Repetitive Control Scheme Research Articles

Modified Smith predictor-based robust tracking control design for fractional-order singular semi-Markovian jump systems

This paper focuses on addressing the robust tracking control problem as well as the compensation of delay and external disturbances for fractional-order singular semi-Markovian jump systems. Moreover, a multi-periodic modified repetitive control scheme is developed to guarantee the exact tracking performance of the considered system. Subsequently, by implementing the Majhi-Atherton modified Smith predictor approach, input delays and disturbances occurring in the addressed system are compensated. Precisely, the incorporation of disturbance estimator with the conventional Smith predictor frame can accurately estimate and attenuate the external disturbances. Further, the linear matrix inequality-based conditions for ascertaining the required results are procured with the aid of Lyapunov stability theory. Following this, by solving the acquired criteria, the precise framework of the gain matrices can be reckoned. Finally, the effectiveness and supremacy of the suggested control approach are assessed by using the outcomes of simulations obtained from two numerical examples.

Position Control of Electro-hydraulic Servo System Based on Repetitive Control Strategy

Background: When performing repetitive work in an electro-hydraulic servo system, the expected tracking signals are often periodic signals, such as trigonometric functions. For this kind of electro-hydraulic servo system, repetitive control is one of the most ideal control strategies. Objective: The objective of this patent technology is to improve the position-tracking performance of the electro-hydraulic servo system and minimize tracking errors by designing and implementing a repetitive control strategy. Methods: The study models an electro-hydraulic servo system, designs a stabilizing controller, and develops a plug-in repetitive controller to enhance EHSS tracking. The regeneration spectrum is used as a stability criterion, and performance is evaluated using statistical metrics like Mean Square Error (MSE), Root Mean Square Error (RMSE), and standard deviation of the tracking error along with tracking performance and steady-state error. Results: The developed controller, validated through simulation analysis and real-time experiments, significantly reduces tracking error and enhances system position tracking accuracy, demonstrating its effectiveness. For instance, the repetitive control strategy outperforms PID and backstepping controllers at 30 mm with 0.5 Hz, achieving an error of 0.2 with an RMSE of 0.0924 and σ of 0.0878. Similar trends are observed at various test conditions, highlighting the consistent and robust performance of the designed repetitive controller. Additionally, the designed repetitive controller demonstrates an average improvement of 75.175% and 62.97% compared to the proportional- integral-derivative and backstepping controllers, respectively. Conclusion: The designed controller provides technical support for position control of the electrohydraulic servo system, achieves position control requirements, and significantly improves positioning accuracy and response.

Current Harmonic Suppression in Maritime Vessel Rudder PMSM Drive System Based on Composite Fractional-Order PID Repetitive Controller

To address the control performance and harmonic suppression issues in maritime vessel rudder permanent magnet servo systems, a fractional-order PID controller was introduced into the existing improved repetitive control strategy. We used the Oustaloup approximation algorithm and particle swarm optimization for tuning the fractional-order PID controller. The optimized parameters substantially improved the control performance. By integrating the fractional-order PID controller with the improved repetitive controller, a composite fractional-order PID repetitive control strategy was formed. Finally, MATLAB/Simulink simulations were conducted to compare and verify the disturbance rejection and harmonic suppression capabilities of the improved control strategy. The results demonstrate its superior control performance, thereby increasing the practicality of the control system in dealing with various situations.

Frequency-adaptive odd-harmonic repetitive control scheme for three-phase shunt active power filters

Repetitive control (RC), which can track the periodic input or suppress the periodic disturbance with a zero steady-state error, is a promising control strategy for shunt active power filters (SAPF). However, the conventional RC (CRC) scheme will suffer a severe performance degradation caused by the grid frequency variations. In this article, a frequency-adaptive odd-harmonic repetitive control scheme with a single and fixed sampling rate is proposed for SAPF to deal with grid frequency variations and provide fast transient response for RC system. The frequency-adaptability of proposed repetitive control scheme can be implemented by updating the coefficients of the approximate expression for the delay unit in repetitive controller. The FIR filter based on Lagrange linear interpolation is used to transform the multirate repetitive control system into single-rate repetitive control system to address the problems caused by the multirate repetitive control system. Moreover, a fractional-order linear compensator with a simple structure is designed to compensate the magnitude and phase of the system accurately. Compared with other classical repetitive control strategies, the proposed repetitive control scheme can provide a better adaptation to the steady-state deviation and dynamic variation of grid frequency and ensure the control performance of SAPF system. Simulation and experimental results verify the effectiveness of the proposed control scheme.

