Abstract: In this work, we investigate the exponential stability of a linear system described by x˙ (t) = Ax(t) − ρBx(t). Here, A generates a semigroup S(t) on a Hilbert space, the operator B is supposed to be of Desch-Schappacher type, which makes the investigation more interesting in many applications. The case of Miyadera-Voigt perturbations is also considered. Sufficient conditions are formulated in terms of admissibility and observability inequalities and the approach is based on some energy estimates. Finally, the obtained results are applied to prove the uniform exponential stabilization of bilinear partial differential equations.
Abstract: As part of the development of a 4D autopilot system for unmanned aerial vehicles (UAVs), i.e. a time-dependent robust trajectory generation and control algorithm, this work addresses the problem of optimal path control based on the flight sensors data output that may be unreliable due to noise on data acquisition and/or transmission under certain circumstances. Although several filtering methods, such as the Kalman-Bucy filter or the Linear Quadratic Gaussian/Loop Transfer Recover Control (LQG/LTR), are available, the utter complexity of the control system, together with the robustness and reliability required of such a system on a UAV for airworthiness certifiable autonomous flight, required the development of a proper robust filter for a nonlinear system, as a way of further mitigate errors propagation to the control system and improve its ,performance. As such, a nonlinear algorithm based upon the LQG/LTR, is validated through computational simulation testing, is proposed on this paper.
Abstract: Three structure-dependent integration methods have been developed for solving equations of motion, which are second-order ordinary differential equations, for structural dynamics and earthquake engineering applications. Although they generally have the same numerical properties, such as explicit formulation, unconditional stability and second-order accuracy, a different performance is found in solving the free vibration response to either linear elastic or nonlinear systems with high frequency modes. The root cause of this different performance in the free vibration responses is analytically explored herein. As a result, it is verified that a weak instability is responsible for the different performance of the integration methods. In general, a weak instability will result in an inaccurate solution or even numerical instability in the free vibration responses of high frequency modes. As a result, a weak instability must be prohibited for time integration methods.
Abstract: Diabetes is a medical condition that can lead to various diseases such as stroke, heart disease, blindness and obesity. In clinical practice, the concern of the diabetic patients towards the blood glucose examination is rather alarming as some of the individual describing it as something painful with pinprick and pinch. As for some patient with high level of glucose level, pricking the fingers multiple times a day with the conventional glucose meter for close monitoring can be tiresome, time consuming and painful. With these concerns, several non-invasive techniques were used by researchers in measuring the glucose level in blood, including ultrasonic sensor implementation, multisensory systems, absorbance of transmittance, bio-impedance, voltage intensity, and thermography. This paper is discussing the application of the near-infrared (NIR) spectroscopy as a non-invasive method in measuring the glucose level and the implementation of the linear system identification model in predicting the output data for the NIR measurement. In this study, the wavelengths considered are at the 1450 nm and 1950 nm. Both of these wavelengths showed the most reliable information on the glucose presence in blood. Then, the linear Autoregressive Moving Average Exogenous model (ARMAX) model with both un-regularized and regularized methods was implemented in predicting the output result for the NIR measurement in order to investigate the practicality of the linear system in this study. However, the result showed only 50.11% accuracy obtained from the system which is far from the satisfying results that should be obtained.
Abstract: In this paper, ways of modeling dynamic measurement
systems are discussed. Specially, for linear system with single-input
single-output, it could be modeled with shallow neural network.
Then, gradient based optimization algorithms are used for searching
the proper coefficients. Besides, method with normal equation and
second order gradient descent are proposed to accelerate the modeling
process, and ways of better gradient estimation are discussed. It
shows that the mathematical essence of the learning objective is
maximum likelihood with noises under Gaussian distribution. For
conventional gradient descent, the mini-batch learning and gradient
with momentum contribute to faster convergence and enhance model
ability. Lastly, experimental results proved the effectiveness of second
order gradient descent algorithm, and indicated that optimization with
normal equation was the most suitable for linear dynamic models.
Abstract: This paper presents parameter estimation of a
single-phase rectifier using extended Kalman filter (EKF). The state
space model has been obtained using Kirchhoff’s current law (KCL)
and Kirchhoff’s voltage law (KVL). The capacitor voltage and diode
current of the circuit have been estimated using EKF. Simulation
results validate the better accuracy of the proposed method as
compared to the least mean square method (LMS). Further, EKF
has the advantage that it can be used for nonlinear systems.
