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This paper presents a globally contracting controller for regulation and dynamic positioning of ships, using only position measurements. For this purpose a globally contracting observer which reconstructs the unmeasured states is constructed. The observer produces accurate estimates of position, slowly varying environmental disturbances (bias terms) and velocity. The estimates are automatically adjusted to the present sea state by gain-scheduling the wave model parameters in the observer. Finally, the estimates are used in a nonlinear PID control law and the stability proof of the observer-controller is based on a separation principle for contracting systems in cascade.