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Optimal Robust PID control for first- and second-order plus dead-time processes
https://ddd.uab.cat/record/213185
The present study proposes a new design method for a proportional-integral-derivative (PID) control system for first-order plus dead-time (FOPDT) and over-damped second-order plus dead-time (SOPDT) systems. What is presented is an optimal PID tuning constrained to robust stability. The optimal tuning is defined for each one of the two operation modes the control system may operate in: servo (reference tracking) and regulation (disturbance rejection). The optimization problem is stated for a normalized second-order plant that unifies FOPDT and SOPDT process models. Different robustness levels are considered and for each one of them, the set of optimal controller parameters is obtained. In a second step, suitable formulas are found that provide continuous values for the controller parameters. Finally, the effectiveness of the proposed method is confirmed through numerical examples. Sato, TakaoFri, 04 Oct 2019 10:33:53 GMThttps://ddd.uab.cat/record/2131852019A proposal for evading the measurement uncertainty in classical and quantum computing :: Application to a resonant tunneling diode and a Mach-Zehnder interferometer
https://ddd.uab.cat/record/213183
Measuring properties of quantum systems is governed by a stochastic (collapse or state-reduction) law that unavoidably yields an uncertainty (variance) associated with the corresponding mean values. This non-classical source of uncertainty is known to be manifested as noise in the electrical current of nanoscale electron devices, and hence it can flaw the good performance of more complex quantum gates. We propose a protocol to alleviate this quantum uncertainty that consists of (i) redesigning the device to accommodate a large number of electrons inside the active region, either by enlarging the lateral or longitudinal areas of the device and (ii) re-normalizing the total current to the number of electrons. How the above two steps can be accommodated using the present semiconductor technology has been discussed and numerically studied for a resonant tunneling diode and a Mach-Zehnder interferometer, for classical and quantum computations, respectively. It is shown that the resulting protocol formally resembles the so-called collective measurements, although, its practical implementation is substantially different. Pandey, DevashishFri, 04 Oct 2019 10:15:45 GMThttps://ddd.uab.cat/record/2131832019A Route to Chaos in the Boros-Moll Map
https://ddd.uab.cat/record/204395
The Boros-Moll map appears as a subsystem of a Landen transformation associated to certain rational integrals and its dynamics is related to their convergence. In the paper, we study the dynamics of a one-parameter family of maps which unfold the Boros-Moll one, showing that the existence of an unbounded invariant chaotic region in the Boros-Moll map is a peculiar feature within the family. We relate this singularity with a specific property of the critical lines that occurs only for this special case. In particular, we explain how the unbounded chaotic region in the Boros-Moll map appears. We especially explain the main contact/homoclinic bifurcations that occur in the family. We also report some other bifurcation phenomena that appear in the considered unfolding. Gardini, LauraThu, 16 May 2019 13:36:19 GMThttps://ddd.uab.cat/record/2043952019Limit cycles for discontinuous planar piecewise linear differential systems separated by an algebraic curve
https://ddd.uab.cat/record/204393
We study how to change the maximum number of limit cycles of the discontinuous piecewise linear differential systems with only two pieces in function of the degree of the discontinuity of the algebraic curve between the two linear differential systems. These discontinuous differential systems appear frequently in applied sciences. Llibre, JaumeThu, 16 May 2019 13:36:18 GMThttps://ddd.uab.cat/record/2043932019Research on the collision avoidance algorithm for fixed-wing UAVs based on maneuver coordination and planned trajectories prediction
https://ddd.uab.cat/record/204102
