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

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.