Tatsuya Sakanushi

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

Abstract Multi-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.

A New Design Method of High-Order Modified Repetitive Control Systems for Reference Inputs with Uncertain Period-Time

This paper considers the design of high-order modified repetitive control systems for periodic reference inputs with uncertain period-time. The objective of this work was to develop a new design method so that the closed-loop high-order modified repetitive control system is robustly stable with high control precision for periodic reference inputs with uncertain period-time. The parametrization of all stabilizing controllers containing three free parameters is proposed based on the Youla-Kucera parameterization. Moreover, to obtain the free parameters, the constraint conditions were converted into stability conditions in the form of Bilinear Matrix Inequalities that can be solved using the available software. In addition, the high control precision is guaranteed by designing the free parameters after the control characteristic of this control system. The validity and effectiveness of the proposed design method were verified by numerical examples.

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 Robust Stabilizing Modified Repetitive Controllers for Time-Delay Plants

In this paper, we examine the parameterization of all robust stabilizing modified repetitive controllers for time-delay plants. The modified repetitive control system is a type of servomechanism designed for a periodic reference input. When modified repetitive control design methods are applied to real systems, the influence of uncertainties in the plant must be considered. The stability problem with uncertainty is known as the robust stability problem. Recently, the parameterization of all stabilizing modified repetitive controllers was obtained. Since the parameterization of all stabilizing modified repetitive controllers was obtained, we can express previous study of robust stabilizing modified repetitive controller in a uniform manner and can design a stabilizing modified repetitive controller systematically. However, the parameterization of all robust stabilizing modified repetitive controllers for time-delay plants has not been obtained. In this paper, we clarify the parameterization of all robust stabilizing modified repetitive controllers for time-delay plants.

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.

The parameterization of all robust stabilizing simple repetitive controllers for multiple-input/multiple-output plants

Abstract The simple repetitive control system proposed by Yamada et al. is a type of servomechanism for the periodic reference input. That is, the simple 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 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 et al. clarified the parameterization of all stabilizing simple repetitive controllers. Recently, the parameterization of all robust stabilizing simple 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 repetitive controllers for multiple-input/multiple-output plants. Since many real plants include uncertainty and have multiple-input and multiple-output, this is the important problem to solve. The purpose of this paper is to propose the parameterization of all robust stabilizing simple repetitive controllers for multiple-input/multiple-output plants.

The parameterization of all stabilizing modified Smith predictors for non-square time-delay plants

Abstract The modified Smith predictor is well known as an effective time-delay compensator for a plant with large time-delays, and several papers on the modified Smith predictor have been published. The parameterization of all stabilizing modified Smith predictors for multiple-input/multiple-output time-delay plants was obtained by Yamada et al. However, they do not examine the parameterization of all stabilizing modified Smith predictors for non-square time-delay plants. The purpose of this paper is to expand the result by Yamada et al. and to propose the parameterization of all stabilizing modified Smith predictors for non-square time-delay plants. Control characteristics of the control system using obtained parameterization of all stabilizing modified Smith predictors are also given.

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

Abstract In 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.

The Parametrization of All Robust Stabilizing Modified Repetitive Controllers for Time-Delay Plants with the Specified Input-Output Frequency Characteristic

The modified repetitive control system is a type of servo mechanism designed for a periodic reference input. Recently, the parametrization of all stabilizing modified repetitive controllers is obtained by Satoh and Yamada. Since the parametrization of all stabilizing modified repetitive controllers is obtained, we can express previous studies of modified repetitive control system in a uniform manner. In addition, a modified repetitive control system can be designed systematically. Yamada, Satoh and Mei pointed out that using the method by Satoh and Yamada, it is complicated to specify the input-output frequency characteristic and gave the parametrization of all robust stabilizing modified repetitive controllers with the specified input-output frequency characteristic. However, the parametrization of all robust stabilizing modified repetitive controllers for timedelay plants with the specified input-output frequency characteristic has not been considered yet. In this paper, for easy to specify the input-output frequency characteristic, we clarify the parametrization of all robust stabilizing modified repetitive controllers for time-delay plants with the specified input-output frequency characteristic.

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 infinite number of poles. 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.