Energy-based modeling of electric motors

We propose a new approach to model electrical machines based on energy considerations and construction symmetries of the motor. We detail the approach on the Permanent-Magnet Synchronous Motor and show that it can be extended to Synchronous Reluctance Motor and Induction Motor. Thanks to this approach we recover the usual models without any tedious computation. We also consider effects due to non-sinusoidal windings or saturation and provide experimental data

Aspects of bond graph modelling in control

Abstract available: p. i

Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one

Published versio

Design of Optimal Sparse Feedback Gains via the Alternating Direction Method of Multipliers

We design sparse and block sparse feedback gains that minimize the variance amplification (i.e., the $H_2$ norm) of distributed systems. Our approach consists of two steps. First, we identify sparsity patterns of feedback gains by incorporating sparsity-promoting penalty functions into the optimal control problem, where the added terms penalize the number of communication links in the distributed controller. Second, we optimize feedback gains subject to structural constraints determined by the identified sparsity patterns. In the first step, the sparsity structure of feedback gains is identified using the alternating direction method of multipliers, which is a powerful algorithm well-suited to large optimization problems. This method alternates between promoting the sparsity of the controller and optimizing the closed-loop performance, which allows us to exploit the structure of the corresponding objective functions. In particular, we take advantage of the separability of the sparsity-promoting penalty functions to decompose the minimization problem into sub-problems that can be solved analytically. Several examples are provided to illustrate the effectiveness of the developed approach.Comment: To appear in IEEE Trans. Automat. Contro

Dynamically Stable 3D Quadrupedal Walking with Multi-Domain Hybrid System Models and Virtual Constraint Controllers

Hybrid systems theory has become a powerful approach for designing feedback controllers that achieve dynamically stable bipedal locomotion, both formally and in practice. This paper presents an analytical framework 1) to address multi-domain hybrid models of quadruped robots with high degrees of freedom, and 2) to systematically design nonlinear controllers that asymptotically stabilize periodic orbits of these sophisticated models. A family of parameterized virtual constraint controllers is proposed for continuous-time domains of quadruped locomotion to regulate holonomic and nonholonomic outputs. The properties of the Poincare return map for the full-order and closed-loop hybrid system are studied to investigate the asymptotic stabilization problem of dynamic gaits. An iterative optimization algorithm involving linear and bilinear matrix inequalities is then employed to choose stabilizing virtual constraint parameters. The paper numerically evaluates the analytical results on a simulation model of an advanced 3D quadruped robot, called GR Vision 60, with 36 state variables and 12 control inputs. An optimal amble gait of the robot is designed utilizing the FROST toolkit. The power of the analytical framework is finally illustrated through designing a set of stabilizing virtual constraint controllers with 180 controller parameters.Comment: American Control Conference 201

Power flow control of a doubly-fed induction machine coupled to a flywheel

We consider a doubly-fed induction machine –controlled through the rotor voltage and connected to a variable local load- that acts as an energy-switching device between a local prime mover (a flywheel) and the electrical power network. The control objective is to optimally regulate the power flow which is achieved commuting between two different steady-state regimes. We first show that zero dynamics of the system is only marginally stable complicating its control via feedback linearization. Instead, we apply the energy-based Interconnection and Damping Assignment Passivity-Based Control technique that does not require stable invertibility. It is shown that the partial differential equation that appears in this method can be obviated fixing the desired closed-loop total energy and adding new terms to the interconnection structure. Furthermore, to obtain a globally defined control law we introduce a state-dependent damping term that has the nice interpretation of effectively decoupling the electrical and mechanical parts of the system. This results in a globally asymptotically stabilizing controller parameterized by two degrees of freedom, which can be used to implement the power management policy. An indirect adaptive scheme for the rotor and stator resistances is also introduced. The controller is simulated and shown to work satisfactorily for various realistic load changes

Power Flow Control of a Doubly-Fed Induction Machine Coupled to a Flywheel

We consider a doubly–fed induction machine controlled through the rotor voltage and connected to a variable local load—that acts as an energy–switching device between a local prime mover (a flywheel) and the electrical power network. The control objective is to optimally regulate the power flow, and this is achieved by commuting between different steady–state regimes. We first show that the zero dynamics of the system is only marginally stable, thus complicating its control via feedback linearization. Instead, we apply the energy–based Interconnection and Damping Assignment Passivity–Based Control technique that does not require stable invertibility. It is shown that the partial differential equation that appears in this method can be circumvented by fixing the desired closed-loop total energy and adding new terms to the interconnection structure. Furthermore, to obtain a globally defined control law we introduce a state–dependent damping term that has the nice interpretation of effectively decoupling the electrical and mechanical parts of the system. This results in a globally convergent controller parameterized by two degrees of freedom, which can be used to implement the power management policy. The controller is simulated and shown to work satisfactorily for various realistic load changes.Peer Reviewe

On modelling and stabilizability of voltage-controlled piezoelectric material

In this paper, we present a new piezoelectric actuator and piezoelectric composite model and show the well-posedness of these systems. Furthermore, we show that the piezoelectric composite is stabilizable for certain system parameters. In this work, we also review several piezoelectric beams, actuators, and composite models and provide improved definitions of the different electromagnetic considerations, i.e. fully dynamic electromagnetic field, quasi-static electric field, and the static lectric field assumption.Comment: 19 pages, 5 figures, 2 tables. This work is intended to be submitted for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl