Abstract: This study investigates the benefits of implementing the semi-active devices in relation to passive viscous damping in the context of seismically isolated bridge structures. Since the intrinsically nonlinear nature of semi-active devices prevents the direct evaluation of Laplace transforms, frequency response functions are compiled from the computed time history response to sinusoidal and pulse-like seismic excitation. A simple semi-active control policy is used in regard to passive linear viscous damping and an optimal non-causal semi-active control strategy. The control strategy requires optimization. Euler-Lagrange equations are solved numerically during this procedure. The optimal closed-loop performance is evaluated for an idealized controllable dash-pot. A simplified single-degree-of-freedom model of an isolated bridge is used as numerical example. Two bridge cases are investigated. These cases are; bridge deck without the isolation bearing and bridge deck with the isolation bearing. To compare the performances of the passive and semi-active control cases, frequency dependent acceleration, velocity and displacement response transmissibility ratios Ta(w), Tv(w), and Td(w) are defined. To fully investigate the behavior of the structure subjected to the sinusoidal and pulse type excitations, different damping levels are considered. Numerical results showed that, under the effect of external excitation, bridge deck with semi-active control showed better structural performance than the passive bridge deck case.
Abstract: This paper presents a nonlinear differential model,
for a three-bladed horizontal axis wind turbine (HAWT) suited
for control applications. It is based on a 8-dofs, lumped
parameters structural dynamics coupled with a quasi-steady sectional
aerodynamics. In particular, using the Euler-Lagrange Equation
(Energetic Variation approach), the authors derive, and successively
validate, such model. For the derivation of the aerodynamic model,
the Greenbergs theory, an extension of the theory proposed by
Theodorsen to the case of thin airfoils undergoing pulsating flows,
is used. Specifically, in this work, the authors restricted that theory
under the hypothesis of low perturbation reduced frequency k,
which causes the lift deficiency function C(k) to be real and equal
to 1. Furthermore, the expressions of the aerodynamic loads are
obtained using the quasi-steady strip theory (Hodges and Ormiston),
as a function of the chordwise and normal components of relative
velocity between flow and airfoil Ut, Up, their derivatives, and
section angular velocity ε˙. For the validation of the proposed model,
the authors carried out open and closed-loop simulations of a 5
MW HAWT, characterized by radius R =61.5 m and by mean chord
c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec.
The first analysis performed is the steady state solution, where
a uniform wind Vw = 11.4 m/s is considered and a collective
pitch angle θ = 0.88◦ is imposed. During this step, the authors
noticed that the proposed model is intrinsically periodic due to
the effect of the wind and of the gravitational force. In order
to reject this periodic trend in the model dynamics, the authors
propose a collective repetitive control algorithm coupled with a PD
controller. In particular, when the reference command to be tracked
and/or the disturbance to be rejected are periodic signals with a
fixed period, the repetitive control strategies can be applied due to
their high precision, simple implementation and little performance
dependency on system parameters. The functional scheme of a
repetitive controller is quite simple and, given a periodic reference
command, is composed of a control block Crc(s) usually added
to an existing feedback control system. The control block contains
and a free time-delay system eτs in a positive feedback loop, and a
low-pass filter q(s). It should be noticed that, while the time delay
term reduces the stability margin, on the other hand the low pass
filter is added to ensure stability. It is worth noting that, in this
work, the authors propose a phase shifting for the controller and
the delay system has been modified as e^(−(T−γk)), where T is the
period of the signal and γk is a phase shifting of k samples of the
same periodic signal. It should be noticed that, the phase shifting
technique is particularly useful in non-minimum phase systems, such
as flexible structures. In fact, using the phase shifting, the iterative
algorithm could reach the convergence also at high frequencies.
Notice that, in our case study, the shifting of k samples depends
both on the rotor angular velocity Ω and on the rotor azimuth
angle Ψ: we refer to this controller as a spatial repetitive controller.
The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades.
The performance of the spatial repetitive controller is compared
with an industrial PI controller. In particular, starting from wind
speed velocity Vw = 11.4 m/s the controller is asked to maintain the
nominal angular velocity Ωn = 1.266rad/s after an instantaneous
increase of wind speed (Vw = 15 m/s). Then, a purely periodic
external disturbance is introduced in order to stress the capabilities
of the repetitive controller. The results of the simulations show that,
contrary to a simple PI controller, the spatial repetitive-PD controller
has the capability to reject both external disturbances and periodic
trend in the model dynamics. Finally, the nominal value of the
angular velocity is reached, in accordance with results obtained with
commercial software for a turbine of the same type.
Abstract: In this paper, we propose the variational approach to solve single image defogging problem. In the inference process of the atmospheric veil, we defined new functional for atmospheric veil that satisfy edge-preserving regularization property. By using the fundamental lemma of calculus of variations, we derive the Euler-Lagrange equation foratmospheric veil that can find the maxima of a given functional. This equation can be solved by using a gradient decent method and time parameter. Then, we can have obtained the estimated atmospheric veil, and then have conducted the image restoration by using inferred atmospheric veil. Finally we have improved the contrast of restoration image by various histogram equalization methods. The experimental results show that the proposed method achieves rather good defogging results.
Abstract: State Dependent Riccati Equation (SDRE) approach is
a modification of the well studied LQR method. It has the capability of being applied to control nonlinear systems. In this paper the technique
has been applied to control the single inverted pendulum (SIP) which represents a rich class of nonlinear underactuated systems. SIP
modeling is based on Euler-Lagrange equations. A procedure is developed
for judicious selection of weighting parameters and constraint handling. The controller designed by SDRE technique here gives better results than existing controllers designed by energy based techniques.