3-DoF spherical parallel robot

In recent decades, application of system identification theory in control background has been developed, significantly. In this regard, a promising structure was proposed as self-tuning regulators (STR). The stability and performance of such adaptive controllers were highly dependent to the initial conditions and speed of convergence of identified parameters. Moreover, the corresponding adaptation rules mainly suffer from system uncertainties, disturbances, and insufficient excitation. In order to overcome such crucial challenges, a structure is proposed in this paper which is indeed inspired from indirect STRs: the control methodology based on sliding mode control and a robust adaptive law. Thereafter, one can formulate the adaptation rules as an extended continuous-time Recursive Least square (RLS), which simultaneously reduces identification and output tracking errors. On the other hand, under insufficient excitations, adaptive schemes mainly face estimation wind-up. By inspiration from classic damped l