Semiglobal nonlinear output regulation with adaptive internal model

Internal Model Based Framework for Tracking and Fault Tolerant Control of a Permanent Magnet Synchronous Motor

“…Moreover the profile h(w) will be assumed to be polynomial in w: hence the class of signal considered is no more restricted to a simple purely linear case, but will take into account a polynomial combination of constant and sinusoidal signals with unknown frequencies, amplitudes and phases. All those assumptions allow us to cast the tracking problem as a problem of output regulation, (see (Byrnes et al, 1997b), (Gentili and van der Schaft, 2003)) complicated by the lack of knowledge of the matrix S (see (Serrani et al, 2001), (Bonivento et al, 2004b)), and suggests to look for a controller which embeds an internal model of the exogenous signals, augmented by an adaptive part in order to estimate the characteristic frequencies. In order to show how the port-Hamiltonian formalism could be really helpful to describe the problem and to find an elegant solution, it is now possible to define a change of coordinates and introduce a new error system again fitting in the port-Hamiltonian framework: we will point out that the tracking problem is now cast as a regulation problem complicated by the presence of exogenous "virtual" disturbance signals.…”

Tracking and disturbance rejection for fully actuated mechanical systems

“…In Byrnes et al (1997) and Isidori (1995), the exogenous signal is generated by an exosystem and the existence of the controller requires the solvability of the Byrnes-Isidori regulator equations. Recent results on the output regulation of nonlinear systems can be found in Isidori (2003), Delli Priscoli (2004), Huang and Chen (2004) and Serrani, Isidori, and Marconi (2001).…”

Output Regulation with Redundant Measurements

“…A nonlinear enhancement of this theory, which uses a combination of geometry and nonlinear dynamical systems theory, was initiated by pioneering works of [4]- [6] who showed how to design a controller that provides a local solution near an equilibrium point, in the presence of exogenous signals which were produced by a Poisson stable system. Since these early contributions, the theory has experienced a tremendous growth, culminating in the recent development of design methods able to handle issues of global convergence (as in [7], [8]), the case of parametric uncertainties affecting the autonomous (linear) system which generates the exogenous signals (such as in [9], [10]), the case of nonlinear exogenous systems (such as in [11], [12]), or a combination thereof (as in [13]). A thorough presentation of several recent advances in this area can also be found in the recent books [14]- [16].…”