In this paper, we presents a robust adaptive control system design method in the work coordinate of the robot arm for conveyor tracking. In the design, if the weighting function $L_K$ is smaller than the design parameter then the transient characteristics of system becomes stable, if $L_K$ is larger than then the system becomes unstable. Proposed design method presented here is based on model referenece adaptive control and Popov stability theorem. By the utiliza/tion of an auxilary input, it is improved the transent characteristics of the system in comparison with the conventional model reference adptive control, since the rate of V and V(t) is large. The usefulness of a proposed design method has been confirmed by computer simulations.