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 purpose of this paper is to provide a practical
example to the Linear Quadratic Gaussian (LQG) controller. This
method includes a description and some discussion of the discrete
Kalman state estimator. One aspect of this optimality is that the
estimator incorporates all information that can be provided to it. It
processes all available measurements, regardless of their precision, to
estimate the current value of the variables of interest, with use of
knowledge of the system and measurement device dynamics, the
statistical description of the system noises, measurement errors, and
uncertainty in the dynamics models.
Since the time of its introduction, the Kalman filter has been the
subject of extensive research and application, particularly in the area
of autonomous or assisted navigation. For example, to determine the
velocity of an aircraft or sideslip angle, one could use a Doppler
radar, the velocity indications of an inertial navigation system, or the
relative wind information in the air data system. Rather than ignore
any of these outputs, a Kalman filter could be built to combine all of
this data and knowledge of the various systems- dynamics to
generate an overall best estimate of velocity and sideslip angle.
Abstract: The growth and interconnection of power networks in many regions has invited complicated techniques for energy management services (EMS). State estimation techniques become a powerful tool in power system control centers, and that more information is required to achieve the objective of EMS. For the online state estimator, assuming the continuous time is equidistantly sampled with period Δt, processing events must be finished within this period. Advantage of Kalman Filtering (KF) algorithm in using system information to improve the estimation precision is utilized. Computational power is a major issue responsible for the achievement of the objective, i.e. estimators- solution at a small sampled period. This paper presents the optimum utilization of processors in a state estimator based on KF. The model used is presented using Petri net (PN) theory.