Trajectory Tracking via Interconnection and Damping Assignment Passivity-Based Control for a Permanent Magnet Synchronous Motor  
[PERSON]  
1 Centre de Recherche Royallieu, Roberval (Mechanics, Energy and Electricity), Universite de Technologie de Compiegne, CS 60319, CEDEX, 602005 Compiegne, France; [EMAIL_ADDRESS]  
[PERSON]  
2 Facultad de Ingenieria, Universidad Nacional Autonoma de Mexico, Ciudad de Mexico 04510, Mexico; [EMAIL_ADDRESS]  
[PERSON]  
3 Facultad de Ingenieria, Universidad Autonoma de San Luis Potosi, San Luis Potosi 78290, Mexico 3 Facultad de Ingenieria, Universidad Autonoma de San Luis Potosi 78290, Mexico; [EMAIL_ADDRESS]  
[PERSON]  
3 Facultad de Ingenieria, Universidad Autonoma de San Luis Potosi 78290, Mexico 3 Facultad de Ingenieria, Universidad Autonoma de San Luis Potosi 78290, Mexico 3 Facultad de Ingenieria, Universidad Autonoma de San Luis Potosi 78290, Mexico; san Luis Potosi 78290, Mexico; [EMAIL_ADDRESS]  
[PERSON]  
3 Facultad de Ingenieria, Universidad Autonoma de San Luis Potosi 7 On the other hand, passivity-based control (PBC) is the name of a well-established technique [13] which performs stabilization by rendering the system passive to a desired storage function and injecting damping [17]. It has become an essential tool in nonlinear control design because of its straightforward application to physical systems. Interconnection and damping assignment passivity-based control (IDA-PBC) is an extension that has been introduced by [PERSON] et al. [15] as a controller design methodology that regulates the behavior of nonlinear systems assigning a desired port-controlled Hamiltonian (PCH) structure to the closed loop. Since the introduction of IDA-PBC, many controllers have been reported in the literature such as mechanical systems [16; 17], power systems [18; 19], and electrical machines [20; 21], among others. However, this methodology has been used mainly to solve regulation control problems, while the trajectory tracking control problem has not been investigated so far [22; 23]. In this sense, the stabilization problem of PCH systems has been much investigated because it can be performed by modifying the energy function and injecting damping. In contrast, for trajectory tracking, the energy function of the systems has to be modified into a time-varying function, which implies that the property of passivity is spoilt. For this reason, [PERSON] et al. propose a framework to achieve trajectory tracking for PCH systems, which consists of converting it into one of stabilization. The strategy is based on constructing an error system as another PCH system to stabilize it at the origin. Consequently, trajectory tracking is achieved by preserving the Hamiltonian structure by generalized canonical transformations. In addition, [PERSON] et al. prove that trajectory tracking is feasible for time-varying PCH systems [23; 24]. However, a few works on this problem use the IDA-PBC methodology in the literature, and moreover, a well-defined methodology for trajectory tracking control has not been reported yet. Nevertheless, in the work of [PERSON] [25], a procedure to solve this problem is presented, specifically for the trajectory tracking of mechanical underactuated systems. The approach, in the same way as [PERSON] et al., is based on the idea of constructing the tracking error system and then stabilizing it to the origin in order to ensure trajectory tracking with the difference that the realizable trajectories have a unique role because of their PCH structure, and the way to determinate each of them is to invert the realizable trajectory system. The purpose of this paper is to present a control scheme that solves the position, speed, and torque trajectory tracking control problem for PMSM. The main feature of the contribution is two-fold since, on the one hand, it has a solid mathematical base inspired by the results presented in [25], which leads to formally proved stability properties, while, on the other hand, the practical control problem of PMSM is solved, achieving high performance.