187 research outputs found
Dominance analysis of linear complementarity systems
The paper extends the concepts of dominance and p-dissipativity to the
non-smooth family of linear complementarity systems. Dominance generalizes
incremental stability whereas p-dissipativity generalizes incremental
passivity. The generalization aims at an interconnection theory for the design
and analysis of switching and oscillatory systems. The approach is illustrated
by a detailed study of classical electrical circuits that switch and oscillate
Synchronization of Nonlinear Circuits in Dynamic Electrical Networks with General Topologies
Sufficient conditions are derived for global asymptotic synchronization in a
system of identical nonlinear electrical circuits coupled through linear
time-invariant (LTI) electrical networks. In particular, the conditions we
derive apply to settings where: i) the nonlinear circuits are composed of a
parallel combination of passive LTI circuit elements and a nonlinear
voltage-dependent current source with finite gain; and ii) a collection of
these circuits are coupled through either uniform or homogeneous LTI electrical
networks. Uniform electrical networks have identical per-unit-length
impedances. Homogeneous electrical networks are characterized by having the
same effective impedance between any two terminals with the others open
circuited. Synchronization in these networks is guaranteed by ensuring the
stability of an equivalent coordinate-transformed differential system that
emphasizes signal differences. The applicability of the synchronization
conditions to this broad class of networks follows from leveraging recent
results on structural and spectral properties of Kron reduction---a
model-reduction procedure that isolates the interactions of the nonlinear
circuits in the network. The validity of the analytical results is demonstrated
with simulations in networks of coupled Chua's circuits
Colpitts Chaotic Oscillator Coupling with a Generalized Memristor
By introducing a generalized memristor into a fourth-order Colpitts chaotic oscillator, a new memristive Colpitts chaotic oscillator is proposed in this paper. The generalized memristor is equivalent to a diode bridge cascaded with a first-order parallel RC filter. Chaotic attractors of the oscillator are numerically revealed from the mathematical model and experimentally captured from the physical circuit. The dynamics of the memristive Colpitts chaotic oscillator is investigated both theoretically and numerically, from which it can be found that the oscillator has a unique equilibrium point and displays complex nonlinear phenomena
Permanent Magnet Synchronous Motors are Globally Asymptotically Stabilizable with PI Current Control
This note shows that the industry standard desired equilibrium for permanent
magnet synchronous motors (i.e., maximum torque per Ampere) can be globally
asymptotically stabilized with a PI control around the current errors, provided
some viscous friction (possibly small) is present in the rotor dynamics and the
proportional gain of the PI is suitably chosen. Instrumental to establish this
surprising result is the proof that the map from voltages to currents of the
incremental model of the motor satisfies some passivity properties. The
analysis relies on basic Lyapunov theory making the result available to a wide
audience
Monotone one-port circuits
Maximal monotonicity is explored as a generalization of the linear theory of
passivity, aiming at an algorithmic input/output analysis of physical models.
The theory is developed for maximal monotone one-port circuits, formed by the
series and parallel interconnection of basic elements. An algorithmic method is
presented for solving the periodic output of a periodically driven circuit
using a maximal monotone splitting algorithm, which allows computation to be
separated for each circuit component. A new splitting algorithm is presented,
which applies to any monotone circuit defined as a port interconnection of
monotone elements
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