Multi-period Repetitive Controllers Research Articles

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.

A Control Strategy of Islanded Microgrid With Nonlinear Load for Harmonic Suppression

A control strategy of islanded microgrid is proposed in this paper against the harmonic circulation of the inverters and the Point of Common Coupling (PCC) voltage harmonic distortion of the microgrid caused by nonlinear load. The reference voltage of the inverter’s outer voltage loop is given by the decoupling control of the fundamental and harmonic components. Virtual synchronous generator (VSG) is adopted in fundamental domain. In harmonic domain, adaptive harmonic compensation and harmonic virtual impedance are applied to obtain the harmonic components of the reference voltage of the outer voltage loop. The hybrid control strategy combining P control and repetitive control in parallel is adopted in the outer voltage loop. Multi-period repetitive control (MPRC) with fast repetitive control (FRC) is adopted to improve the tracking control performance of the main harmonic components of the given reference voltage. Fractional order delay approximated by Lagrange interpolation polynomial FIR filter is applied in MPRC for different repetitive control periods at the fixed sampling period. The output harmonic current of the inverters can be distributed autonomously according to the capacity of the inverters to suppress the harmonic circulation, and the suppression of the PCC voltage harmonic distortion is realized. Simulation based on Matlab/Simulink and hardware-in-loop(HIL) test are carried out, and the results show that the proposed control strategy is effective.

FES based wrist tremor suppression using multi-periodic repetitive control

Abstract Tremor is a very common motor disorder, mainly manifested as involuntary, periodic and rhythmic movement in any part of the body, especially in hands and upper-limbs, which seriously affects the life quality of patients. Functional electrical stimulation (FES) has been shown a promising technique to suppress tremor. Most existing FES based design methods assume tremor is a single frequency signal which however is a highly idealized simplification of the real case which contains multiple-frequency or even a frequency band, therefore limiting their practical performance. To address this problem, this paper proposes a controller design method based on multi-periodic repetitive control that is capable of suppressing tremor signal with multiple frequencies. Simulation and experimental results verify the effectiveness of the proposed method.

Multi-Period Repetitive Control for Nonparametric Uncertain Systems

This paper addresses the period-signal tracking problem for a class of nonparametric uncertain systems with several periodic time-varying disturbances, where there is no common multiple among the period lengths of reference signal and disturbances, or the common multiple is difficult to be obtained even if it exists. A multi-period repetitive control scheme is proposed by using Lyapunov approach, with robust technique and unsaturated multi-period repetitive learning technique being integratedly used to compensate uncertainties and periodic disturbances. As the repetitive cycle increases, the system output can track its reference signal perfectly over its full period. Through rigorous analysis, we prove that the estimations themselves are bounded, which is better than the boundedness in the sense of $L_{2}$ norm obtained in many existing unsaturated learning results. In the end, an illustrative examples is provided to demonstrate the efficacy of the proposed multi-period repetitive control scheme.

A design method for robust stabilizing multi-period repetitive controllers for multiple-input/multiple-output time-delay plants

A design method for robust stabilizing multi-period repetitive controllers for multiple-input/multiple-output time-delay plants

Robust stabilizing simple multi-period repetitive controllers for multiple-input/multiple-output time-delay plants

The simple multi-period repetitive control system proposed by Yamada and Takenaga is a type of servomechanism for a periodic reference input. That is, the simple multi-period repetitive control system follows the periodic reference input with a small steady state error, even if a periodic disturbance or uncertainty exists in the plant. In addition, simple multi-period repetitive control systems ensure that the transfer functions from the periodic reference input to the output and from the disturbance to the output have a finite number of poles. Yamada et al. clarified the parameterization of all stabilizing simple multi-period repetitive controllers. Recently, Sakanushi et al. proposed the parameterization of all robust stabilizing simple multi-period repetitive controllers for multiple-input/multiple-output plants with uncertainty. However, their method cannot be applied to time-delay plants. In this paper, we propose the parameterization of all robust stabilizing simple multi-period repetitive controllers for multiple-input/multiple-output time-delay plants.

