This paper presents a nonlinear velocity observer of the tether deployment using the Immersion and Invariance technique, and the velocity observer design problem is recast as a problem of designing an attractive and invariant manifold inside the Hamiltonian framework. The passivity-based control theory is used to define an expected Hamiltonian function, and the stability of the designed velocity observer is addressed by using the passivity-based methodology. Finally, a simple tension control law with measurable and unmeasurable states is employed for controlling the tether deployment, where the unmeasurable states use the proposed velocity observer. Numerical simulations demonstrate that the proposed velocity observer is working successfully. Sensitivity analyses are conducted to test the effectiveness and robustness of the proposed velocity observer.

This paper presents a nonlinear velocity observer of tether deployment using the immersion and invariance technique, and the velocity observer design problem is recast as a problem of designing an attractive and invariant manifold inside the Hamiltonian framework. The passivity-based control theory is used to define an expected Hamiltonian function, and the stability of the designed velocity observer is addressed by using the passivity-based methodology. Finally, a simple tension control law with measurable and unmeasurable states is employed for controlling the tether deployment, where the unmeasurable states use the proposed velocity observer. Numerical simulations demonstrate that the proposed velocity observer is working successfully. Sensitivity analyses are conducted to test the effectiveness and robustness of the proposed velocity observer.