Abstract: A class of implicit systems is known as a more
generalized class of systems than a class of explicit systems. To
establish a control method for such a generalized class of systems, we
adopt model predictive control method which is a kind of optimal
feedback control with a performance index that has a moving
initial time and terminal time. However, model predictive control
method is inapplicable to systems whose all state variables are not
exactly known. In other words, model predictive control method is
inapplicable to systems with limited measurable states. In fact, it
is usual that the state variables of systems are measured through
outputs, hence, only limited parts of them can be used directly. It is
also usual that output signals are disturbed by process and sensor
noises. Hence, it is important to establish a state estimation method
for nonlinear implicit systems with taking the process noise and
sensor noise into consideration. To this purpose, we apply the model
predictive control method and unscented Kalman filter for solving
the optimization and estimation problems of nonlinear implicit
systems, respectively. The objective of this study is to establish a
model predictive control with unscented Kalman filter for nonlinear
implicit systems.
Abstract: Recently, the effectiveness of random dither
quantization method for linear feedback control systems has
been shown in several papers. However, the random dither
quantization method has not yet been applied to nonlinear feedback
control systems. The objective of this paper is to verify the
effectiveness of random dither quantization method for nonlinear
feedback control systems. For this purpose, we consider the attitude
stabilization problem of satellites using discrete-level actuators.
Namely, this paper provides a control method based on the random
dither quantization method for stabilizing the attitude of satellites
using discrete-level actuators.
Abstract: In this paper, we consider the parametrization of the
discrete-time systems without the unit-delay element within the
framework of the factorization approach. In the parametrization,
we investigate the number of required parameters. We consider
single-input single-output systems in this paper. By the investigation,
we find, on the discrete-time systems without the unit-delay element,
three cases that are (1) there exist plants which require only one
parameter and (2) two parameters, and (3) the number of parameters
is at most three.
Abstract: In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the l2-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.
Abstract: This paper presents modeling and control of a highly nonlinear system including, non-interacting two spherical tanks using iterative learning control (ILC). Consequently, the objective of the paper is to control the liquid levels in the nonlinear tanks. First, a proportional-integral-derivative (PID) controller is applied to the plant model as a suitable benchmark for comparison. Then, dynamic responses of the control system corresponding to different step inputs are investigated. It is found that the conventional PID control is not able to fulfill the design criteria such as desired time constant. Consequently, an iterative learning controller is proposed to accurately control the coupled nonlinear tanks system. The simulation results clearly demonstrate the superiority of the presented ILC approach over the conventional PID controller to cope with the nonlinearities presented in the dynamic system.
Abstract: This paper presents a design of dynamic feedback
control based on observer for a class of large scale Lipschitz nonlinear
systems. The use of Differential Mean Value Theorem (DMVT) is to
introduce a general condition on the nonlinear functions. To ensure
asymptotic stability, sufficient conditions are expressed in terms of
linear matrix inequalities (LMIs). High performances are shown
through real time implementation with ARDUINO Duemilanove
board to the one-link flexible joint robot.
Abstract: In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.
Abstract: In wireless communications, 3GPP LTE is one of the solutions to meet the greater transmission data rate demand. One issue inherent to this technology is the PAPR (Peak-to-Average Power Ratio) of OFDM (Orthogonal Frequency Division Multiplexing) modulation. This high PAPR affects the efficiency of power amplifiers. One approach to mitigate this effect is the Crest Factor Reduction (CFR) technique. In this work, we simulate the impact of Hard Limited Clipping Crest Factor Reduction technique on BER (Bit Error Rate) in OFDM based Systems. In general, the results showed that CFR has more effects on higher digital modulation schemes, as expected. More importantly, we show the worst-case degradation due to CFR on QPSK, 16QAM, and 64QAM signals in a linear system. For example, hard clipping of 9 dB results in a 2 dB increase in signal to noise energy at a 1% BER for 64-QAM modulation.
Abstract: Uncertainties related to fatigue damage estimation of
non-linear systems are highly dependent on the tail behaviour
and extreme values of the stress range distribution. By using
a combination of the First Order Reliability Method (FORM)
and Monte Carlo simulations (MCS), the accuracy of the fatigue
estimations may be improved for the same computational efforts.