Multi-Period Discrete-Time Repetitive Control for Permanent Magnet Linear Synchronous Motor

While tracking the periodic input signal, the position-dependent periodic thrust ripple caused by ending effect, load disturbance and the friction of the permanent magnet linear synchronous motor (PMLSM) will reduce the servo performance of the system. Especially when the periods of the reference input signal and thrust fluctuation interference signal are not synchronous, the precision of periodic signal tracked by the servo system is reduced, which lead to the reduction of the servo system’s periodic signal tracking precision. Therefore, a multi-period discrete repetitive controller using two improved prototype repetitive controllers which are incomplete parallel to restrain\track the multi-period input signal was designed. Theoretical analysis and simulation results show that the proposed scheme can improve the precision of the system tracking periodic signals and restrain the periodic thrust fluctuations effectively.

A Design Method for Simple Multi-Period Repetitive Controllers with the Specified Input-Output Frequency Characteristic

A Design Method for Simple Multi-Period Repetitive Controllers with the Specified Input-Output Frequency Characteristic

Linear Optimal Multi-periodic Repetitive Control - A Low Order Controller Scheme

This article proposes a new method for treating the computational problem in discrete time linear multi-periodic repetitive control systems, where the reference signal includes several periodic components with already known periods. As periods get large, the computational problem becomes prominent. This work thus investigates the frequency contents of reference signals, where the order of original repetitive controller is lowered by considering only a reduced number of poles, namely, the most important contributors to the total energy of the multi-periodic reference signal. A lower order multi-periodic repetitive controller is designed which assures BIBO stability of the closed-loop system, and approximate tracking is achieved. Finally, experimental tests on a non-minimum phase spring mass damper system demonstrate the effectiveness of this new controller.

A Design Method for Two-Degree-of-Freedom Multi-Period Repetitive Control Systems with the Specified Frequency Characteristic

Multi-period repetitive controllers improve the disturbance attenuation characteristic of themodified repetitive control system that follows the periodic reference input with small steady stateerror. Recently, the parameterization of all stabilizing multi-period repetitive controllers was studied.However, when the parameterization of all stabilizing multi-period repetitive controllers is used, theinput-output characteristic and the feedback characteristic cannot be specified separately. From thepractical point of view, it is desirable to specify the input-output characteristic and the feedback characteristicseparately. In addition, the parameterization is useful to design stabilizing controllers. Fromthis view-point, the parameterization of all stabilizing two-degree-of-freedom multi-period repetitivecontrollers those can specify the input-output characteristic and the disturbance attenuation characteristicseparately was solved by Yamada et al. However, when we design a stabilizing two-degree-offreedommulti-period repetitive controllers using the parameterization proposed by Yamada et al, thefrequency characteristic of the control system cannot be settled so easily. From the practical point ofview, the frequency characteristic of the control systems are required to be easily settled. This problemcan be solved by obtaining the parameterization of all stabilizing two-degree-of-freedom multi-periodrepetitive controllers with the specified frequency characteristic. In this paper, we propose the parameterizationof all stabilizing two-degree-of-freedom multi-period repetitive controllers with thespecified frequency characteristic.

A Design Method for Robust Stabilizing Simple Multi-Period Repetitive Controllers for Multiple-Input/Multiple-Output Plants

The multi-period repetitive control system is type of servomechanism for a periodic reference input. Even if a plant does not include time-delays, using multi-period repetitive controllers, the transfer function from the periodic reference input to the output and that from the disturbance to the output of the multi-period repetitive control system generally have infinite numbers of poles. To specify the input-output characteristic and the disturbance attenuation characteristic easily, Yamada and Takenaga proposed the concept of simple multi-period repetitive control systems, such that the controller works as a stabilizing multi-period repetitive controller and transfer functions from the periodic reference input to the output and from the disturbance to the output have finite numbers of poles. In addition, the parameterization of all stabilizing simple multi-period repetitive controllers was clarified. Recently, the parameterization of all robust stabilizing simple multiperiod repetitive controllers for the plant with uncertainty was clarified by Yamada et al. However, they did not clarify the parameterization of all robust stabilizing simple multi-period repetitive controllers for multiple-input/multiple-output plants. In this paper, we propose the parameterization of all robust stabilizing simple multi-period repetitive controllers for multiple-input/multiple-output plants.

