Passivity based trajectory tracking control with predefined local linear error dynamics

In this contribution a new systematic approach is presented to achieve desired local linear error dynamics for trajectory tracking of a nonlinear plant, where passivity based control by interconnection and damping assignment (IDA-PBC) is used to stabilize the error dynamics. Especially in the tracking case the solvability of the matching PDEs may restrict a state-independent dissipation matrix for the resulting time-varying port-Hamiltonian (pH) closed loop system to be singular. This in turn may impede to prove stability with the closed loop energy as a time-varying Lyapunov function. As a consequence an extension of the approach of local linear dynamics assignment for the resulting pH system, which has been introduced in a previous paper, is proposed. A factorization of the state- and time-dependent design matrix can ensure complete damping of the closed loop system, while the principal part of the matching PDEs remains state-independent to simplify the solvability conditions and the solution itself. The application of the approach is presented with the magnetic levitation experiment, including the estimation and optimization of the domain of attraction.