INTERNAL MODEL BASED FRAMEWORK FOR TRACKING AND FAULT TOLERANT CONTROL OF A PERMANENT MAGNET SYNCHRONOUS MOTOR 1 Claudio Bonivento ∗ Luca Gentili ∗,2 Andrea Paoli ∗ ∗ CASY-DEIS-University of Bologna, Via Risorgimento 2, 40136, Bologna, Italy. email: {cbonivento,lgentili,apaoli}@deis.unibo.it Abstract: In this paper an adaptive internal model based control scheme is designed to deal with tracking and input disturbance suppression problems for a permanent magnet synchronous motor. More in detail we show how to design a controller able to guarantee the perfect asymptotic tracking of unknown exogenous trajectories belonging to a certain family, embedding in the regulator the internal model of this family; the theoretical machinery exploited in order to prove the global asymptotical stability of the solution exposed is the nonlinear output regulation theory, specialized for the energy-based port- Hamiltonian formalism. Copyright c 2005 IFAC. Keywords: Permanent magnet motor, internal model based control, port-Hamiltonian systems, fault tolerant control 1. INTRODUCTION In this paper we are interested in solving a tracking problem for a permanent magnet synchronous mo- tor: this is a simple but very significant issue as the tracking of a particular velocity profile is probably the main task to take into account dealing with permanent magnet motors. Moreover the design procedure pre- sented is proved to be able to deal with another im- portant issue: a fault tolerant control design problem taking into account the arise of spurious harmonics in the electrical variables, superimposing to the con- trol inputs. More in detail we show how to design a controller able to guarantee the perfect asymptotic tracking of unknown exogenous trajectories belonging to a certain family and, at the same time, overcome the possible presence of spurious harmonics superim- posing to the voltage inputs; the theoretical machinery 1 This work was supported by MIUR and EC-Project IFATIS partly funded by the European Commission in the IST programme 2001 of the 5th EC framework programme (IST-2001-32122). 2 Corresponding author. exploited in order to prove the global asymptotical stability of the solution exposed is the nonlinear out- put regulation theory (the regulator will embed the internal model of the possible trajectory/fault family) specialized for the energy-based port-Hamiltonian for- malism. This formalism is in fact really helpful to de- scribe the problem, starting from an energetic descrip- tion of the synchronous motor, and to find an elegant solution (for synchronous permanent motor tracking literature see (Shouse and Taylor, 1994a), (Shouse and Taylor, 1994b), (Shouse and Taylor, 1998), (Zhu et al., 2000), (Dawson et al., 1976), (Ortega et al., 2002) and references therein). In the next section the permanent magnet synchronous motor model is presented and the tracking problem is stated: a suitable change of coordinates will be intro- duced in order to obtain an error system again fitting in the port-Hamiltonian framework; it will be shown that the tracking problem can be cast as a regulation and input disturbance suppression problem for the error system and, in Section 3, an internal model based controller is designed in order to globally and asymp-