A design method for two-degree-of-freedom multi-period repetitive controllers for multiple-input/multiple-output systems

AbstractMulti-period repetitive controller was proposed by Gotou et al., in order to improve the disturbance attenuation characteristic of modified repetitive control systems and that follows the periodic reference input with small steady state error. Recently, the parameterization of all stabilizing multi-period repetitive controllers was studied. However, when the parameterization of all stabilizing multi-period repetitive controllers is used, the input-output characteristic and the feedback characteristic cannot be specified separately. From the practical point of view, it is desirable to specify the input-output characteristic and the feedback characteristic separately. In addition, the parameterization is useful to design stabilizing controllers. Yamada et al. solved this problem by obtaining the parameterization of all stabilizing two-degree-of-freedom multi-period repetitive controllers. However, the method by Yamada et al. cannot be applied to multiple-input/multiple-output plants. Because, the method by Yamada et al. uses the characteristic of single-input/single-output system. In this paper, we propose the parameterization of all stabilizing two-degree-of-freedom multi-period repetitive controllers for multiple-input/multiple-output systems.

The parameterization of all robust stabilizing simple multi-period repetitive controllers with the specified input-output characteristic

AbstractIn this paper, we propose the parameterization of all robust stabilizing simple multi-period repetitive controllers with the specified input-output characteristic. Recently, Yamada et al. proposed the parameterization of all robust stabilizing simple multi-period repetitive controllers for the plant with uncertainty such that the controller works as a robust stabilizing multi-period repetitive controller and transfer functions from the periodic reference input to the output and from the disturbance to the output have finite numbers of poles. However, using the method by Yamada et al., it is complex to specify the low-pass filters in the internal model for the periodic reference input of which the role is to specify the input-output characteristic. Because, the low-pass filters are related to three kinds of free parameters in the parameterization proposed by Yamada et al. Our proposed parameterization in this paper overcome this problem by specifying the low-pass filters in the internal model for the periodic reference input beforehand. That is, using our parameterization, we can design a robust stabilizing simple multi-period repetitive control system which has desirable input-output characteristic more easily than the method proposed by Yamada et al.

A Design Method for Robust Stabilizing Simple Multi-Period Repetitive Controllers for Time-Delay Plants with the Specified Input-Output Characteristic

The simple multi-period repetitive control system proposed by Yamada and Takenaga is a type of servomechanism for the periodic reference input. That is, the simple multi-period repetitive control system follows the periodic reference input with small steady state error, even if a periodic disturbance or uncertainty exists in the plant. In addition, simple multi-period repetitive control systems make transfer functions from the periodic reference input to the output and from the disturbance to the output have finite numbers of poles. Yamada and Takenaga clarified the parameterization of all stabilizing simple multi-period repetitive controllers. Recently, the parameterization of all robust stabilizing simple multi-period repetitive controllers for time-delay plants with uncertainty was clarified by Yamada et al. However, using the method by Yamada et al., it is complex to specify the low-pass filters in the internal model for the periodic reference input of which the role is to specify the input-output characteristic. The purpose of this paper is to propose the parameterization of all robust stabilizing simple multi-period repetitive controllers for time-delay plants with the specified input-output characteristic such that the input-output characteristic can be specified beforehand.

The Parameterization of All Stabilizing Multi-Period Repetitive Controllers for Time-Delay Plants with the Specified Input-Output Characteristic

In this paper, we examine the parameterization of all stabilizing multi-period repetitive controllers for single-input/single-output time-delay plants with the specified input-output characteristic. The parameterization is the problem to find all stabilizing controllers. The parameterization of all stabilizing multi-period repetitive controllers for non-minimum-phase plants and that of all stabilizing multi-period repetitive controllers for time-delay plants were solved by Yamada and Satoh. However, using the method by Yamada and Satoh, we cannot settle input-output characteristics easily. Because the input-output characteristic is related to four free parameters. If the parameterization of all stabilizing multi-period repetitive controllers with the specified input-output characteristic, which is the parameterization when low-pass filters are settled beforehand, is obtained, we can specify the input-output characteristic easily. In this paper, we propose the parameterization of all stabilizing multi-period repetitive controllers for time-delay plants with the specified input-output characteristic.

A Design Method for Two-Degree-of-Freedom Multi-Period Repetitive Control Systems

Multi-period repetitive controllers improve the disturbance attenuation characteristic of the modified repetitive control system that follows the periodic reference input with a small steady state error. Recently, the parameterization of all stabilizing multi-period repetitive controllers was studied. However, when the parameterization of all stabilizing multi-period repetitive controllers is used, the input-output characteristic and the feedback characteristic cannot be specified separately. From the practical point of view, it is desirable to specify the input-output characteristic and the feedback characteristic separately. In addition, the parameterization is useful to design stabilizing controllers. Therefore, the problem of obtaining the parameterization of all stabilizing two-degree-of-freedom multi-period repetitive controllers that can specify the input-output characteristic and the disturbance attenuation characteristic separately is important to solve. In this paper, we propose the parameterization of all stabilizing two-degree-of-freedom multi-period repetitive controllers.

