Survey on Passivity Based Control of Induction Machine

Abstract

Induction machines (IM) constitute a theoretically interesting and practically important class of nonlinear systems. They are frequently used as wind generators for their power/cost ratio. They are described by a fifth-order nonlinear differential equation with two inputs and only three state variables available for measurement. The control task is further complicated by the fact that IM are subject to unknown (load) disturbances and the parameters can be of great uncertainty. One is then faced with the challenging problem of controlling a highly nonlinear system, with unknown time-varying parameters, where the regulated output, besides being unmeasurable, is perturbed by an unknown additive signal. Passivity-based control (PBC) is a well-established structure-preserving design methodology which has shown to be very powerful to design robust controllers for physical systems described by Euler-Lagrange equations of motion. PBCs provide a natural procedure to "shape" the potential energy yielding controllers with a clear physical interpretation in terms of interconnection of the system with its environment and are robust vis á vis to unmodeled dissipative effects. One recent approach of PBC is the Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) which is a very useful technique to control nonlinear systems assigning a desired (Port-Controlled Hamiltonian) structure to the closed-loop. The aim of this paper is to give a survey on different PBC of IM. The originality of this work is that the author proves that the well known field oriented control of IM is a particular case of the IDA-PBC with disturbance.

Stabilization control of quadrotor helicopter through matching solution by controlled Lagrangian method

“…The concept of energy shaping control was firstly proposed by Takegaki and Arimoto [1], where the potential energy was reshaped to control manipulators. Then the concept was developed under Hamiltonian scheme, where the passivity-based control [2] (PBC) was proposed to formulate the methodology. Under Lagrangian scheme, Bloch et al [3] firstly stabilized a certain class of underactuated mechanical system by CL approach.…”