Passivity Based Control for Permanent-Magnet Synchronous Motors

Abstract

The Passivity based control (PBC) is a well established technique which has proved very powerful to design robust control for physical system, especially electrical machinery. The PBC have clear physical interpretation in terms of interconnection system with its environment, and are robust overlooked non dissipative effects modelled. These features are extremely valuable in practical implementations of controllers. In this chapter, we show how the PBC can be used to control the speed of permanents magnets synchronous motor (PMSM). In first part, we consider the Euler-Lagrange model in the -referential to design the Passivity Based Voltage Controller. The dq-model of the PMSM is considered to design the Passivity Based current Controller in the second part. The idea of Passivity Based Control (PBC) design is to reshape the natural energy of the system and inject the required damping in such a way that the control objective is achieved. Expected advantages of this approach are the enhanced robustness properties, which stem from the fact that conciliation of system nonlinearities is avoided. The technique has its roots in classical mechanics (Arnold, 1989) and was introduced in the control theory in the seminal paper (Takegaki & Arimoto, 1981). This method has been instrumented as the solution of several robot manipulator (Ailon & Ortega, 1993; Ortega & Spong; Takegaki & Arimoto, 1981) induction motor (Gokder & Simaan, 1997; Kim et al., 1997; Ortega et al., 1996, 1997; Ortega & Loria), and power electronics (Sira-Ramirez et al., 1995), which were intractable with other stabilization techniques. PBC was also combined with other techniques (Achour & Mendil, 2007; Ortega & GarciaCanseco 2004a, 2004b; Qiu & Zhao, 2006; Petrovic et al., 2001; Travieso-Torres et al., 2006, 2008). The design of two single-input single-output controllers for induction motors based on adaptive passivity is presented in (Travieso-Torres et al., 2008). Given their nature, the two controllers work together with field orientation block. In ((Travieso-Torres et al., 2006), a cascade passivity-based control scheme for speed tracking purposes is proposed. The scheme is valid for a certain class of nonlinear system even with unstable zero dynamic, and it is also useful for regulation and stabilization purposes. A methodology based on energy shaping and passivation principles has been applied to a PMSM in (Petrovic et al., 2001). The interconnection and damping structures of the system were assigned using the PortControlled Hamiltonian (PCH) structure. The resulting scheme consists of a steady state feedback to which a nonlinear observer is added to estimate the unknown load torque. The