Mitsuaki Ishitobi

A stability condition of zeros of sampled multivariable systems

This note derives a new condition for zeros of sampled multivariable systems to be stable for sufficiently small sampling periods. It is a natural extension of Hagiwaras result for single-input-single-output systems (1993) to multivariable systems.

Improvement of stability of zeros in discrete-time multivariable systems using fractional-order hold

This paper is concerned with the stability of zeros of the discrete-time multivariable systems composed of a fractional-order hold (FROH), a continuous -time plant and a sampler in cascade. The properties of the limiting zeros are studied and a condition for obtaining stable zeros for sufficiently small sampling periods is derived. An approximate fractional-order hold (AFROH) is proposed as an implementation of FROH. It is shown that the AFROH as well as the FROH can locate the zeros of discrete-time multivariable systems inside the stable region and improve stability properties when the zero-order hold (ZOH) cannot. Experimental results of adaptive control with AFROH demonstrate a significant improvement of control performance compared with the use of a ZOH.

Stable zeros of sampled low-pass systems

Abstract This paper studies analytical forms of criteria for ensuring that all zeros of a discrete system are stable when a continuous-time, strictly proper and low-pass plant is sampled by use of a zero order hold. Necessary and sufficient conditions for stable zeros of a sampled system are developed. They are related to coefficients of a continuous-time transfer function and to a sampling period. This paper also presents sufficient conditions which are expressed in terms of coefficients of a continuous-time transfer function.

Conditions for stable zeros of sampled systems

A criterion for there being no unstable discrete zeros is derived in terms of coefficients of a continuous-time transfer function and of a sampling period when a continuous-time, stable, and strictly proper plant is sampled. It is also shown that the shortest sampling period ensuring minimum-phase behavior can be calculated from a simple equation. >

RIPPLE-SUPPRESSED MULTIRATE ADAPTIVE CONTROL

Abstract This paper deals with adaptive control of linear time-invariant systems with unknown parameters and with two sampling rates: a slower one for the output and a faster one for the input. It is known that intersample ripples often arise in the outputs of the closed-loop multirate systems although multirate control has interesting advantages. In this paper, a ripple-suppressed multirate adaptive control scheme is proposed. A simulation example is given to show the effectiveness of the presented algorithm.

Zero dynamics of sampled-data models for nonlinear systems

One of the approaches to sampled-data controller design for nonlinear continuous-time systems consists of obtaining an appropriate model and then proceeding to design a controller for the model. Then, it is important to derive a good approximate sampled-data model because the exact sampled- data model for nonlinear systems is often unavailable to the controller designers. Recently, Yuz and Goodwin have proposed an accurate sampled-data model which includes extra zero dynamics, so-called the sampling zero dynamics, corresponding to the relative degree of the continuous-time nonlinear system. This paper shows that a more accurate sampled-data model is required for a controlled Van der Pol system with the relative degree two. The reason is that the closed-loop system becomes unstable when a controller design method based on cancellation of the zero dynamics is applied, and the phenomenon seems related to the instability of the sampling zero dynamics of the more accurate sampled-data model. Further, this paper derives a more accurate model than that of Yuz and Goodwin for continuous-time nonlinear systems with the relative degree two, and presents a condition which assures the stability of the sampling zero dynamics of the obtained model.

Stability of zero dynamics of sampled-data nonlinear systems

Abstract One of the approaches to sampled-data controller design for nonlinear continuous-time systems consists of obtaining an appropriate model and then proceeding to design a controller for the model. Hence, it is important to derive a good approximate sampled-data model because the exact sampled-data model for nonlinear systems is often unavailable to the controller designers. Recently, Yuz and Goodwin have proposed an accurate approximate model which includes extra zero dynamics corresponding to the relative degree of the continuous-time nonlinear system. Such extra zero dynamics are called sampling zero dynamics. A more accurate sampled-data model is, however, required when the relative degree of a continuous-time nonlinear plant is two. The reason is that the closed-loop system becomes unstable when the more accurate sampled-data model has unstable sampling zero dynamics and a controller design method based on cancellation of the zero dynamics is applied. This paper derives the sampling zero dynamics of the more accurate sampled-data model and shows a condition which assures the stability of the sampling zero dynamics of the model. Further, it is shown that this extends a well-known result for the stability condition of linear systems to the nonlinear case.

Asymptotic Properties and Stability Criteria of Zeros of Sampled-Data Models for Decouplable MIMO Systems

This note analyzes the zeros of the sampled-data models corresponding to continuous-time decouplable MIMO systems with all relative degrees less than or equal to two and shows approximate expressions of the zeros as power series expansions with respect to a sampling period. Further, stability criteria of the zeros for small sampling periods are given.

Sampled-data models for affine nonlinear systems using a fractional-order hold and their zero dynamics

One of the approaches to sampled-data controller design for nonlinear continuous-time systems consists of obtaining an appropriate model and then proceeding to design a controller for the model. Hence, it is important to derive a good approximate sampled-data model because the exact sampled-data model for nonlinear systems is often unavailable to the controller designers. Recently, Yuz and Goodwin proposed a more accurate model than the simple Euler model in the case of a zero-order hold. This article derives a sampled-data model for nonlinear systems using a fractional-order hold, and analyzes the zero dynamics of the sampled-data model.

An LMI approach to observer-based guaranteed cost control

This article presents a design method for an observer-based guaranteed cost controller for a class of uncertain linear systems, in which full state variables cannot be measured. The perturbations are assumed to be described by structural uncertainties. The linear matrix inequality (LMI) approach is applied to design the observer-based controller. The controller and observer gains are obtained by solving the LMI optimization and feasibility problems, respectively. A numerical example shows the potential of the proposed method.