Ichijo Hodaka

A Floquet-like factorization for linear periodic systems

In this note, the novel representation is proposed for a linear periodic continuous-time system with T-periodic real-valued coefficients. We prove that a T-periodic real-valued factor and two real-valued matrix exponential functions can be extracted from a state transition matrix, while, in the well-known Floquet representation theorem, a 2T-periodic real-valued factor and a real-valued matrix exponential function are extracted from the state transition matrix. Then we also proved that any T-periodic system can be transformed to a system with T-periodic real-valued trigonometric coefficients using a T-periodic real-valued coordinate transformation, while, in the well-known Lyapunov reducibility theorem, a 2T-periodic real-valued coordinate transformation is utilized to transform the given periodic system into a time-invariant system with real coefficients. This new information can be useful for designing a T-periodic control law.

A note on the input-output structure of linear periodic continuous-time systems with real-valued coefficients

In this paper, a Kalman canonical decomposition of finite-dimensional linear periodic continuous-time systems is considered. This paper firstly investigates the invariance properties of the controllable subspace and the observable subspace. This paper then illustrates a counterexample to the existence of the periodic Kalman canonical decomposition in a typical setting, where the coefficients are restricted to be real-valued and the period of the transformed system is restricted to be the same as the given system. Motivated by this counterexample, this paper gives a self-contained exposition of the periodic Kalman canonical decomposition in real-valued coefficients.

A period-specific realization of linear continuous-time systems

It is a well-known fact that a weighting pattern matrix has a periodic realization if and only if the matrix is separable and periodic. This fact, however, does not cope with a reasonable question of period-specific realization problem: for a given weighting pattern matrix and a given positive real number, find a periodic realization corresponding to the given matrix and with a period equal to the given number. This paper answers the question by showing that the period-specific realization problem has a solution if and only if the given weighting pattern matrix is separable and has a period equal to the given positive real number. To this end, two types of period-specific realizations are constructed. One is with a constant A-matrix whose dimension is not necessarily minimal among all possible period-specific realizations. The other is with a non-constant and periodically time-varying A-matrix whose dimension turned out minimal among all possible period-specific realizations.

Maximum parametrization of the set of all solutions to linear periodic systems.

Abstract In the Floquet representation theorem, a state transition matrix whose second argument is 0 is represented as a product of a real-valued periodic matrix function and a real-valued matrix exponential function. In contrast, we have proposed a novel representation as a product of a real-valued periodic matrix function and two real-valued matrix exponential functions. In this note, the structure of the previously proposed representation is intensively investigated in terms of the maximum parametrization.

The use of mathematics and electric circuit simulator software in the learning process of wireless power transfer for electrical engineering students

Wireless Power Transfer (WPT) isa technique to deliver the electrical power from the source to the load without using wires or conductors. The physics of WPT is well known and basically learned as a course in high school. However, it is very recent that WPT is useful in practical situation: it should be able to transfer electric power in a significant efficiency. It means that WPT requires not much knowledge to university students but may attract students because of cutting edge technique of WPT. On the other hand, phenomena of WPT is invisible and sometimes difficult to imagine. The objective of this paper is to demonstrate the use of mathematics and an electric circuit simulator using MATHEMATICA software and LT-SPICE software in designing a WPT system application. It brings to a conclusion that the students as well the designer can take the benefit of the proposed method. By giving numerical values to circuit parameters, students acquires the power output and efficiency of WPT system. The average power...

Embedded system based on PWM control of hydrogen generator with SEPIC converter

The objective of this paper is to design and to produce a micro electrical plant system based on fuel cell for teaching material-embedded systems in technical vocational training center. Based on this, the student can experience generating hydrogen by fuel cells, controlling the rate of hydrogen generation by the duty ration of single-ended primary-inductor converter(SEPIC), drawing the curve rate of hydrogen to duty ratio, generating electrical power by using hydrogen, and calculating the fuel cell efficiency when it is used as electrical energy generator. This project is of great importance insofar as students will need to acquire several skills to be able to realize it such as continuous DC DC conversion and the scientific concept behind the converter, the regulation of systems with integral proportional controllers, the installation of photovoltaic cells, the use of high-tech sensors, microcontroller programming, object-oriented programming, mastery of the fuel cell systeThe objective of this paper is to design and to produce a micro electrical plant system based on fuel cell for teaching material-embedded systems in technical vocational training center. Based on this, the student can experience generating hydrogen by fuel cells, controlling the rate of hydrogen generation by the duty ration of single-ended primary-inductor converter(SEPIC), drawing the curve rate of hydrogen to duty ratio, generating electrical power by using hydrogen, and calculating the fuel cell efficiency when it is used as electrical energy generator. This project is of great importance insofar as students will need to acquire several skills to be able to realize it such as continuous DC DC conversion and the scientific concept behind the converter, the regulation of systems with integral proportional controllers, the installation of photovoltaic cells, the use of high-tech sensors, microcontroller programming, object-oriented programming, mastery of the fuel cell syste

A Criterion on Existence and Uniqueness of Behavior in Electric Circuit

Behavior of electric circuits can be observed by solving circuit equations symbolically as well as numerically. In general, symbolic computation for circuits with certain number of circuit elements needs much more time than numerical computation. It is reasonable to check the existence and uniqueness of the solution to circuit equations beforehand in order to avoid computation for the case of no solution. Indeed, some circuits have no solution; in that case, one should notice it and avoid to wait meaningless computation. This paper proposes a new theorem to check whether given circuit equations have a solution and their voltages and currents of all circuit elements are uniquely determined or not. The theorem is suitable for developing a computer algorithm and helps quick symbolic computation for electric circuits.

High Power Wireless Power Transfer Driven by Square Wave Inputs

A power source used in wireless power transfer generates an AC wave to transfer electric power to a load which is not connected electrically but connected electromagnetically to the power source. In this paper, the power and efficiency are compared when a sinusoidal and a square waves which are typical AC waves are applied as power source voltage outputs. The condition under which the two waves respectively transfer equivalent power with electric wires is examined to figure out the effect of different waves. Then the power and efficiency are calculated by a mathematical approach with practical values of elements on various situations. Finally, this paper explores how input waves should be chosen for ideal wireless power transfer.

A symbolic equation modeler for electric circuits

When users analyze symbolically physical phenomena, software products which partially help them write a symbolic equation to the phenomena are available. In electric engineering, there are a few software products which compute symbolically voltages and currents of electric circuits. They cover the frequency response analysis on behavior of linear time-invariant (LTI) circuits. However, they do not cover symbolic computation on the time response of circuits. This paper introduces a software product which generates a model for computing the time response of LTI circuits.

Factorizing the Monodromy Matrix of Linear Periodic Systems

Abstract This note proposes a new approach to computing the Kalman canonical decomposition of finite-dimensional linear periodic continuous-time systems by extending the Floquet theory. Controllable and observable subspaces are characterized by factorizing the monodromy matrix. Then, the conditions for the existence of several periodic Kalman canonical decompositions are extensively studied. The relations to the Floquet factorization, the Floquet-like factorization, and the period-specific realization are also discussed.