Design of Discrete-time Repetitive Control System Based on Two-dimensional Model

This paper presents a novel design method for discrete-time repetitive control systems （RCS） based on two-dimensional （2D） discrete-time model. Firstly, the 2D model of an RCS is established by considering both the control action and the learning action in RCS. Then, through constructing a 2D state feedback controller, the design problem of the RCS is converted to the design problem of a 2D system. Then, using 2D system theory and linear matrix inequality （LMI） method, stability criterion is derived for the system without and with uncertainties, respectively. Parameters of the system can be determined by solving the LMI of the stability criterion. Finally, numerical simulations validate the effectiveness of the proposed method.

Dynamic Stiffness Analysis of Repetitive Control System

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

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 theTHDof the ac current,thus lowering the power factor.Therefore,the current closed-loop for suppressing 6k±1 harmonics is essential tomeet 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.

Observer-based Iterative and Repetitive Learning Control for a Class of Nonlinear Systems

In this paper, both output-feedback iterative learning control(ILC) and repetitive learning control(RLC) 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.

Continuous rotary motor electro-hydraulic servo system based on the improved repetitive controller

In order to suppress the periodic interference of the continuous rotary electro-hydraulic servo motor,this paper makes the motor tracking the periodic signals with high accuracy,and improves the influence of friction interference to the performance of continuous rotary electro-hydraulic servo motor.The mathematic model of the electro-hydraulic position servo system of the continuous rotary motor was established,and the compound control method was adopted based on the repetitive control,feed forward and PID to suppress the friction interference.Through the simulation,the result confirms that the compound control method decreases the tracking error of the system,increases the robust performance of the system and improves the performance of the continuous rotary electro-hydraulic servo motor.

Design of Decentralized Multi-input Multi-output Repetitive Control Systems

This paper presents the design of decentralized repetitive control （RC） for multi-input multi-output （MIMO） systems. An optimization method is used to obtain a RC compensator that ensures system stability and good tracking performance. The designed compensator is in the form of a stable, low order, and causal filter, in which the compensator can be implemented separately without being merged with the RC internal model. This will reduce complexity in the implementation. Simulation results and comparison study are given to demonstrate the effectiveness of the proposed design. The novelty of design is also verified in experiments on a 2 degrees of freedom （DOF） robot.

FBFN-based adaptive repetitive control of nonlinearly parameterized systems

An adaptive repetitive control scheme is presented for a class of nonlinearly parameterized systems based on the fuzzy basis function network （FBFN）. The parameters of the fuzzy rules are tuned with adaptive schemes. To attenuate chattering effectively, the discontinuous control term is approximated by an adaptive PI control structure. The bound of the discontinuous control term is assumed to be unknown and estimated by an adaptive mechanism. Based on the Lyapunov stability theory, an adaptive repetitive control law is proposed to guarantee the closed-loop stability and the tracking performance. By means of FBFNs, which avoid the nonlinear parameterization from entering into the adaptive repetitive control, the controller singularity problem is solved. The proposed approach does not require an exact structure of the system dynamics, and the proposed controller is utilized to control a model of permanent-magnet linear synchronous motor subject to significant disturbances and parameter uncertainties. The simulation results demonstrate the effectiveness of the proposed method.

Design of observer-based discrete repetitive-control system based on 2D model

A discrete observer-based repetitive control(RC) design method for a linear system with uncertainties was presented based on two-dimensional(2D) system theory. Firstly, a 2D discrete model was established to describe both the control behavior within a repetition period and the learning process taking place between periods. Next, by converting the designing problem of repetitive controller into one of the feedback gains of reconstructed variables, the stable condition was obtained through linear matrix inequality(LMI) and also the gain coefficient of repetitive system. Numerical simulation shows an exceptional feasibility of this proposal with remarkable robustness and tracking speed.

Design and analysis of dual-mode structure repetitive control based hybrid current regulation scheme for active power filters

An all-digital hybrid current regulation scheme for the single-phase shunt active power filter （APF） is presented. The proposed hybrid current control scheme integrates the deadbeat control and the dual-mode structure repetitive control （DMRC） so that it can offer superior steady-state performance and good transient features. Unlike the conventional schemes, the proposed scheme-based APF can compensate both the odd and the even order harmonics in grid. The detailed design criteria and the stability analysis of the proposed hybrid current controller are presented. Moreover, an improved structure which incorporates the proposed hybrid controller and the resonant controller for tracking specific order harmonics is given. The relationships between the resonant controller and different repetitive control schemes are discussed. Experimental results verify the effectiveness and advantages of the proposed hybrid control scheme.

