Adaptive sliding-mode controller based on the ‘Super-Twist’ state observer for control of the Stewart platform

To provide a highly efficient control of nonlinear systems in the presence of nonmodeled dynamics and external perturbations, a new control law with feedback based on the sliding modes with an observer of the ‘Super‐Twist’ kind was proposed. For acceptable use of the continuous observer signal in the controller, presented were adaptive laws for adjustment of the control system parameters. Using the methods of Lyapunov function, system stability (convergence to a zone) was proved. This technique was proposed as an example of control and stabilization of the position of a parallel manipulator (Gough–Stewart platform). The presented mechanism with six degrees of freedom is used to control the secondary mirror of the ‘Large Millimeter Telescope Alfonso Serrano’ situated in the state of Puebla, Mexico.