IIR filter-based compensator with modified feedback repetitive control scheme of voltage source inverter for nonlinear load applications

IIR filter-based compensator with modified feedback repetitive control scheme of voltage source inverter for nonlinear load applications

Performance-optimisation-based repetitive trajectory tracking control for autonomous farming vehicle

The high precision trajectory tracking for the autonomous farming vehicle (AFV) is closely related to work quality and crop yield. Farmland operations are usually repetitive tillages, and the farmland soil is relatively soft, slippery, and uneven, which can easily lead to uncertain problems such as slippage, parameter perturbation, and external disturbance. This paper proposes a finite-time repetitive trajectory tracking control strategy integrated with particle swarm optimisation (PSO) and equivalent input disturbance (EID) for the AFV to achieve performance optimisation. The repetitive control framework with finite-time convergence technique can effectively realise the iterative convergence performance of the repetitive trajectory tracking. The PSO algorithm is integrated into determining the control gains to optimise the dynamic and steady-state performances of the trajectory tracking control system. The EID method enhances the tracking precision and robustness to internal and external disturbances. Under MATLAB/Simulink and CarSim co-simulation environment, the effectiveness and advantages of the designed control strategy are illustrated by comparing it with the traditional repetitive control, the EID-based PI control, the active-disturbance-rejection-control-based nonsingular terminal sliding mode control, as well as the sliding-mode-observer-based integral sliding mode control strategies for a farming vehicle.

Divergent Component of Motion Planning and Adaptive Repetitive Control for Wearable Walking Exoskeletons.

Wearable walking exoskeletons show great potentials in helping patients with neuro musculoskeletal stroke. Key to the successful applications is the design of effective walking trajectories that enable smooth walking for exoskeletons. This work proposes a walking planning method based on the divergent component of motion to obtain a stable joint angle trajectory. Since periodic and nonperiodic disturbances are ubiquitous in the repeating walking motion of an exoskeleton system, a major challenge in the walking control of wearable exoskeleton is the joint angle drift problem, that is, the joint angle motion trajectories are not necessarily periodic due to the presence of disturbance. To address this challenge, this work develops an adaptive repetitive control strategy to guarantee that the motion trajectories of joint angle are repetitive. In particular, by treating the disturbance as system uncertainties, an adaptive controller is designed to compensate for the uncertainties based on an integral-type Lyapunov function. A fully saturated learning approach is then developed to achieve asymptotic tracking of repetitive walking trajectories. Extensive experiments are carried out to demonstrate the effectiveness of the tracking performance.

Design of General Parametric Repetitive Control Using IIR Filter With Application to Piezo-Actuated Nanopositioning Stages