Repetitive PD control strategy with inverse transfer function compensation for CVCF inverter

A novel repetitive control strategy for the output waveform of single-phase CVCF inverters is presented. In this scheme, the inverse transfer function of inverter is used as a compensator to obtain stable and satisfy harmonic rejection. Besides, PD controller is adopted to improve transient performance. Simulation and experimental results, which are gotten from a DSP-based 400Hz, 5.5KW inverter, indicate that the proposed control scheme can achieve not only low THD during steady-state operation but also fast transient response during load step change.

Effect of Combined Low-frequency Repetitive Transcranial Magnetic Stimulation and Virtual Reality Training on Upper Limb Function in Subacute Stroke:a Double-blind Randomized Controlled Trail

The effect of combined low-frequency repetitive transcranial magnetic stimulation（LF r TMS） and virtual reality（VR） training in patients after stroke was assessed. In a double-blind randomized controlled trial, 112 patients with hemiplegia after stroke were randomly divided into two groups： experimental and control. In experimental group, the patients received LF r TMS and VR training treatment, and those in control group received sham r TMS and VR training treatment. Participants in both groups received therapy of 6 days per week for 4 weeks. The primary endpoint including the upper limb motor function test of Fugl-meyer assessment（U-FMA） and wolf motor function test（WMFT）, and the secondary endpoint including modified Barthel index（MBI） and 36-item Short Form Health Survey Questionnaire（SF-36） were assessed before and 4 weeks after treatment. Totally, 108 subjects completed the study（55 in experimental group and 53 in control group respectively）. After 4-week treatment, the U-FMA scores [mean difference of 13.2, 95% confidence interval（CI） 3.6 to 22.7, P〈0.01], WMFT scores（mean difference of 2.9, 95% CI 2.7 to 12.3, P〈0.01）, and MBI scores（mean difference 16.1, 95% CI 3.8 to 9.4, P〈0.05） were significantly increased in the experimental group as compared with the control group. The results suggested the combined use of LF r TMS with VR training could effectively improve the upper limb function, the living activity, and the quality of life in patients with hemiplegia following subacute stroke, which may provide a better rehabilitation treatment for subacute stroke.

Improved Repetitive Control for High-Precision Satellite Rendezvous

This paper is focused on control design for high-precision satellite rendezvous systems.A relative motion model of leader-follower satellites described by relative orbit elements(ROE)is adopted,which has clear geometric meaning and high accuracy.An improved repetitive control(IRC)scheme is proposed to achieve high-precision position and velocity tracking,which utilizes the advantage of repetitive control to track the signal precisely and conquers the effects of aperiodic disturbances by adding a nonsingular terminal sliding mode(NSTSM)controller.In addition,the nonlinear state error feedback(NLSEF)is used to improve the dynamic performance of repetitive controller and the radial basis function(RBF)neural networks are employed to approximate the unknown nonlinearities.From rigorous Lyapunov analysis,the stability of the whole closed-loop control system is guaranteed.Finally,numerical simulations are carried out to assess the efficiency and demonstrate the advantages of the proposed control scheme.

An Improved Repetitive Control Strategy for LCL Grid-Connected Inverter

This paper proposes a cascade repetitive control strategy based on odd internal mode,and combines it with proportional-integral(PI)control to establish a compound repetitive control system for improving the quality of grid connected current of LCL grid connected inverter.More specifically,the proposed method could effectively improve the control effect of grid-connected current of LCL inverter,restrain current harmonics and reduce the distortion rate of grid-connected current.Simulation experiment is conducted to verify the proposed repetitive control strategy,and the verification results show that,compared with traditional PI control,the proposed improved compound repetitive control strategy has a higher response speed,and the steady-state and dynamic performance have also been significantly improved.

Science Letters:Controllable high repetition rate gain-switchedNd:YVO_4 microchip laser

We demonstrated a monolithic, compact, diode-pumped gain-switched Nd:YVO4 laser at 1.064 μm wavelength with controllable repetition rate of 1 Hz to 25 kHz. Stable gain-switched pulse train with maximum repetition rate of 25 kHz and pulse width of 16 ns was obtained.

