Abstract: This paper provides a state estimation method for
automatic control systems of nonlinear vehicle dynamics. A nonlinear
tire model is employed to represent the realistic behavior of a vehicle.
In general, all the state variables of control systems are not precisedly
known, because those variables are observed through output sensors
and limited parts of them might be only measurable. Hence, automatic
control systems must incorporate some type of state estimation. It is
needed to establish a state estimation method for nonlinear vehicle
dynamics with restricted measurable state variables. For this purpose,
unscented Kalman filter method is applied in this study for estimating
the state variables of nonlinear vehicle dynamics. The objective of
this paper is to propose a state estimation method using unscented
Kalman filter for nonlinear vehicle dynamics. The effectiveness of
the proposed method is verified by numerical simulations.
Abstract: Controlling the flow of fluids is a challenging problem
that arises in many fields. Burgers’ equation is a fundamental
equation for several flow phenomena such as traffic, shock waves,
and turbulence. The optimal feedback control method, so-called
model predictive control, has been proposed for Burgers’ equation.
However, the model predictive control method is inapplicable to
systems whose all state variables are not exactly known. In practical
point of view, it is unusual that all the state variables of systems are
exactly known, because the state variables of systems are measured
through output sensors and limited parts of them can be only
available. In fact, it is usual that flow velocities of fluid systems
cannot be measured for all spatial domains. Hence, any practical
feedback controller for fluid systems must incorporate some type of
state estimator. To apply the model predictive control to the fluid
systems described by Burgers’ equation, it is needed to establish
a state estimation method for Burgers’ equation with limited
measurable state variables. To this purpose, we apply unscented
Kalman filter for estimating the state variables of fluid systems
described by Burgers’ equation. The objective of this study is to
establish a state estimation method based on unscented Kalman filter
for Burgers’ equation. The effectiveness of the proposed method is
verified by numerical simulations.
Abstract: The introduction of tilt-rotor aircraft into the existing civilian air transportation system will provide beneficial effects due to tilt-rotor capability to combine the characteristics of a helicopter and a fixed-wing aircraft into one vehicle. The disposability of reliable tilt-rotor simulation models supports the development of such vehicle. Indeed, simulation models are required to design automatic control systems that increase safety, reduce pilot's workload and stress, and ensure the optimal aircraft configuration with respect to flight envelope limits, especially during the most critical flight phases such as conversion from helicopter to aircraft mode and vice versa. This article presents a process to build a simplified tilt-rotor simulation model, derived from the analysis of flight data. The model aims to reproduce the complex dynamics of tilt-rotor during the in-flight conversion phase. It uses a set of scheduled linear transfer functions to relate the autopilot reference inputs to the most relevant rigid body state variables. The model also computes information about the rotor flapping dynamics, which are useful to evaluate the aircraft control margin in terms of rotor collective and cyclic commands. The rotor flapping model is derived through a mixed theoretical-empirical approach, which includes physical analytical equations (applicable to helicopter configuration) and parametric corrective functions. The latter are introduced to best fit the actual rotor behavior and balance the differences existing between helicopter and tilt-rotor during flight. Time-domain system identification from flight data is exploited to optimize the model structure and to estimate the model parameters. The presented model-building process was applied to simulated flight data of the ERICA Tilt-Rotor, generated by using a high fidelity simulation model implemented in FlightLab environment. The validation of the obtained model was very satisfying, confirming the validity of the proposed approach.
Abstract: This paper is concerned with a system of
Hamilton-Jacobi-Bellman equations coupled with an autonomous
dynamical system. The mathematical system arises in the differential
game formulation of political economy models as an infinite-horizon
continuous-time differential game with discounted instantaneous
payoff rates and continuously and discretely varying state variables.
The existence of a weak solution of the PDE system is proven and
a computational scheme of approximate solution is developed for a
class of such systems. A model of democratization is mathematically
analyzed as an illustration of application.
Abstract: Higher order ΔΣ Modulator (DSM) is basically an
unstable system. The approximate conditions for stability cannot be
used for the design of a DSM for industrial applications where risk is
involved. The existing second order, single stage, single bit, unity
feedback gain , discrete DSM cannot be used for the normalized full
range (-1 to +1) of an input signal since the DSM becomes unstable
when the input signal is above ±0.55. The stability is also not
guaranteed for input signals of amplitude less than ±0.55. In the
present paper, the above mentioned second order DSM is modified
with input signal dependent forward path gain. The proposed DSM is
suitable for industrial applications where one needs the digital
representation of the analog input signal, during each sampling
period. The proposed DSM can operate almost for the full range of
input signals (-0.95 to +0.95) without causing instability, assuming
that the second integrator output should not exceed the circuit supply
voltage, ±15 Volts.
Abstract: This article presents a computationally tractable probabilistic model for the relation between the complex wavelet coefficients of two images of the same scene. The two images are acquisitioned at distinct moments of times, or from distinct viewpoints, or by distinct sensors. By means of the introduced probabilistic model, we argue that the similarity between the two images is controlled not by the values of the wavelet coefficients, which can be altered by many factors, but by the nature of the wavelet coefficients, that we model with the help of hidden state variables. We integrate this probabilistic framework in the construction of a new image registration algorithm. This algorithm has sub-pixel accuracy and is robust to noise and to other variations like local illumination changes. We present the performance of our algorithm on various image types.
Abstract: Newton-Raphson State Estimation method using bus
admittance matrix remains as an efficient and most popular method to
estimate the state variables. Elements of Jacobian matrix are computed
from standard expressions which lack physical significance. In this
paper, elements of the state estimation Jacobian matrix are obtained
considering the power flow measurements in the network elements.
These elements are processed one-by-one and the Jacobian matrix H is
updated suitably in a simple manner. The constructed Jacobian matrix
H is integrated with Weight Least Square method to estimate the state
variables. The suggested procedure is successfully tested on IEEE
standard systems.
Abstract: In this research we show that the dynamics of an action potential in a cell can be modeled with a linear combination of the dynamics of the gating state variables. It is shown that the modeling error is negligible. Our findings can be used for simplifying cell models and reduction of computational burden i.e. it is useful for simulating action potential propagation in large scale computations like tissue modeling. We have verified our finding with the use of several cell models.
Abstract: This paper discusses two observers, which are used
for the estimation of parameters of PMSM. Former one, reduced
order observer, which is used to estimate the inaccessible parameters
of PMSM. Later one, full order observer, which is used to estimate
all the parameters of PMSM even though some of the parameters are
directly available for measurement, so as to meet with the
insensitivity to the parameter variation. However, the state space
model contains some nonlinear terms i.e. the product of different
state variables. The asymptotic state observer, which approximately
reconstructs the state vector for linear systems without uncertainties,
was presented by Luenberger. In this work, a modified form of such
an observer is used by including a non-linear term involving the
speed. So, both the observers are designed in the framework of
nonlinear control; their stability and rate of convergence is discussed.