Multi-period Repetitive Control System Research Articles

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.

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 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 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 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.

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.

A Design Method for Robust Stabilizing Simple Multi-Period Repetitive Controllers for Time-Delay Plants

A multi-period repetitive control system is a type of servomechanism for a periodic reference input. Even if a plant does not include time-delay, 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 an in¯nite number of poles. When the transfer function from the periodic reference input to the output and that from the disturbance to the output have an in¯nite number of poles, it is difficult to settle the input-output characteristic and the disturbance attenuation characteristic of the multi-period repetitive control system. In order 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 the transfer function from the periodic reference input to the output and that from the disturbance to the output have a ¯nite number of poles. However, the method by Yamada and Takenaga cannot be applied to time-delay plants with uncertainty. The purpose of this paper is to propose the concept of robust stabilizing simple multi-period repetitive controllers for time-delay plants with uncertainty and to clarify the parametrization of all robust stabilizing simple multi-period repetitive controllers for time-delay plants with uncertainty.

A design method of robust stabilizing simple multi-period repetitive controllers

A multi-period repetitive control system is a type of servomechanism for a periodic reference input. Even if a plant does not include time-delay, 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 an infinite number of poles. In order to specify the input-output characteristic and the disturbance attenuation characteristic easily, Yamada et al. propose the concept of simple multi-period repetitive control systems such that the controller works as a stabilizing multi-period repetitive controller and the transfer function from the periodic reference input to the output and that from the disturbance to the output have a finite number of poles. However, the method by Yamada et al. cannot apply for the plant with uncertainty. The purpose of this paper is to propose the concept of robust stabilizing simple multi-period repetitive controllers for the plant with uncertainty and to clarify the parametrization of all robust stabilizing simple multi-period repetitive controllers.

A Design Method for a Robust Stabilizing Multi-Period Repetitive Control System for Multiple-Input/Multiple-Output Plants with Specied Input-Output Frequency Characteristic Using the Parameterization

The multi-period repetitive control system is a type of servomechanism for a periodic reference input. Recently, the parameterization of all robust stabilizing multi-period repetitive controllers for multipleinput/ multiple-output plants with uncertainty was obtained by Chen et al. However, using their method, it is complex to specify the low-pass filter in the internal model for the periodic reference input of which the role is to specify the input-output frequency characteristic. Because, the low-pass filter is related to four free parameters in the parameterization proposed by Chen et al. Chen et al. examined the parameterization of all robust stabilizing multi-period repetitive controllers for multiple-input/multiple-output plants with specified input-output frequency characteristic such that the input-output frequency characteristic can be specified beforehand. However, they omitted complete proof on account of space limitations. This paper gives the complete proof and demonstrates the effectiveness of the parameterization. The control characteristics of the system are presented, along with a design procedure for a robust stabilizing multi-period repetitive controller with specified input-output frequency characteristic. A numericalexample is presented to illustrate the effectiveness of the proposed method.