Adaptive passivity-based control extended for unknown control direction

Abstract

This research extends the design of adaptive passivity-based controllers (APBC), proposing a normalized APBC (NAPBC) for nonlinear dynamical systems with a direction of control unknown. The plant also has an accessible single-input and a single-output, smooth behavior, linear explicit parametric dependence, and unknown parameters. The proposed method can handle unknown control direction through an alternate and more straightforward method than Nussbaum gains, having two fewer parameters. We present the stability proof of the controlled system. Besides, the proposed NAPBC expands the tuning method for normalized fixed gains or time-varying gains, reducing the trial and error procedure. Finally, we apply the proposed methodology step by step to a conical tank-scale pilot plant. Comparative experimental results show the proposed NAPBC has better indexes ISI, Ess, MO, IAE, and Ts.

Keywords: Adaptive passivity-based control; Conical tank; Nonlinear control; Unknown control direction.