Block Synthesis of Tracking System for Inverted Pendulum via Sigmoidal Feedbacks

In this paper the authors consider the tracking problem of the angular position of the inverted pendulum with an electric actuator. The problem is posed in the presence of unknown unmatched disturbances, parametric uncertainties, and incomplete measurements. Moreover, constructive restrictions on the state variables and control action are set. The solution of the posed problem based on the construction of the block controllable form with sigmoidal feedbacks and sigmoidal true control synthesis. It is shown that the using of sigmoidal functions help to satisfy the given restrictions, to avoid sufficient overshoot at the beginning of transient responses. The observation problem is posed for the estimation of needed signals for the realization of the control law. The reduced order state observer with sigmoidal corrective action is presented for the solution of this problem.