A robust control algorithm is developed for attitude control of an air spindle testbed based on variable structure control. The variable structure control approach is formulated for underactuated systems with actuated accelerations as control inputs. First order sliding surfaces are defined per actuated degrees of freedom as a linear combination of the tracking position and velocity errors of both actuated and unactuated coordinates. The controller law is determined based on Lyapunov theory and is shown to be asymptotically stable for the tiled air spindle axis where gravitational effects are included but only marginally stable for the vertical axis. Multiple step sliding surfaces are proposed to achieve asymptotic stability in the latter case. Simulations of the controller performance verify its effectiveness and accuracy.
Active control of mechanical vibrations using dynamic variable structure control
