Repetitive Control Scheme Research Articles

Research on hybrid controller utilizing proportional and repetitive control scheme for Permanent Magnet Servo System

Due to the existence of high amount stator current harmonics caused by the inverter nonlinearity, the operation performance of Permanent Magnet Servo System (PMSS) used Proportional–Integral (PI) controller will be affected. To suppress the current harmonics in the PMSS, a hybrid controller utilizing proportional and repetitive control scheme for the current loop is proposed. Firstly, the phase-frequency characteristic and the magnitude–frequency characteristic for the hybrid controller bode diagrams are analysed. To improve the open-loop gain in the frequency band of high-proportion harmonics and compensate the phase lag, the hybrid controller parameter setting method is also studied. Furthermore, the stability and the anti-interference ability of the PMSS used hybrid controller are analysed through Lyapunov theory. Finally, the PMSS model is established through Matlab/Simulink software, and the operation performances of the PMSS utilizing different current loop controllers are studied. The simulation results show that the proposed hybrid controller can suppress the current harmonics and the output torque ripple effectively.

6-Step Discrete ZNN Model for Repetitive Motion Control of Redundant Manipulator

In this article, the repetitive motion control of redundant manipulators is investigated. First, a repetitive motion control scheme is presented, and a continuous zeroing neural network (CZNN) model is obtained for solving the scheme. Meanwhile, the development of a discrete zeroing neural network (DZNN) model is desired for convenient computational processing. Based on this, this article proposes a 6-step discretization formula, which has high precision. By using the 6-step discretization formula and the 4-step backward difference formula, a 6-step DZNN (6SDZNN) model is further proposed to handle the repetitive motion control scheme. Theoretical analyses verify the efficacy of the 6SDZNN model. Additionally, some discrete forms of conventional models are developed for comparison. Computer simulations on the basis of the 4-link redundant manipulator are carried out, verifying the theoretical analyses and showing the efficacy of the 6SDZNN model. Finally, physical experiments on the basis of the Kinova Jaco <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> manipulator substantiate the practicability of the 6SDZNN model.

Multiperiodic Repetitive Control for Functional Electrical Stimulation-Based Wrist Tremor Suppression

Intention tremor refers to the rhythmic and involuntary contraction and relaxation of muscles with movement toward a target, which is a common sequela of multiple sclerosis and usually occurs in the distal joints of the upper limb. Functional electrical stimulation (FES) is feasible for tremor suppression because of its fewer side effects, low cost, and portability. Most existing FES-based design methods assume that tremor is a single-frequency signal, though it is multifrequency in reality. The idealized simplification will limit the performance of tremor suppression. To address the problem, this article proposes an FES-based multiperiodic repetitive control (MP-RC) scheme to suppress multiple frequency wrist tremors. First, a nonlinear wrist musculoskeletal model with a Hammerstein structure is established. Then, a control strategy combining the model inverse linearization control and MP-RC is proposed for tremor suppression. A frequency-modified inverse RC algorithm and a gradient-based RC algorithm are developed to regulate the FES level. Finally, comparative experiments on four unimpaired participants and an intention tremor patient are conducted to validate the effectiveness of the proposed control schemes. Experimental results show that the MP-RC scheme can suppress tremors by up to 90.52%. Compared with the traditional filter-based feedback controller and the single-periodic repetitive controller, the proposed multiperiodic repetitive controller can achieve an average of 26% and 16% improvement, respectively, in tremor suppression, demonstrating the advantages of the proposed design.

Fractional-Order Multiperiodic Odd-Harmonic Repetitive Control of Programmable AC Power Sources

In this article, a generic plug-in fractional-order multiperiodic odd harmonic repetitive control (FOMP-OHRC) scheme is proposed to provide a simple high-performance control solution to the programmable ac power sources. The proposed FOMP-OHRC scheme evolves from the plug-in multiperiodic OHRC scheme, which can take both advantages of the multiperiodic OHRC controller and the feedback controller—the feedback controller provides fast response and good robustness, and the plug-in multiperiodic OHRC controller offers accurate compensation of the multiperiodic signals. The stability criteria and the control gain tuning rules have been developed to facilitate the analysis and synthesis of the plug-in multiperiodic OHRC scheme. More critically, in order to exactly compensate the multiperiodic signals with unavoidable fractional periods in practice, the multiperiodic OHRC controller is transformed into the FOMP-OHRC controller by substituting the fractional period elements with the Lagrange-polynomial-based interpolation filters. Experimental results indicated the programmable ac power source with the proposed FOMP-OHRC can generate required multiperiodic voltages with high accuracy, fast transient response, and good robustness.

