Yoshiyuki Sakawa

Optimal control of container cranes

A dynamical model of container cranes is derived by using Lagranges equation. When a ship is loaded or unloaded with containers, the total motion of the container load is divided into five fundamental sections. For each fundamental type of motion, the optimal control is calculated such that the corresponding trajectory satisfies the specified boundary conditions and that the swing of the container load during the transfer is minimized. A new algorithm which is employed for computing the optimal control is explained in detail. Some results of numerical computation are also shown.

Modeling and feedback control of a flexible arm

When a flexible arm is rotated by a motor about an axis through the arms fixed end, transverse vibration may occur. The motor torque should be controlled in such a way that the motor rotates by a specified angle, while simultaneously stabilizing vibration of the flexible arm so that it is arrested as soon as possible at the end of rotation. In this paper, we first derive a partial differential equation and a set of boundary conditions governing the vibration. Then, a feedback control system which incorporates a dynamic compensator is designed using sensor outputs. A set of experiments has been constructed to demonstrate control strategies for a flexible arm, where a strain gage was used as a vibration sensor and a microcomputer was equipped as a controller. Several satisfactory experimental results are shown.

Modeling and quasi-static hybrid position/force control of constrained planar two-link flexible manipulators

A method is proposed whereby both contact force exerted by a flexible manipulator and position of end-effector while in contact with a surface are controlled. The authors derive dynamic equations of joint angles, vibrations of flexible links, and contact force by means of Hamiltons principle. On the basis of some assumptions the authors derive the quasi-static equations and design the hybrid position/force controller of the flexible manipulator. A set of experiments for the hybrid control of the flexible manipulator using a force sensor has been carried out. Several experimental results are shown. >

On global convergence of an algorithm for optimal control

This paper presents an algorithm for the solution of optimal control problems with constraints on the control, but without constraints on the trajectory or the terminal state. In this algorithm, reduction of a cost at each iteration is guaranteed. Global convergence conditions for the algorithm are investigated and an example is worked out.

Modeling and control of coupled bending and torsional vibrations of flexible beams

An evolution equation which governs coupled bending and torsional vibrations of flexible beams with a tip body is derived based on Lagrangian dynamics. A feedback control scheme is shown for suppressing the vibrations. >

Optimal control of a rotary crane

This paper is concerned with the optimal control of a rotary crane, which makes two kinds of motion (rotation and hoisting) at the same time. The optimal control which transfers a load to a desired place as fast as possible and minimizes the swing of the load during the transfer, as well as the swing at the end of transfer, is calculated on the basis of a dynamic model. A new computational technique is employed for computing the optimal control, and several numerical results are presented.

Feedback stabilization of a class of distributed systems and construction of a state estimator

In this paper, we study feedback stabilization of a class of distributed systems governed by partial differential equations of parabolic type and its application to constructing a state estimator for asymptotic state identification. It is proved that, when a controller (an observation) can be arbitrarily constructed, observability (controllability) of the system is necessary and sufficient for stabilizing the system so that it has an arbitrarily large damping constant. As an application of this result, it is shown that a state estimator can be constructed, the output of which approaches asymptotically the real state of the system with an arbitrary convergence rate.

Optimal filtering in linear distributed-parameter systems†

Abstract The optimal filter of Kalman type is derived for linear distributed-parameter systems, which are subjected to both white gaussian distributed noise and boundary noise. The measurement data are also corrupted by white gaussian noise. It is assumed that the number of measuring instruments is finite; therefore, the measurement data are taken at several points of spatial domain. The Wiener—Hopf equation is obtained by applying the calculus of variations technique, from which the filter partial differential equations for the optimal estimate and its covariance matrix can be derived. The optimal estimate and its covariance are expanded into the series of eigenfunctions of the homogeneous partial differential equation with the homogeneous boundary condition. Thus a system of ordinary differential equations for coefficient functions of the series is derived

A simple model of flexible manipulators with six axes and vibration control by using accelerometers

A simple model of flexible manipulators having a heavy end-effector is presented by introducing a set of equivalent springs which represent all flexibility of manipulators. The equations of vibrations of the end-effector and the equations of motion of robot links are derived on the basis of the proposed model. Accelerometers are installed on the end-effector for measuring the vibrations, and output signals of the accelerometers are fedback for suppressing the vibrations. A feedback control law incorporating a state observer is proposed, and stability problem of the feedback system is treated by using small gain theorem. Several satisfactory experimental results are shown.

Feedback Control of a Flexible Manipulator with a Parallel Drive Mechanism

A flexible manipulator having a parallel drive mechanism is treated. Only the forearm of the manipulator is assumed to be flexible, because it is slender and carries a heavy end-ef fector. The elastic vibration of the arm, which is due to its flexibility, and the position of the driving motors should be controlled simultaneously. On the basis of the mathematical model developed in our previous paper, we construct an optimal feedback control system by using the outputs of sev eral sensors. A set of experiments for the point-to-point position control was carried out with a microcomputer, which controls the whole servo system and plays the role of dynamic compensator. Several satisfactory experimental results are shown.