Fumitoshi Matsuno

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.

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.

Modelling and control of a flexible manipulator with a parallel drive mechanism

Abstract 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-effector. Both the elastic vibration of the arm, which occurs owing to flexibility, and the position of the driving motors should be controlled simultaneously. A partial differential equation and the boundary conditions that govern the clastic vibration of the arm are derived, and the related eigenvalue problem is solved. On the basis of a finite-dimensional modal model of the distributed-parameter systems, an optimal feedback control system is constructed by using the outputs of several sensors.

Quasi-static hybrid position/force control of a flexible manipulator

A method is proposed whereby both the contact force exerted by a flexible manipulator and the position of the end effector while in contact with a surface are controlled. Exact dynamic equations for joint angles, vibration of the flexible link, and constraint force are derived by means of Hamiltons principle. A controller for the hybrid position/force control of the flexible manipulator is designed on the basis of the obtained model. 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.<<ETX>>

Quasi-static hybrid position/force control of two-degree-of-freedom flexible manipulators

A method is proposed whereby both the contact force exerted by a flexible manipulator and the position of the end-effector while in contact with a surface are controlled. The authors first derive the exact dynamic equations of joint angles, vibration of the flexible links, and contact force by means of the Hamiltons principle. Then, a controller for the hybrid position/force control of the flexible manipulator is designed on the basis of the model obtained. 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.<<ETX>>

Dynamic hybrid position/force control of a flexible manipulator which has two degrees of freedom and flexible second link

A method is proposed whereby both the contact force exerted by a flexible manipulator and the position of the end-effector while in contact with a surface are controlled. The authors approximate elastic deformations by means of B-spline functions and derive dynamic equations of joint angles. A controller for the hybrid position/force control of the flexible manipulator is designed on the basis of the singular perturbation method.<<ETX>>

EXPERIMENTAL STUDY ON FEEDBACK CONTROL OF COUPLED BENDING AND TORSIONAL VIBRATIONS OF FLEXIBLE BEAMS

Abstract Modeling and control of flexible beams has received a great deal of attention in recent years. When a tip-body of a flexible beam is a rigid body, not only bending vibration but also torsional vibration will occur. In this paper, we model the coupled bending and torsional vibrations as a set of decoupled partial differential equations with a set of coupled boundary conditions. The whole set of dynamic equations will be rewritten together as an evolution equation in a properly defined Hilbert space. It will be proven that a differential operator governing the system is selfadjoint and has a compact inverse. A stabilizing feedback control law of a rotation motor will be established on the basis of modal analysis. Experimental methods are discussed in detail, and the results demonstrate the effectiveness of the dynamic model and the proposed control law.

Modelling and vibration control of a flexible manipulator with three axes by using accelerometers

Industrial robots have lumped flexibility at joints as well as distributed flexibility due to the elasticity of their arms. Because of the flexibility, undesirable vibration occurs during motion. In this paper, an equivalent spring which represents the flexibility is introduced, and the equations of motion of robot links and equations of vibration of the end-effector are derived by using Lagrangian dynamics. Motor torques should be controlled in such a way that the required response of the motor positions is achieved and at the same time the vibration disappears as quickly as possible. For measuring the vibration, three accelerometers are installed at the tip of the forearm. A robust feedback control law is derived by using the root locus technique. Several successful experimental results are given.

Optimal control of temperature distribution by using scanning control

This paper treats the optimal control of temperature distribution by using scanning control. The temperature distribution is governed by a partial differential equation with a forcing term of the Dirac delta function type. The problem is to minimize the deviation of temperature distribution from the desired distribution at a given time by controlling both intensity and position of the heat source. On the basis of a set of ordinary non-linear differential equations derived by the Galerkin approximations, the optimal control is calculated by employing an iterative algorithm. Several numerical results are presented.