Explicit and Implicit IDA-PBC Design and Implementation for a Portal Crane

Abstract

The interconnection and damping assignment passivity-based control (IDA-PBC) is well-known for regulating the behavior of nonlinear systems. In underactuated mechanical systems (UMSs), its application requires the satisfaction of matching conditions, which in many cases demands to solve partial differential equations (PDEs). Only recently, the IDA-PBC method has been extended to UMSs in implicit representation, where the system dynamics are described by a set of differential-algebraic equations. In some system classes, this implicit model allows to circumvent the PDE obstacle and to construct an output-feedback law. This paper discusses the design and real-system implementation of the total energy shaping IDA-PBC with an optimal local performance for a portal crane system in implicit port-Hamiltonian representation. The implicit controller is compared with the simplified (explicit) IDA-PBC, introduced by Xue and Zhiyong (2017), which also shapes the total energy and avoids PDEs.