Power Quality Improvement in Three-Phase Grid Connected Photovoltaic Cells using MMC with Fuzzy Logic Controller

In modular multilevel converter (MMC), the sub modules which perform switching actions, it may produce higher order harmonics when involved with fluctuating capacitor voltages and when it gets superimposed with the circulating currents, it will increase their magnitude which results into increased system losses. In this research work, we have implemented a repetitive control scheme which consists of three components: PI controller, moving average filter and repetitive controller. It is applied to MMC equipped with fuzzy controlled logic, which controls the harmonics by suppressing them up to a significant level. The proposed model is designed for three phase applications and the simulation results clearly define the effectiveness of the control mechanism. Photovoltaic’s (PV) is a method of generating electrical power by converting sunlight into direct current electricity using semiconducting materials that exhibit the photovoltaic effect. A photovoltaic system employs solar panels composed of a number of solar cells to supply usable solar power. Power generation from solar PV has long been seen as a clean sustainable [1] energy technology which draws upon the planet’s most plentiful and widely distributed renewable energy source – the sun. The direct conversion of sunlight to electricity occurs without any moving parts or environmental emissions during operation. KEYWORDS: MMC, Fuzzy Logic, Harmonic Suppression, Three phases, Repetitive Control, SIMULINK

Preview repetitive control for polytopic nonlinear discrete-time systems.

In this study, a preview repetitive control (PRC) strategy was developed for uncertain nonlinear discrete-time systems subjected to a previewable periodic reference signal. The proposed preview repetitive controller was designed such that the system output tracked a previewable periodic reference signal even with model uncertainties and nonlinear terms. An augmented two-dimensional (2D) model was constructed based on the 2D model approach and state augmented technique. Second, considering the state unmeasured and periodic tracking reference signal, a static output PRC law was designed using the linear matrix inequality (LMI) techniques. Finally, the effectiveness of the proposed controller was verified through two illustrative examples.

Research on Compound PID Control Strategy Based on Input Feedforward and Dynamic Compensation Applied in Noncircular Turning.

The fast tool servo (FTS) control strategy is the control core of high-speed noncircular turning. This method should ensure high-speed and precision positioning and have the corresponding anti-interference ability in the micro-stroke motion with dynamic changes of tool feed and load. Most of the previous FTS control studies used the repetitive control and speed feedforward control strategy, which achieved promising results under ideal machining conditions. However, this strategy showed some defects in the real-world complex and changeable working conditions such as time-varying cutting force, intermittent cutting and fluctuating machine spindle speed. This paper proposed and implemented a compound proportional integral derivative control strategy based on input feedforward and dynamic compensation in noncircular turning. This technique successfully met the motion requirements of the high responsiveness of micro-stroke in noncircular turning and overcame disturbances from complex time variations of the cutting force, intermittent cutting case of the product and fluctuations of machine spindle speed. According to the findings, the machining tracking error was less than ±2 µm. Experimental results demonstrated the excellent tracking performance and machining effect of this control strategy.

General High-Order Selective Harmonic Repetitive Control for PWM Converters

In this article, a general high-order selective harmonic repetitive control (HO-SHRC) scheme is proposed, which is composed of a standard high-order repetitive controller structure and a new order-expandable SHRC. Different from conventional SHRC, the proposed new SHRC is capable of being applied into the standard high-order repetitive control (HORC) structure for generating any high-order SHRC. The proposed HO-SHRC can be used to improve the steady-state tracking accuracy of the pulsewidth modulation (PWM) converter systems and is robust to system frequency variations without changing the controller parameters online. The order expansion of the controller will lead to the increase of the implementation complexity, but it will bring the overall improvement of the controller performance, such as the improvement of frequency adaptability, steady-state tracking accuracy, and dynamic performance. Therefore, HO-SHRC can achieve a good compromise between the controller performance and the implementation complexity. Moreover, the proposed HO-SHRC provides a general structure for various repetitive controls (RCs), such as conventional RC (CRC), odd-harmonic RC (OHRC), high-order CRC (HO-CRC), and HO-odd-harmonic RC (HO-OHRC). Application examples of second-order (SO)- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$6k~\pm $ </tex-math></inline-formula> 1 RC-controlled three-phase PWM inverter show the effectiveness and advantages of the proposed control scheme.