Study on High Accuracy Hybrid Controller for Periodic Motion Control

In order to realize high accuracy control for periodic motion,a hybrid controller with grey prediction was presented in this paper.Incorporating the grey prediction,repetitive control,and the traditional Proportional-Integral-Differential(PID)control,a design method of the grey prediction repetitive PID(GRPID)control algorithm was investigated,according to the characteristics of the periodic motion control.The hybrid control algorithm can estimate unsure parameters and disturbance of system using grey prediction,and compensate control in terms of the prediction results,and this may improve control quality and robustness of repetitive control for controlling periodic motion.An example was carried out to verify the feasibility of the controller.The simulation results show that this algorithm has better performances than that of the conventional repetitive control system.It indicates the presented control method is more suitable for control system of periodic motion.

Robust adaptive repetitive learning control for a class of time-varying nonlinear systems with unknown control direction

A robust adaptive repetitive learning control method is proposed for a class of time-varying nonlinear systems. Nussbaum-gain method is incorporated into the control design to counteract the lack of a priori knowledge of the control direction which determines the motion direction of the system under any input. It is shown that the system state could converge to the desired trajectory asymptotically along the iteration axis through repetitive learning. Simulation is carried out to show the validity of the proposed control method.

Design of a Discrete-time Output-feedback Based Repetitive-control System

This paper deals with the problem of designing a robust discrete output-feedback based repetitive-control system for a class of linear plants with periodic uncertainties. The periodicity of the repetitive-control system is exploited to establish a two-dimensional （2D） model that converts the design problem into a robust stabilization problem for a discrete 2D system. By employing Lyapunov stability theory and the singular-value decomposition of the output matrix, a linear-matrix-inequality （LMI） based stability condition is derived. The condition can be used directly to design the gains of the repetitive controller. Two tuning parameters in the LMI enable the preferential adjustment of control and learning. A numerical example illustrates the design procedure and demonstrates the validity of the method.

Damping forced oscillations in power system via interline power flow controller with additional repetitive control

With the continuous expansion of power systems and the application of power electronic equipment, forced oscillation has become one of the key problems in terms of system safety and stability. In this paper, an interline power flow controller (IPFC) is used as a power suppression carrier and its mechanism is analyzed using the linearized state-space method to improve the system damping ratio. It is shown that although the IPFC can suppress forced oscillation with well-designed parameters, its capability of improving the system damping ratio is limited. Thus, combined with the repetitive control method, an additional repetitive controller (ARC) is proposed to further dampen the forced power oscillation. The ARC control scheme is characterized by outstanding tracking performance to a system steady reference value, and the main IPFC controller with the ARC can provide higher damping, and further reduce the amplitude of oscillations to zero compared with a supplementary damping controller (SDC). Simulation results show that the IPFC with an ARC can not only greatly reduce the oscillation amplitude, but also actively output the compensation power according to the reference value of the ARC tracking system.

On-Line Adaptive Repetitive Controller for Power Factor Correction Systems

When the fundamental frequency is shifting, it is hard for traditional repetitive controller to work at the resonant frequencies. In this paper, a novel adaptive repetitive controller for power factor correction systems is proposed to suppress the current harmonics. Through the controller, the shifting sampling times of the repetitive controller in a fundamental period can be obtained. Mathematical analysis, simulations and physical experiments have validated the effectiveness of the adaptive repetitive controller.

Nanometer-Order Contouring Control in a Feed Drive System Using Linear Ball Guides by Applying a Combination of Modified Disturbance Observer and Repetitive Control

This paper proposes a quadrant glitch compensation method to achieve nanometer-level accuracy of contouring control for a feed drive system using linear ball guides.The proposed method is a combination of a modified disturbance observer(“disturbance suppressor”)and an improved repetitive control scheme.Sinusoidal motion tests with 1 mm amplitude and 0.1 Hz driving frequency were conducted using a single-axis feed drive system to verify the quadrant glitch compensation ability of this method.First,the repeatability of the quadrant glitches in the experimental system was verified,which is the most important characteristic required for compensation via repetitive control.Then,by applying the combination of disturbance suppressor and conventional repetitive control,the amplitudes of the quadrant glitches were decreased to less than 1 nm;in other words,the ratio of the magnitude of the quadrant glitch to the amplitude of the position reference was less than 1/1,000,000.However,for both compensation schemes mentioned before,vibrations were generated when the feed speed increased.Moreover,the amplitudes increased with the number of repetitions.The reason for the vibrations was identified as the repetitive control mechanism.To suppress these vibrations,the repetitive control was applied only to narrowed regimes near the quadrant glitches.Thus,the maximum contouring error was decreased to 2 nm.In addition,the nonlinear spring behavior of the linear ball guides was confirmed to affect the stability of the control systems.