The method is applied to a bottom-fixed, monopile-supported large
offshore wind turbine, which is a non-linear and dynamically sensitive
system. Different curve fitting techniques to the fatigue damage
distribution have been used depending on the sea-state dependent
response characteristics, and the effect of a bi-linear S-N curve is
discussed. Finally, analyses are performed on several environmental
conditions to investigate the long-term applicability of this multistep
method. Wave loads are calculated using state-of-the-art theory, while
wind loads are applied with a simplified model based on rotor thrust
coefficients.
Abstract: A two wheel inverted pendulum (TWIP) vehicle is built with two hub DC motors for motion control evaluation. Arduino Nano micro-processor is chosen as the control kernel for this electric test plant. Accelerometer and gyroscope sensors are built in to measure the tilt angle and angular velocity of the inverted pendulum vehicle. Since the TWIP has significantly hub motor dead zone and nonlinear system dynamics characteristics, the vehicle system is difficult to control by traditional model based controller. The intelligent model-free fuzzy sliding mode controller (FSMC) was employed as the main control algorithm. Then, intelligent controllers are designed for TWIP balance control, and two wheels synchronization control purposes.
Abstract: In population dynamics the study of both, the
abundance and the spatial distribution of the populations in a
given habitat, is a fundamental issue a From ecological point of
view, the determination of the factors influencing such changes
involves important problems. In this paper a mathematical model to
describe the temporal dynamic and the spatiotemporal dynamic of the
interaction of three populations (pollinators, plants and herbivores) is
presented. The study we present is carried out by stages: 1. The
temporal dynamics and 2. The spatio-temporal dynamics. In turn,
each of these stages is developed by considering three cases which
correspond to the dynamics of each type of interaction. For instance,
for stage 1, we consider three ODE nonlinear systems describing
the pollinator-plant, plant-herbivore and plant-pollinator-herbivore,
interactions, respectively. In each of these systems different types of
dynamical behaviors are reported. Namely, transcritical and pitchfork
bifurcations, existence of a limit cycle, existence of a heteroclinic
orbit, etc. For the spatiotemporal dynamics of the two mathematical
models a novel factor are introduced. This consists in considering
that both, the pollinators and the herbivores, move towards those
places of the habitat where the plant population density is high.
In mathematical terms, this means that the diffusive part of the
pollinators and herbivores equations depend on the plant population
density. The analysis of this part is presented by considering pairs of
populations, i. e., the pollinator-plant and plant-herbivore interactions
and at the end the two mathematical model is presented, these models
consist of two coupled nonlinear partial differential equations of
reaction-diffusion type. These are defined on a rectangular domain
with the homogeneous Neumann boundary conditions. We focused
in the role played by the density dependent diffusion term into
the coexistence of the populations. For both, the temporal and
spatio-temporal dynamics, a several of numerical simulations are
included.
Abstract: In this paper, we consider the two-stage compensator
designs of SISO plants. As an investigation of the characteristics of
the two-stage compensator designs, which is not well investigated
yet, of SISO plants, we implement three dimensional visualization
systems of output signals and optimization system for SISO plants by
the parametrization of stabilizing controllers based on the two-stage
compensator design. The system runs on Mathematica by using
“Three Dimensional Surface Plots,” so that the visualization can
be interactively manipulated by users. In this paper, we use the
discrete-time LTI system model. Even so, our approach is the
factorization approach, so that the result can be applied to many
linear models.
Abstract: The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.
Abstract: Maximum Power Point Tracking (MPPT) has played a vital role to enhance the efficiency of solar photovoltaic (PV) power generation under varying atmospheric temperature and solar irradiation. However, it is hard to track the maximum power point using conventional linear controllers due to the natural inheritance of nonlinear I-V and P-V characteristics of solar PV systems. Fuzzy Logic Controller (FLC) is suitable for nonlinear system control applications and eliminating oscillations, circuit complexities present in the conventional perturb and observation and incremental conductance methods respectively. Hence, in this paper, FLC is proposed for tracking exact MPPT of solar PV power generation system under varying solar irradiation conditions. The effectiveness of the proposed FLC-based MPPT controller is validated through simulation and analysis using MATLAB/Simulink.