Ichiro Jikuya

Rate Damping of a Spacecraft Using Two Single-Gimbal Control Moment Gyros

In this study, the problem of rate damping a spacecraft by using two single-gimbal control moment gyros in an arbitrary configuration is considered. A feedback control law for a two- single-gimbal control moment gyro system is designed based on Lyapunov analysis and is applicable to the fault-tolerant control of a redundant-single-gimbal control moment gyro system, such as a pyramid-type system. A steady-state analysis is conducted and presented in detail. Rate damping is achieved for almost all initial conditions if the total angular momentum of the spacecraft is less than the sum of the angular momenta of the single-gimbal control moment gyros, in which case the angular velocity of the spacecraft is decreased to zero. In contrast, rate damping is not achieved if the total angular momentum of the spacecraft is greater than the sum of the angular momenta of the single-gimbal control moment gyros, in which case the spacecraft converges to a spinning motion for almost all initial conditions. The results of ...

Kalman Canonical Decomposition of Linear Time-Varying Systems

In this paper, a Kalman canonical decomposition of finite-dimensional linear time-varying continuous-time systems is revisited. Two types of Kalman canonical decompositions are considered; one is collectively dubbed the intervalwise Kalman canonical decomposition and the other is collectively dubbed the global Kalman canonical decomposition. Each type is classified into subtypes resulting from variants of controllabilities (i.e., controllability, reachability, and influenceability) and observabilities (i.e., observability, determinability, and visibility). This paper first investigates the invariance properties of subspaces resulting from variants of controllabilities and observabilities. This paper then gives a self-contained exposition of each Kalman canonical decomposition on an interval. The main result is to prove the existence of intervals on each of which each Kalman canonical decomposition exists. Moreover, the relations among different Kalman canonical decompositions are extensively studied and t...

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.

Instability caused by parasitic resistances in piezoelectric shunt damping system with negative capacitor

This paper studies the stability problem for a piezoelectric shunt damping system with a simple negative capacitor circuit. A key issue is to consider perturbations of parasitic series and parallel-leakage resistances in a piezoelectric element. Then, it is a bit surprising that the perturbed system becomes unstable, in particular, due to the effect of the parasitic leakage resistance. This instability phenomenon is analytically proved based on the Routh-Hurwitz stability criterion and is also demonstrated by numerical simulations. This paper then illustrates robustification of a negative capacitor circuit by inserting a negative resistance in parallel with the negative capacitor in the simple negative capacitor circuit. This robustification is also demonstrated by a numerical simulation.

On Kalman canonical decomposition of linear periodic continuous-time systems with real coefficients

Abstract In this note, structural decomposition of linear periodic continuous-time systems is discussed. A fundamental problem to decompose a state of a periodic system into controllable and uncontrollable parts is conjectured to be achieved by a continuously differentiable and periodic coordinate transformation with the same period of the system, however there is a counterexample to this conjecture. Hence we derive a condition for the existence of such a coordinate transformation. We also prove that, by relaxing a class of coordinate transformation, it is always possible to construct a periodic coordinate transformation with the double period of the periodic system.

Sensor-less parameter estimation of electromagnetic transducer and experimental verification

In this paper, a new sensor-less parameter estimation method is proposed for electromagnetic shunt damping. The purpose is to estimate parameters of an electromagnetic transducer and a vibrating structure. The frequency domain measurements of an electrical admittance are only supposed to be available but any other sensor measurements are not; therefore, the estimation problem is nontrivial. Two types of numerical optimization, a linear optimization to select an initial seed and a nonlinear optimization to determine a final estimate, are presented. The effectiveness of the method is demonstrated by vibration control experiments as well as parameter estimation experiments.

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.

On the Use of the Averaging Method for the Characteristic Multiplier Placement Problem

This paper proposes a novel approach for desining a periodic state feedback control law for a class of continuous-time linear periodic systems. The control law generates the sufficiently high frequency sinusoidal in the coefficient of the closed loop systems, then the closed loop solution is shown to be exponentially stable based on the averaging method. It is also shown that the closed loop solution is approximated by the solution of the average system.