The achievable performance with repetitive control is limited due to its inherent sensitivity to the frequency shift away from the intended periodic frequencies and the undesired gain amplification of the aperiodic disturbances. To address these limitations, the paper proposed a general parametric repetitive control (GPRC) method based on the IIR filter with the features of low-order and excellent magnitude responses to result in better tracking performance in diverse applications. By analyzing its sensitivity function, it is found that the design of GPRC can be converted to the explicit parametric design of an IIR high pass filter. The controller design process and the stability analysis are presented in detail. To show the effectiveness of GPRC, comparative experiments are conducted via tracking sinusoids, triangular trajectories and other complex trajectories with multi-frequency components. The experimental results show that, in contrast with the conventional repetitive control (CRC) and a modified repetitive control (MRC), the GPRC exhibits excellent robustness against the frequency shift and advanced performance at the aperiodic frequencies. The tracking results of the sinusoids show that the maximum tracking error obtained with GPRC for a frequency shift of 3 Hz decreases from 0.0259 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu m$</tex-math> </inline-formula> (CRC) and 0.2207 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu m$</tex-math> </inline-formula> (MRC) to 0.0101 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu m$</tex-math> </inline-formula> at the nominal frequency of 1000 Hz, demonstrating the merits of the proposed GPRC. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —To enable automation systems, one of the crucial requirements is to track repetitive references with high precision. Although the normal repetitive control (RC) based schemes are successfully applied to improve the tracking accuracy of periodic trajectories, the existing RC schemes suffer from the problems of lower robustness against frequency shift and the unwanted gain amplification at the aperiodic frequencies due to Bode’s sensitivity integral. To overcome this problem, this paper proposes a novel general parametric repetitive control (GPRC) method via characterizing the loop properties quantitatively based on the IIR high pass filter design. Focusing on specific issues, the detailed variations to handle the errors at only the odd-and even-harmonics are also demonstrated. This framework leads to a flexible solution in practical implementations. The experimental validation on a piezo-actuated nanopositioning stage is comparatively presented in terms of tracking accuracy and rejection ability of the gain amplification at the aperiodic frequencies. With its flexibility and effectiveness, the proposed GPRC can be easily implemented in diverse applications.

A Fast Repetitive Control Strategy for a Power Conversion System

With the expansion of renewable energy sources, the stable and high-quality operation of microgrids composed of new energy sources has attracted widespread attention. Among them, the power conversion system (PCS), as an important part of microgrids, plays a crucial role in their operation and management. The PCS operation modes are classified into grid-connected and off-grid modes. However, in off-grid mode, due to the access of nonlinear and unbalanced loads, the output voltage quality of a PCS is worse, and the voltage waveform distortion is serious. To solve these problems, a fast repetitive control (FRC) strategy is proposed for a power conversion system with an Active Neutral Point Clamped (ANPC) architecture of three levels. The voltage loop control strategy can be applied to the voltage/frequency (V/f) mode and the grid-forming mode. The control strategy can effectively realize the suppression of the harmonics of the output voltage and has a 100% capability to carry unbalanced loads. Finally, a 1725 kVA PCS prototype is developed, and the proposed control strategy is verified using the MT3200 HIL semiphysical simulator of ModelingTech in the V/f mode as an example. This practically verifies the feasibility and validity of the proposed control strategy, which has a certain degree of engineering practicability and reference due to the simplicity of the design and the ease of realization.

Simulation system of intelligent photovoltaic grid-connected inverter considering fuzzy PI control

The grid connected inverter is the core component of the photovoltaic grid connected power generation system, which mainly converts the direct current of the photovoltaic matrix into alternating current that meets the grid connected requirements, playing a key role in the efficient and stable operation of the photovoltaic grid connected power generation system.This paper uses fuzzy PI control model which to improve the performance of intelligent photovoltaic grid-connected inverter to simulate the intelligent photovoltaic inverter system, using mathematical analysis and reasoning methods for model analysis,adopts two-stage three-phase LCL grid-connected inverter, establishes mathematical models in two-phase synchronous rotating and two-phase static coordinate systems, and adopts an active damping strategy based on grid-connected current. Based on existing research and empirical analysis,aiming at the disadvantage of poor dynamic response of repetitive control, an improved repetitive control strategy is adopted, and the controller is analyzed from two aspects of stability and dynamic performance, and the simulation model of photovoltaic grid-connected power generation system is built. Use experimental analysis method to verify the effectiveness of the model in this article,The experimental results show that the simulation system of intelligent photovoltaic grid-connected inverter considering fuzzy PI control proposed in this paper has certain effects.

An adaptive discretized RNN algorithm for posture collaboration motion control of constrained dual-arm robots.

