Further advancements on the output-feedback global continuous control for the finite-time and exponential stabilisation of bounded-input mechanical systems: desired conservative-force compensation and experiments

ABSTRACT

Global Saturating-Proportional Saturating-Derivative (SP-SD) type continuous control for the finite-time or (local) exponential stabilisation of mechanical systems with bounded inputs is achieved avoiding velocity variables in the feedback, and further simplified through desired conservative-force compensation. The proposed output-feedback controller is not a simple extension of the on-line compensation case but it rather proves to entail a closed-loop analysis with considerably higher degree of complexity that gives rise to more involved requirements. Interestingly, the proposal even shows that actuators with higher power-supply capabilities than in the on-line compensation case are required. Other important analytical limitations are further overcome through the developed algorithm. Experimental tests on a multi-degree-of-freedom robot corroborate the efficiency of the proposed approach.

KEYWORDS:

• Output feedback
• finite-time stabilisation
• mechanical systems
• desired conservative-force compensation
• bounded inputs

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The integration in (6(6) ${\mathcal{U}}_{\mathrm{ol}}\left(q\right)={\mathcal{U}}_{\mathrm{ol}}\left(q_0\right)+{\int }_{q_0}^q{g}^{\mathrm{T}}\left(z\right)\mathrm{d}z$(6) ) takes into account the conservative nature of g, as pointed for instance in Mendoza, Zavala-Río, Santibáñez, and Reyes (2015a, Note 1, p. 2009).

2 Notice that if ${\sigma }_{1j}$ and ${\sigma }_{2j}$ are (both) chosen to be non-decreasing, then $B_j=max\{\underset{\varsigma \to \mathrm{\infty }}{lim}\left[{\sigma }_{1j}\right(\varsigma )+{\sigma }_{2j}(\varsigma \left)\right],\underset{\varsigma \to -\mathrm{\infty }}{lim}-[{\sigma }_{1j}\left(\varsigma \right)+{\sigma }_{2j}\left(\varsigma \right)]\}$.

3 In any radial direction, ${\mathcal{U}}_{\ell }\left(x_1\right)$ is strictly increasing, and consequently $x_1=0_n$ is the unique stationary point of ${\mathcal{U}}_{\ell }\left(x_1\right)$.

Additional information

Funding

The authors were supported by Consejo Nacional de Ciencia y Tecnología (CONACYT), Mexico; second and fourth authors: grant numbers CB-2014-01-239833 and CB-2016-282807, respectively.