Yuichi Sawada

Active control of flexible structures subject to distributed and seismic disturbances

The purpose of this paper is to present a method of active control for suppressing the vibration of a mechanically flexible cantilever beam which is subject to a distributed random disturbance and also a seismic input at the clamped end. First, the mathematical model of the flexible structure is established by a stochastic partial differential equation which describes the Euler-Bernoulli type distributed parameter system with internal viscous damping and subject to the seismic and distributed random inputs. Second, the distributed parameter model, which is considered as an infinite-dimensional system, is reduced to a finite-dimensional one by using the modal expansion, and split into the controlled part and the uncontrolled (residual) one. The principal approach is to regard the observation spillover due to uncontrolled part as a colored observation noise and construct an estimator, and then we construct the optimal control system. Finally, simulation studies are presented by using a real earthquake accelerogram data.

Collision detection for a flexible cantilever-beam subject to random disturbance based on innovation process

In this paper, an algorithm for detection of collisions for a flexible cantilever-beam subject to random disturbance based on a model-based fault diagnosis method is presented. The mathematical model of the flexible cantilever-beam is described by an Euler-Bernoulli type partial differential equation. The collision detection filter is constructed based on the Kalman filter for the finite-dimensional system corresponding to the mathematical model of the flexible beam. If collisions of the flexible beam and environmental obstacles occur, the statistics of the residual signal (innovation process) change. To detect such a statistical change of the residual signal due to the collision, a chi-squared like test is introduced. Several numerical results are presented.

Bilateral Control of Nonlinear Flexible Master-Slave Arms Using High-Geared Servomotor with Time-Varying Delay

This paper investigates a bilateral control system for nonlinear flexible master-slave arms (FMSA) using a high-geared servomotor with time-varying delays. The proposed bilateral control system consists of rigid master and flexible slave arms connected by a communication network and controlled by proportional derivative (PD) and proportional derivative and strain (PDS) controllers. The flexible arm is actuated by a high-geared servomotor and modeled as a nonlinear system. Both arms are connected via the communication network, which causes the time-varying delay. To control the master and slave arms, PD and PDS controllers including information on angular velocity error of both arms are designed. Since the total energy of our system is regarded as a candidate Lyapunov function, stability of the proposed system is proved via the Lyapunov theorem. Furthermore, passivity is also proved. Numerical simulations are performed to confirm performance of the proposed FMSA system.

Detection of collisions for a flexible beam subject to random disturbance

This paper presents an approach to detection of collisions for a flexible cantilever-beam subject to random disturbance by using model-based fault diagnosis method. The mathematical model of the flexible cantilever-beam is assumed to be described by the Euler-Bernoulli type partial differential equation. The collision detection filter is constructed based on the Kalman filter with respect to the finite-dimensional model corresponding to the mathematical model of the flexible beam. If collisions of the flexible beam and with environmental objects occur, the statistics of the residual signal (innovation process) are change. To detect such statistical change of the residual signal due to the collision, the chi-squared like test is introduced. In this paper, numerical and experimental results are presented.

Aldol-type carbon bond formation of ethereal oxonium ylide

The Rh(2)-catalyzed reaction of 2-(3-diazo-1,1-dimethyl-2-oxopropyl)-2-methyldioxolane (1b) with arylaldehyde in the presence of (Me)3SiCl and Ti(i-PrO)4 gave 2-aryl-(hydroxy)methyl-8,8-dimethyl-7-methylene-3,6-dioxocane-1-one (6) and 2-aryl(hydroxy)methyl-4-(2-chloroethoxy)-4,5,5-trimethyl-3-oxacyclopentanone (7); these are the first examples of C–C bond formation of ethereal oxonium ylide via enol silyl ether intermediates.

Wave control of a class of flexible beams by an idea of imaginary beam

This paper proposes a method of wave control for a class of uniform flexible beams by introducing an idea of a fictitious beam with finite length and distributed damping. This beam is assumed to be connected serially at the free-end of the real beam of interest, and its function is to act as an absorber to absorb the energy conveyed by travelling waves. For the damping force two kinds of damping term, viscous and Kelvin-Voigt type dampings are considered, and their optimal coefficients are determined by solving the parameter optimization problem to minimize the absorption efficiency becomes maximum. Furthermore several simulations were performed.

Collision detection and suspend control of parallel- structured single-link flexible arms

This paper presents a method of collision detection and suspend control for parallel-structured single-link flexible arms. The exact dynamics of parallel-structured single-link flexible arm are described by quite complex nonlinear partial and ordinary differential equations, In this paper, such parallel-structured flexible arms are approximately modeled by a single-link flexible arm consisting of a flexible beam with the same boundary conditions as the parallel-structured one. Collision of the parallel-structured flexible arm and an undesirable obstacle is detected using the innovation process of Kalman filter based on the measured data of strain sensors pasted on the side of the arm. The proposed controller for the arm has the following two objectives: i) to rotate the flexible arm from the initial position to the desired position; ii) to safely suspend the rotation of the arm when the collision is detected.

Active attenuation of the sound outflowing from a one-dimensional duct

In this paper, a feedback controller for reducing intensity of sound waves outflowing from a one-dimensional duct is established based on the modal representation approach. The duct is supposed to have a fan at one end and several electric speakers as actuators equipped on the wall of the duct. The noisy sound due to the fan is modeled by white Gaussian noise. The mathematical model of sound pressure in the duct is described by a kind of wave equations. In order to derive finite-dimensional controller, the solution of the mathematical model is expanded by modal functions. The controller is constructed using the LQG theory, and its efficacy is demonstrated by simulation studies.

Active noise control of sound wave in a one-dimensional duct

This paper describes a feedback controller for reducing traveling waves in a one-dimensional duct with air flow. The one end of the relevant duct is open to the air, and a fan is installed at the other end. In order to control and reduce the noisy sound radiating from the open end of the duct, the amplitude of the traveling waves propagating to the open end from the fan should be minimized, because the power of sound radiation from the open end depends on the amplitude of the traveling waves. Based on the mathematical model derived earlier by the authors (1997) on the sound pressure in the duct, a finite-dimensional controller is designed for the electric speaker equipped near the open-end of the duct to reduce the noise from flowing outside. Simulation studies provide some numerical results.

Solution of a differential game with geographically distributed resources

We present a computer tool for finding a local Nash solution to an adversarial game in which the units of two opposing teams are distributed over a large geographical area. The differential game consists of a quadratic payoff function and a set of ordinary differential equations describing the system dynamics of the unit distribution over a discretized geographical area. The optimum strategy for each team is determined using an iterative algorithm for finding a local Nash equilibrium solution for the game. Experimental results are presented that demonstrate the validity of this concept.