Orientation of radio-telescope secondary mirror via adaptive sliding mode control

In this work a parallel manipulator (Stewart platform) is used to align and maintain the position of the secondary mirror of a radio-telescope. The six degrees of freedom platform gives the significant advantage of reaching the maximum performance for the positioning tasks. The near-singularity condition of the platform is analyzed and is handled by implementation of a new control law based on sliding mode with inner regularization procedure. Herein, the finite-time convergence of closed-loop system derived from designed control in the presence of external as well as internal disturbances/uncertainties is proved. The effectiveness of the proposed controller is verified via numerical simulation. We show that Sliding Mode Control with a gain matrix adaptation based on the Equivalent Control method can significantly reduce the undesirable chattering effect an therefore avoid the possible damages.