An application of the parametrization of all multi-period repetitive controllers for reduction of rotational unevenness in motors

Multi-period repetitive controllers were proposed by Gotou et al., in order to improve the disturbance attenuation characteristic of modified repetitive control systems. Rec ently, the parametrization of all stabilizing multi-perio d repetitive controllers was obtained. Since the parametrization of all stabilizing multi-period repetitive controllers was obta ined, we can express previous studies of multi-period repetitive co ntrollers in a uniform manner. In addition, a multi-period r epetitive controller can be designed systematically. However, an application of control system using the parametrization of all stabilizing multi-period repetitive controllers has not examined yet. In this paper, we show the effectiveness of the control system using the parametrization of all stabilizing multi-period repet itive controllers for reduction of rotational unevenness i n motors.

A Design Method for Two-Degree-of-Freedom Simple Multi-Period Repetitive Control Systems

The multi-period repetitive (MPR) control system is a type of servomechanism for periodic reference inputs. Using MPR controllers, transfer functions from the reference input to the output and from the disturbance to the output of the MPR control system have infinite numbers of poles. To specify the input-output characteristic and the disturbance attenuation characteristic easily, Yamada and Takenaga proposed MPR control systems, named simple multi-period repetitive (simple MPR) control systems, where these transfer functions have finite numbers of poles. In addition, Yamada and Takenaga clarified the parameterization of all stabilizing simple MPR controllers. However, using the simple MPR repetitive controller by Yamada and Takenaga, we cannot specify the input-output characteristic and the disturbance attenuation characteristic separately. From the practical point of view, it is desirable to specify the input-output characteristic and the disturbance attenuation characteristic separately. The purpose of this paper is to propose the parameterization of all stabilizing two-degree-of-freedom (TDOF) simple MPR controllers that can specify the input-output characteristic and the disturbance attenuation characteristic separately.

A Design Method for Simple Multi-Period Repetitive Controllers for Multiple-Input/Multiple-Output Plants

The multi-period repetitive control system is a type of servomechanism for a periodic reference input. Even if a plant does not include time-delays, using multi-period repetitive controllers, the transfer function from the periodic reference input to the output and that from the disturbance to the output of the multi-period repetitive control system generally have infinite numbers of poles. To specify the input-output characteristic and the disturbance attenuation characteristic easily, Yamada and Takenaga proposed the concept of simple multi-period repetitive control systems, such that the controller works as a stabilizing multi-period repetitive controller and transfer functions from the periodic reference input to the output and from the disturbance to the output have finite numbers of poles. In addition, the parameterization of all stabilizing simple multi-period repetitive controllers was clari¯ed. However, Yamada and Takenaga did not clarify the parameterization of all stabilizing simple multi-period repetitive controllers for multiple-input/multiple-output plants. The purpose of this paper is to propose the parameterization of all stabilizing simple multi-period repetitive controllers for multiple-input/multiple-output plants.

The Parameterization of All Stabilizing Multi-Period Repetitive Controllers for Multiple-Input/Multiple-Output Plants With the Specified Input-Output Frequency Characteristic

In this paper, we examine the parameterization of all stabilizing multi-period repetitive controllers for multiple-input/multiple-output plants with the specified input-output frequency characteristic. The parameterization of all stabilizing multi-period repetitive controllers, those are used to improve the disturbance attenuation characteristics of the repetitive controller, for non-minimum phase systems was solved by Yamada et al. However, when we design a stabilizing multi-period repetitive controller using the parameterization by Yamada et al., the input-output frequency characteristic of the control system cannot be settled so easily. From the practical point of view, the input-output frequency characteristic of the control systems is required to be easily settled. This problem is solved by obtaining the parameterization of all stabilizing multi-period repetitive controllers with the speci¯ed input-output frequency characteristic. However, no paper has proposed the parameterization of all stabilizing multi-period repetitive controllers for multiple-input/multiple-output plants with the speci¯ed input-output frequency characteristic. In this paper, we propose the parameterization of all stabilizing multi-period repetitive controllers for multiple-input/multiple-output plants with the specified input-output frequency characteristic.