A more exhaustive study on the finite‐time and exponential tracking continuous control for constrained‐input mechanical systems: Improved design and experiments

A more exhaustive study on the finite-time/exponential tracking continuous control for mechanical systems with input constraints is developed. The resulting control scheme is characterized by the inclusion of position-error and velocity-error correction terms which are suitably shaped to achieve the concerned types of convergence. Such a shaping is carried out through control parameters that act as exponential weights on the gained position and velocity errors. As an innovative aspect of the proposal, such exponential weights are not restricted to satisfy a fixed equivalence relation among them but rather a wider comparative one. This gives rise to a wider spectrum of finite-time convergent closed-loop trajectories and gives an optional type of (unconventional) exponential convergence (in addition to the conventional one), which enlarges the controller potential for performance adjustment. This is further potentiated through a more generalized saturating structure on the error correction terms, that includes the usual saturating-proportional saturating-derivative type one as a particular case. The improved design is supported through a more general analysis based on more general strict Lyapunov functions, stating more solid analytical bases for possible design extensions on the accomplishment of other (more complex) control objectives. The study is further supported through experimental tests on a 3-degree-of-freedom robot manipulator.