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.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1 The integration in (Equation6(6) (6) ) takes into account the conservative nature of g, as pointed for instance in Mendoza, Zavala-Río, Santibáñez, and Reyes (Citation2015a, Note 1, p. 2009).
2 Notice that if and are (both) chosen to be non-decreasing, then .
3 In any radial direction, is strictly increasing, and consequently is the unique stationary point of .