Global stabilisation of the PVTOL aircraft with lateral force coupling and bounded inputs

Abstract

This work is devoted to prove that the nonlinear control scheme previously proposed by Zavala-Río, Fantoni and Lozano for the global stabilisation of the planar vertical take-off and landing (PVTOL) aircraft with bounded inputs neglecting the lateral force coupling is robust with respect to the parameter characterising such a lateral force coupling, ϵ, as long as such a parameter takes small enough values. In other words, global stabilisation is achieved even if ϵ > 0, provided that such a parameter be sufficiently small. As far as the authors are aware, such a property has not been proved in other existing control schemes when the value of ϵ is not known. The presented methodology is based on the use of embedded saturation functions. Furthermore, experimental results of the control algorithm implemented on a real prototype are presented.

Keywords:

• PVTOL aircraft
• global stabilisation
• bounded inputs
• saturations
• nonlinear control
• robustness

Notes

Notes

1. Notice, from the vertical motion equation in the system dynamic model, whether the lateral force coupling is neglected as in (2) or considered as in (1), that U ₁ > 1 is a necessary condition for the PVTOL to be stabilisable at any desired position. Indeed, any steady-state condition implies that the aircraft weight be compensated.

2. Such an assumption will be proved to be satisfied with D = M ₄₁ + M ₄₂ + M ₃₁ in the second part of the proof.

3. Recall that this was assumed in the first part of the proof. Thus, it is shown that such an assumption is actually a fact.

4. In particular, for any τ ≥ 0, |z ₂(t)| ≤ |z ₂(0)| + Fτ and , ∀t ∈ [0, τ], where , with B _{u 2} = M ₄₁ + M ₃₂, while |z ₄(t)| ≤ |z ₄(0)| + (F + 1)τ and , ∀t ∈ [0, τ].