1,236 research outputs found
Geometric Phase and Modulo Relations for Probability Amplitudes as Functions on Complex Parameter Spaces
We investigate general differential relations connecting the respective
behavior s of the phase and modulo of probability amplitudes of the form
\amp{\psi_f}{\psi}, where is a fixed state in Hilbert space
and is a section of a holomorphic line bundle over some complex
parameter space. Amplitude functions on such bundles, while not strictly
holomorphic, nevertheless satisfy generalized Cauchy-Riemann conditions
involving the U(1) Berry-Simon connection on the parameter space. These
conditions entail invertible relations between the gradients of the phase and
modulo, therefore allowing for the reconstruction of the phase from the modulo
(or vice-versa) and other conditions on the behavior of either polar component
of the amplitude. As a special case, we consider amplitude functions valued on
the space of pure states, the ray space , where
transition probabilities have a geometric interpretation in terms of geodesic
distances as measured with the Fubini-Study metric. In conjunction with the
generalized Cauchy-Riemann conditions, this geodesic interpretation leads to
additional relations, in particular a novel connection between the modulus of
the amplitude and the phase gradient, somewhat reminiscent of the WKB formula.
Finally, a connection with geometric phases is established.Comment: 11 pages, 1 figure, revtex
Adiabatic driving and parallel transport for parameter-dependent Hamiltonians
We use the Van Vleck-Primas perturbation theory to study the problem of
parallel transport of the eigenvectors of a parameter-dependent Hamiltonian.
The perturbative approach allows us to define a non-Abelian connection
that generates parallel translation via unitary transformation of
the eigenvectors. It is shown that the connection obtained via the perturbative
approach is an average of the Maurer-Cartan 1-form of the one-parameter
subgroup generated by the Hamiltonian. We use the Yang-Mills curvature and the
non-Abelian Stokes' theorem to show that the holonomy of the connection
is related to the Berry phase
HOSM State Estimation and Robust PID Control of a Chemical Process
This paper presents some results of the authors’ studies on robust estimation and control for chemical processes. Here, an observer-based controller is designed for a chemical process. A High Order Sliding Mode Observer (HOSMO) for state and parameter estimation is synthesized and, a Multi-Variable PID (MV-PID) controller is calculated using the estimated variables. The HOSMO presents insensitivity and robustness against a class of uncertainties in the system, and the MV-PID allows the tracking of slow-varying and piecewise constant references, which are often proposed to drive chemical processes. Numerical simulations show
that the observer-based controller presents a good performance in presence of parametric variations, which often are presented in chemical processes; the proposed structure is compared with a First Order Sliding Mode Observer (FOSMO) coupled with a MV-PID.CinvestavUniversidad Nacional de Colombi
State and Parameter Estimation of a CSTR
In the continuation of authors’ studies on estimation and control for Continuous Stirred-Tank Reactors (CSTR), a new structure to estimate the concentration of reactive state, the global heat transfer coefficient, and the heat of reaction parameters is proposed here. This
scheme consist of an Observer Based Estimator (OBE) connected in cascade with a High Order Sliding Mode Observer (HOSMO). The OBE estimates the global heat transfer coefficient, and the HOSMO estimates the heat of reaction, and the concentration of reactive. Numerical simulations show that the whole structure presents a good performance in presence of parametric variations, which often are presented in chemical processes.Universidad Nacional de ColombiaCINVESTA
Estrategias de control y estimación de estado por modos deslizantes para un horno eléctrico
Este artÃculo presenta el diseño de un observador por modos
deslizantes de segundo orden para una planta con
modelo lineal, asumiendo ruido en la variable medida.
Adicionalmente se propone un controlador de alto orden
por modos deslizantes para una de las variables de estado
asociadas al proceso. Para finalizar, se realiza un ejemplo
con las respectivas simulaciones.
This paper presents the design of a sliding mode observer
for a second order linear plant model, assuming noise in
the measured variable. Additionally, high order controller
for sliding for state variables associated with the process
modes is proposed. Finally, an example is made with the
respective simulations.Universidad Nacional de ColombiaCINVESTAVColciencia
Diseño un controlador robusto basado en observador para el modelo lineal de un helicóptero de un grado de libertad (VTOL)
Este artÃculo propone un controlador basado en observador para un modelo de helicóptero tipo VTOL de un grado de libertad. El objetivo de control es mantener la posición del VTOL en un punto de operación, a pesar de las incertidumbres ocasionadas por inexactitud en el modelo y ruido en las mediciones. El controlador y el observador son diseñados con base en algoritmos que inducen modos deslizantes en el sistema en lazo cerrado, ofreciendo caracterÃsticas de robustez y convergencia en tiempo finito. Los resultados de simulación muestran un buen desempeño del esquema propuesto tanto en condiciones de ausencia de ruido como cuando se consideran mediciones ruidosas.Universidad Nacional de ColombiaCinvestavColcienciasBanco Mundia
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