Atsushi Arakawa

Optimal control and sensitivity analysis of two links flexible arm with three degrees of freedom

The modeling and control method for a flexible robotic arm with three degrees of freedom is described. Under the assumption that the links vibrate both transversely and torsionally, the dynamics of the three degrees of freedom flexible robotic arm is derived. To estimate the state of the system, an observer is employed. The control algorithm is designed by using optimal control theory based on the quadratic performance index approach. This control method is shown to suppress the coupled vibrations. Sensitivity analysis is carried out when there are some inaccuracies in the payloads weight or the links length. The way to find the stable domain of these parameters is presented, and some simulation results are provided.<<ETX>>

H/sub infinity / control of a flexible robotic arm (effect on parameter uncertainties on stability)

Describes the stability of a flexible robotic arm when its mathematical model contains parameter uncertainties. The authors employ the H/sub infinity / control method which includes the LQ optimal control, and is robust. To estimate the stability domain of a closed-loop system, one must find the rate at which the system matrix A and the control matrix B change when a parameter changes. These rates are difficult to find, because the elements of the matrices change nonlinearly when the parameter changes. They calculate the rates approximately and obtain the stability domain by using the Routh condition. They also show some simulation results, demonstrating that the modeled stability domain of the one-degree-of-freedom flexible arm can be enlarged by appropriately choosing the arbitrary matrices of the H/sub infinity / control law.<<ETX>>