which ensures improved tracking performance and robustness against system uncertainties over a wide bandwidth. The proposed design is applied to a linear actuator (LA) with friction and payload variations. The robust stability analysis presented in this study demonstrates the effectiveness of the proposed method in the presence of multiple system uncertainties. Both simulation and experimental results validate the improvement. While, the comparison study shows the superiority of the proposed approach.

Observer-based iterative and repetitive learning control for a class of nonlinear systems

In this paper, both output-feedback iterative learning control &#x0028 ILC &#x0029 and repetitive learning control &#x0028 RLC &#x0029 schemes are proposed for trajectory tracking of nonlinear systems with state-dependent time-varying uncertainties. An iterative learning controller, together with a state observer and a fully-saturated learning mechanism, through Lyapunov-like synthesis, is designed to deal with time-varying parametric uncertainties. The estimations for outputs, instead of system outputs themselves, are applied to form the error equation, which helps to establish convergence of the system outputs to the desired ones. This method is then extended to repetitive learning controller design. The boundedness of all the signals in the closed-loop is guaranteed and asymptotic convergence of both the state estimation error and the tracking error is established in both cases of ILC and RLC. Numerical results are presented to verify the effectiveness of the proposed methods.

Laplace-type integral transform for time-varying periodic repetitive controller design

In this article, Laplace-type integral transformation is introduced to construct the recursive algorithm of the repetitive controller to regulate time-varying periodic signal. A theoretical analysis of Laplace-type integral transformation operator is adopted for time-varying repetitive controller design, where the stability and performance of the proposed repetitive control system are addressed. The implementation of the repetitive control strategy is investigated by a simulated example of the cycle ergometer. Results are given to illustrate that the proposed method is effectively used to analysis repetitive control system for the time-varying periodic signal regulation.

Repetitive Control of Electrical Stimulation for Tremor Suppression

Tremor is a rapid involuntary movement often seen in patients with neurological conditions such as multiple sclerosis and Parkinson’s disease. This debilitating oscillation can be suppressed by applying functional electrical stimulation (FES) within a closed-loop control system. However, conventional implementations use classical control methods and have proved capable of only limited performance. This paper establishes the feasibility of embedding repetitive control (RC) action to exploit the capability of learning from experience to completely suppress tremor at the wrist via FES regulated co-contraction of wrist extensors/flexors. A nonlinear model structure and associated identification procedure are first proposed to guarantee stability and performance of the RC system. Then a linearizing control approach is developed to facilitate transparent RC design, together with a mechanism to preserve patients’ voluntary intention. Experimental evaluation is performed with both unimpaired and neurologically impaired participants using a validated wrist-rig. For the former group, a novel electromechanical system is employed to induce tremor artificially. Results are bench-marked against a well-known classical filtering technique to establish the efficacy of the RC approach. These confirm that the proposed control system with the developed model identification procedure can increase tremor suppression by 43.3% compared with conventional filtering. In addition, the mechanism reduces the interference of RC action with voluntary motion by 20.2% compared with conventional filtering.