Although there are many studies on repetitive motion control of robots, few schemes and algorithms involve posture collaboration motion control of constrained dual-arm robots in three-dimensional scenes, which can meet more complex work requirements. Therefore, this study establishes the minimum displacement repetitive motion control scheme for the left and right robotic arms separately. On the basis of this, the design mentality of the proposed dual-arm posture collaboration motion control (DAPCMC) scheme, which is combined with a new joint-limit conversion strategy, is described, and the scheme is transformed into a time-variant equation system (TVES) problem form subsequently. To address the TVES problem, a novel adaptive Taylor-type discretized recurrent neural network (ATT-DRNN) algorithm is devised, which fundamentally solves the problem of calculation accuracy which cannot be balanced well with the fast convergence speed. Then, stringent theoretical analysis confirms the dependability of the ATT-DRNN algorithm in terms of calculation precision and convergence rate. Finally, the effectiveness of the DAPCMC scheme and the excellent convergence competence of the ATT-DRNN algorithm is verified by a numerical simulation analysis and two control cases of dual-arm robots.

A Generic Multi-Frequency Repetitive Control Scheme for Power Converters

A Generic Multi-Frequency Repetitive Control (GMFRC) scheme, is proposed to perfectly compensate for all kinds of periodic signals including multi-frequency signals, where multiple selective harmonic repetitive controllers in parallel are added into a stable instantaneous feedback control loop to achieve overall satisfactory performance. The GMFRC scheme provides a general framework for housing various repetitive control and even resonant control schemes in power electronic conversion and other extensive engineering applications. A universal approach to the analysis and synthesis of the digital GMFRC scheme has been developed, which includes the stability criteria and control gain rules. More important, the digital GMFRC controller is transformed into a general fractional-order one for exact compensation of multi-frequency signals and other fractional-order periodic signals in practice. An application example of a 5kVA three-phase PWM inverter under a fractional-order GMFRC scheme is provided. Experimental results demonstrated that the proposed GMFRC scheme can force the inverter to produce required mono-frequency or multi-frequency voltages with high accuracy, fast response and good robustness.

Current harmonic suppression for PMSM driven system utilizing PI-DFT-RC controller

The permanent magnet synchronous motor (PMSM) driven by the two-level voltage inverters features some drawbacks, such as dead-zone time, nonlinearity and other factors, leading to high amount harmonics in the stator currents. Additionally, the current harmonics amplitude will be decayed with the increasing of the harmonic order, and the main current harmonic components can be illustrated as 6th control signal harmonics. To improve the current harmonics suppression efficiency and maintain the simplicity of the PMSM driven system, the relationships between traditional repetitive controller and bandpass filter are analysed firstly. And then, a proportional–integral​ discrete Fourier transform repetitive control (PI-DFT-RC) scheme is proposed through adopting independent band-pass filters of state frequencies, which can provide infinite gain in stated frequency. Secondly, the discrete periodic signals for RC controller are analysed, and the lead step for DFT-RC controller is also studied, which can increase the signal tracking accuracy of the driven system. Furthermore, the stability of the driven system used PI-DFT-RC controller is analysed through Lyapunov theory. Finally, the effectiveness of the proposed PI-DFT-RC controller is verified by simulation results.

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.

Spatial Repetitive Impedance Learning Control for Robot-Assisted Rehabilitation

In robot-assisted rehabilitation and leg exoskeletons, humans and robots are required to collaboratively complete repetitive tasks with fixed periodic paths. In such applications, impedance learning control can provide variable impedance regulation for improving the performance of physical interactions; however, designing such control is highly challenging owing to the difficulty in modeling human time-varying dynamics. By exploiting the spatial periodicity characteristics of the desired trajectory and human impedance, we propose a novel spatial repetitive impedance learning control strategy to enhance interaction performance. First, a defined spatial operator serves as the mathematics foundation for constructing the robot dynamics in the spatial domain. Then, a spatial impedance learning controller is designed. In this article, time-varying impedance profiles are estimated using spatial full-saturation iterative learning laws, while robotic parameter uncertainties are estimated using the differential adaptation law with projection modification. We validate the uniform convergence of the tracking error through a Lyapunov-like analysis and demonstrate the control effectiveness using an illustrative example. Compared with related results on temporal repetitive learning control, the proposed control approach can enable human–robot system to complete a repetitive task with unspecified speeds according to the users' strengths and motion capacity.

