Simultaneous interconnection and damping assignment passivity-based control: the induction machine case study

Abstract

We argue in this article that the standard two-stage procedure used in interconnection and damping assignment passivity-based control (IDA–PBC)–consisting of splitting the control action into the sum of energy-shaping and damping injection terms–is not without loss of generality, and effectively reduces the set of systems that can be stabilised with IDA–PBC. To overcome this problem we carry out, simultaneously, both stages and refer to this variation of the method as SIDA–PBC. To illustrate the application of SIDA–PBC we consider the practically important example given by the control problem of the induction machine. First, we show that torque and rotor flux regulation of the induction motor cannot be solved with two stage IDA–PBC. It is, however, solvable with SIDA–PBC. Second, we prove that with SIDA–PBC we can shape the total energy of the full (electrical and mechanical) dynamics of a doubly-fed induction generator used in power flow regulation tasks, while with two stage IDA–PBC only the electrical energy can be shaped. Simulation results of these examples are presented to illustrate the performance improvement obtained with SIDA–PBC.

Keywords:

• nonlinear control
• passivity-based control
• energy-shaping
• induction machine

Acknowledgements

This work has been done in the context of the European sponsored project Geoplex with reference code IST-2001-34166. Further information is available at http://www.geoplex.cc. The work of Carles Batlle, Arnau Dòria-Cerezo and Gerardo Espinosa has been (partially) supported by the Spanish projects MTM 2007-62480, DPI 2007-62582 and CONACyT (51050) and DGAPA-UNAM (IN112908), respectively.

Notes

Note

1. All vectors in the paper are column vectors, even the gradient of a scalar function denoted . When clear from the context the subindex will be omitted.

2. That is, x _☆ is a member of the set .

3. We underscore the difference of the DFIM with respect to the classical (squirrel cage) induction motor (see, e.g., previous section) where the control signals are the stator voltages and the rotor is short-circuited. Also, in DFIM both rotor and stator currents are available for measurement.