PID‐PBC for Nonzero Regulated Output Reference

This chapter provides some answers to the question regarding the case when the desired value for the regulated output – that is, the signal that is fed in the integrator of the proportional‐integral‐derivative (PID) – is nonzero. It explores possible solutions to design PID‐passivity‐based control. After presenting the theoretical results pertaining to the issues, the chapter illustrates their application to the control of power converters, high‐voltage direct‐current (HVDC) power systems, wind energy systems, and permanent‐magnet synchronous motors. For its correct operation, HVDC systems must satisfy a large set of different regulation objectives that are, typically, associated with to the multiple time‐scale behavior of the system. One way to deal with this issue, that prevails in practice, is the use of hierarchical architectures. These are nested control loops, at different time scales, each one providing references for an inner controller. The chapter provides conditions for shifted passivity of port‐Hamiltonian systems.