Dual-Notch-Based Repetitive Control for Tracking Lissajous Scan Trajectories With Piezo-Actuated Nanoscanners

Using Lissajous scan trajectory is a promising way to get rid of issues resulting from the raster scan trajectory in several advanced applications, like atomic force microscopy and fast steering mirror. Although the repetitive control (RC)-based schemes, which are tailed to track periodic trajectories, have been successfully utilized to improve the tracking performance of the Lissajous trajectories, the enabled performance is limited due to the unavoidable dynamic cross-coupling effect. To address this issue, this article proposes a dual-notch-based RC (DNRC) scheme via generating the dual-notch loop shaping behaviors at two sets of fundamental frequencies as well as their harmonics for eliminating the errors distributed at these frequencies. The design process and the parameters determination are provided in detail. Comparative experiments with the modified RC (MRC) and the baseline Proportional-Integral (PI) tracking controller are conducted on a piezo-actuated nanoscanner for typical scanning rates of 50- and 100-Hz. The results show that the maximum tracking error under the scanning rate of 100-Hz is reduced greatly from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.1562~\mu \text {m}$ </tex-math></inline-formula> with PI + MRC and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$7.1788~\mu \text {m}$ </tex-math></inline-formula> with PI to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.0337~\mu \text {m}$ </tex-math></inline-formula> , confirming the effectiveness of the proposed DNRC in high-performance Lissajous scanning.

Control Strategy of Microgrid Inverter Based on H∞ State Feedback Repeated Deadbeat Control

Aiming at the voltage distortion at the microgrid public connection point caused by nonlinear loads, a H∞ state feedback deadbeat repetitive control strategy is proposed to rectify the total harmonic distortion of the output voltage. Firstly, through establishing the state space of the repetitive controller, introducing state feedback, combining the H∞ control theory, and reformulating the system stability problem as a convex optimization problem with a set of linear matrix inequality (LMI) constraints to be solved, high stability control accuracy can be guaranteed and antiharmonic interference strengthened. Secondly, by introducing deadbeat control technology to improve the transient response speed of the system, changes in output voltage caused by load changes can be quickly compensated. Compared with the existing methods, the designed control method has the advantages of good stability, low harmonic content, and fast convergence speed, and the results are easier to verify. Finally, the simulation verifies the effectiveness of the proposed control strategy.

Preview repetitive control for linear discrete‐time periodic systems

AbstractA discrete‐time preview repetitive control (PRC) scheme was proposed for linear discrete‐time periodic systems that were subjected to previewable reference signals. First, the state augmentation technique was used to derive an augmented system that included future information on previewable signals. Second, a two‐dimensional (2D) model was developed for the augmented system so that the control and leaning actions can be adjusted preferentially by using control gains. Sufficient conditions that guarantee the closed‐loop stability of the augmented 2D systems were derived, and the design of a periodic controller with preview action and repetitive control was proposed using the linear matrix inequality approach. Finally, the effectiveness of the proposed PRC was established by using two numerical simulation examples.

Application of Repetitive Control and ANFIS-PI Compound Control Strategy in APF

In order to effectively solve a series of problems caused by harmonics in power system, an active power filter based on ANFIS-PI and repetitive control is designed. The traditional single control method cannot balance control accuracy and response speed, so a compound control strategy is adopted. Repetitive control can produce the same output as the harmonic current, so it can achieve zero steady-state error tracking compensation for each harmonic, but its dynamic performance is not good. As a traditional control method, the PI control method has a fast response speed, but in the actual application process, when the load changes suddenly, that is, when the system parameters change, its tracking effect is not ideal. Therefore, a composite control strategy of ANFIS-PI and repeated control is proposed. It has been proved that its compensation accuracy and dynamic response speed have been significantly improved.

Adaptive current harmonics suppression strategy for grid-tie inverters

Since the observed angle of a phase-locked loop (PLL) is relatively accurate even under distorted grid conditions, the mathematical model of the voltage errors caused by the switching modulation and the dead-time effect are derived as a function of the grid voltage angle in this paper. Based on the model analysis, an adaptive compensation algorithm is proposed to suppress the grid-side current harmonics in three-phase converters. The proposed algorithm fits the unmeasurable voltage errors by a truncated Fourier series expansion, and then takes it as an equivalent disturbance in the current control loop to achieve harmonic compensation. By the feed-forward compensation, the design and tuning of the controller parameters are simplified and separated from the dynamic performance. In addition, the controller can adapt to the grid frequency variation by updating the grid voltage angle with the PLL block. To reduce the computational burden, a simplified version of the proposed method is also presented. Simulation and experiment results show that the proposed methods can suppress the current harmonics and achieve better performance in terms of total harmonic distortion, strong robustness and insensitivity to the grid frequency variations, compared with the traditional PI control or repetitive control strategy.