Band-stop-filter-based repetitive control of fast tool servos for diamond turning of micro-structured functional surfaces

Fast tool servo (FTS) is a promising technique for the high-speed diamond turning of micro-structured functional surfaces due to its fast response capacity. However, the inherent actuator non-linearity, the lightly damped vibration mode and the external disturbance of the FTS would degrade its tracking performance severely and thus restrict its machining ability. To overcome this limitation, a band-stop-filter-based repetitive control (BSF-RC) scheme is proposed in this article to improve the operating performance of the FTS. Firstly, the spectra of the FTS tool paths (FTS-TPs) for machining typical micro-structured functional surfaces with the cylindrical coordinate machining method are analyzed in detail. The results reveal that the frequency components concentrate on the tiny neighborhoods of the rotational frequency of the spindle and its harmonic frequencies. Afterwards, the comb-like band-stop filter used by the BSF-RC is elaborately designed via the cascade of three comb-like notch filters to generate a comb-like band-stop loop shape for covering main spectral components of the FTS-TPs. The analytical expression of the comb-like band-stop filter amplitude as well as the stability condition of the closed-loop control system are derived to provide effective criteria for the parameter selection of the BSF-RC. The experimental validation of the developed BSF-RC scheme is conducted on a five-axis ultra-precision lathe equipped with a self-developed FTS via the diamond turning of three typical micro-structured functional surfaces. The experimental results show that good surface qualities with the maximal form error of a few hundred nanometers and the surface roughness of a several nanometers are achieved for all the obtained micro-structured surfaces by using the BSF-RC scheme under a high spindle speed.

Discrete-Time Design of Dual Internal Model-Based Repetitive Control Systems

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.

Current Harmonic Suppression of BLDC Motor Utilizing Frequency Adaptive Repetitive Controller

Compared to the proportional-integral strategy, the repetitive control strategy possesses high suppression ability for the alternating current (AC) harmonics of control signals. Thus, RC controllers are widely used in closed-loop control systems to suppress the periodic harmonics. In order to further improve the brushless DC (BLDC) motor operation performance, a frequency adaptive repetitive controller (FARC) is proposed, and then a novel current loop scheme that concatenation of proportional-integral controller (PIC) and FARC controller is established in this paper. Firstly, due to the real sampling number of the delay element in the BLDC, the motor control system may not be an integer, the designing process of the FARC parameters was studied, and an adaptive internal model controller and a novel decomposition rule for FARC were designed based on Lagrange interpolation theory. Secondly, the PIC parameters were analyzed through three-dimensional and two-dimensional images of the frequency characteristics. Furthermore, a composite controller that added a forward channel in the novel current loop was proposed, and the stability of the control system used the composite controller was analyzed through Lyapunov theory. It should be noted that the analysis of FARC mainly focused on the simplified structure and the parameter optimization, which is usually ignored in the previous studies. Finally, the BLDC motor control system model was established through Matlab/Simulink software, and the operation performances of the BLDC motor control system utilizing different current loop controllers were studied. The simulation results show that the proposed FARC can reduce current distortion and torque ripples, thus, the BLDC motor operation performances can be improved effectively.

Reliable nonfragile tracking control for switched systems with external disturbances

AbstractWith the assistance of reliable control technique, the nonfragile tracking problem has been proposed in this paper for a class of switched systems with external disturbances under the aegis of modified repetitive controller. Notably, the designed repetitive controller is used to improve the tracking performance of the addressed switched systems. Preciously, the influence of external disturbances are estimated through the improved equivalent‐input‐disturbance strategy, wherein the effect caused by the external disturbances to the output channel are reduced by the aid of modified repetitive control strategy. The fundamental intention of this control synthesis is that the output of the system precisely tracks the reference signal even in the presence of external disturbances and gain fluctuations. For that cause, Lyapunov stability technique in conjunction with average dwell time approach is implemented to obtain adequate conditions in the shape of linear matrix inequalities which insists the exponential stability for the addressed system. Ultimately, the efficiency and supremacy of the proposed control schemes are justified via two numerical examples, wherein it is exposed to view that the developed control strategy is capable of good tracking performance and also estimates the external disturbances efficiently.