Padé-Approximation-Based Preview Repetitive Control for Continuous-Time Linear Systems

This paper concerns a Padé-approximation-based preview repetitive control (PRC) scheme for continuous-time linear systems. Firstly, the state space representation of the repetitive controller is transformed into a nondelayed one by Padé approximation. Then, an augmented dynamic system is constructed by using the nominal state equation with the error system and the state equation of a repetitive controller. Next, by using optimal control theory, a Padé-approximation-based PRC law is obtained. It consists of state feedback, error integral compensation, output integral of repetitive controller, and preview compensation. Finally, the effectiveness of the method is verified by a numerical simulation.

LCL APF based on fractional-order fast repetitive control strategy

LCL APF based on fractional-order fast repetitive control strategy

Multibandwidth Repetitive Control Resisting Frequency Variation in Grid-Tied Inverters

In this article, multibandwidth repetitive control (RC) is developed and applied to a grid-tied inverter to resist grid frequency variation. In the proposed RC, each of the resonant bandwidth is set individually by the gain of the internal model filter. A design procedure for the internal model filter is proposed, which splits the filter into several zero-phase finite impulse response (FIR) filters for reducing the design difficulties. The control structure and stability analysis show that the gain of the multibandwidth RC is increased. An example design procedure for the multibandwidth RC is presented in detail. Comparison experiments with different RCs are performed under deviated grid frequencies, and the results demonstrate the effectiveness of the proposed multibandwidth RC scheme.

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.

Low‐order sliding mode repetitive control for discrete‐time systems under complex disturbance environment

AbstractA novel sliding mode repetitive control scheme is proposed for discrete‐time systems. It aims to address aperiodic disturbances, and simultaneously address a set of disturbances of known frequencies that can be unrelated. The sliding mode handles the former, and a repetitive control algorithm deals with the latter, creating a low‐order sliding model repetitive control law. The approach addresses each disturbance frequency individually. In contrast to the usual repetitive control approach, this allows one to address multiple unrelated frequencies without difficultly. Even when the addressed frequencies are harmonically related, but a relatively small number have significant error, this approach offers both substantial computation benefit, and benefit facilitating improved control of aperiodic disturbances. When both multiperiodic and aperiodic disturbances are present, the system trajectories can converge to a smaller switching band and keep moving within it. When there is only multiperiodic disturbance, the system trajectories will cross the switching surface within every specific steps when in the switching zone, and will converge to zero eventually. Simulation results demonstrate obvious advantages compared with the traditional method.

Repetitive Control Scheme of Robotic Manipulators Based on Improved B-Spline Function

In this paper, a repetitive control scheme of a 2-DOF robotic manipulator based on the improved cubic B-spline curve is proposed. Firstly, a repetitive controller for robotic manipulator is designed, which is composed of an iterative controller and disturbance observer. Then, an improved B-spline optimization scheme is introduced to divide the task of the robotic manipulator into three intervals. A correction function is added to each interval of cubic spline interpolation. Finally, a variety of cases are designed and simulated by MATLAB. The experimental results show that, compared with the conventional B-spline, the improved B-spline has better performance in tracking accuracy and smoothness of motion trajectory. By changing the mechanism of the manipulator, the cases of different weights and lengths are designed. The experimental results in these cases show that the proposed scheme can be applied to most of the 2-DOF robotic manipulator control systems.

Adaptive sliding mode repetitive learning control of the upper-limb exoskeleton with unknown dynamics

This article proposes a new adaptive sliding mode repetitive learning control strategy. The proposed controller can obtain satisfactory position tracking performance in the presence of unknown dynamics and external disturbance. The unknown dynamics parameters of the exoskeleton system can be estimated via an adaptive algorithm, which is used to design the sliding mode control law. Besides, the periodic external disturbance of the system can be compensated by repetitive learning to reduce the tracking error. The stability of the proposed method is demonstrated rigorous by the Lyapunov theory. Using an upper-limb exoskeleton model, simulation results demonstrate the effectiveness of the control strategy. The proposed method has a better control performance than other methods.