This paper presents a novel collision avoidance (CA) algorithm for a cooperative fixed-wing unmanned aerial vehicle (UAV). The method is based on maneuver coordination and planned trajectory prediction. Each aircraft in a conflict generates three available maneuvers and predicts the corresponding planned trajectories. The algorithm coordinates planned trajectories between participants in a conflict, determines which combination of planned trajectories provides the best separation, eventually makes an agreement on the maneuver for collision avoidance and activates the preferred maneuvers when a collision is imminent. The emphasis is placed on providing protection for UAVs, while activating maneuvers late enough to reduce interference, which is necessary for collision avoidance in the formation and clustering of UAVs. The CA has been validated with various simulations to show the advantage of collision avoidance for continuous conflicts in multiple, high-dynamic, high-density and three-dimensional (3D) environments. It eliminates the disadvantage of traditional CA, which has high uncertainty, and takes the performance parameters of different aircraft into consideration and makes full use of the maneuverability of fixed-wing aircraft. Wan, YuMon, 29 Apr 2019 08:39:04 GMThttps://ddd.uab.cat/record/2041022019Assessing concentration changes of odorant compounds in the thermal-mechanical drying phase of sediment-likewastes from olive oil extraction
https://ddd.uab.cat/record/204071
In the industrial production of olive oil, both solid wastes and those produced from their incineration are a serious environmental problem since only 20% w/w of the fruit becomes oil and the rest is waste, mainly orujo and alperujo. A key aspect to transforming these wastes into an important source of energy such as pellets is to recognize the most appropriate time of the year for waste drying, with the objective of minimizing the environmental impact of the volatile compounds contained in the waste. In this work, the emissions produced during thermal-mechanical drying were studied throughout a period of six months of waste storage in which alperujo and orujo were stored in open containers under uncontrolled environmental conditions. The studied emissions were produced when both wastes were dried in a pilot rotary drying trommel at 450 °C to reduce their initial humidity of around 70-80% w/w to 10-15% w/w. Results indicated that when the storage time of the wastes in the uncontrolled environments increased, the emission of odorant compounds during drying also increased as a consequence of the biological and chemical processes occurring in the containers. The main odorant VOCs were quantified monthly for six months at the outlet of the drying trommel. It was determined that the drying of this type of waste could be carried out properly until the third month of storage. Afterwards, the concentration of most VOCs produced widely exceeded the odor thresholds of selected compounds. Hernández, DiógenesFri, 26 Apr 2019 08:56:11 GMThttps://ddd.uab.cat/record/2040712019Microparticle manipulation and imaging through a self-calibrated liquid crystal on silicon display
https://ddd.uab.cat/record/201035
We present in this paper a revision of three different methods we conceived in the framework of liquid crystal on silicon (LCoS) display optimization and application. We preliminarily demonstrate an LCoS self-calibration technique, from which we can perform a complete LCoS characterization. In particular, two important characteristics of LCoS displays are retrieved by using self-addressed digital holograms. On the one hand, we determine its phase-voltage curve by using the interference pattern generated by a digital two-sectorial split-lens configuration. On the other hand, the LCoS surface profile is also determined by using a self-addressed dynamicmicro-lens array pattern. Second, the implementation of microparticle manipulation through optical traps created by an LCoS display is demonstrated. Finally, an LCoS display based inline (IL) holographic imaging system is described. By using the LCoS display to implement a double-sideband filter configuration, this inline architecture demonstrates the advantage of obtaining dynamic holographic imaging of microparticles independently of their spatial positions by avoiding the non-desired conjugate images. Zhang, HaolinTue, 15 Jan 2019 09:39:04 GMThttps://ddd.uab.cat/record/2010352018Periodic orbits bifurcating from a nonisolated zero-Hopf equilibrium of three-dimensional differential systems revisited
https://ddd.uab.cat/record/199371
In this paper, we study the periodic solutions bifurcating from a nonisolated zero–Hopf equilib- rium in a polynomial differential system of degree two in R³. More specifically, we use recent results of averaging theory to improve the conditions for the existence of one or two periodic solutions bifurcating from such a zero–Hopf equilibrium. This new result is applied for studying the periodic solutions of differential systems in R³ having n-scroll chaotic attractors. Cândido, Murilo R.Mon, 12 Nov 2018 12:11:51 GMThttps://ddd.uab.cat/record/1993712018On uniqueness of limit cycles in general Bogdanov-Takens bifurcation
https://ddd.uab.cat/record/199363
In this paper we present a complete study to the well-known Bogdanov-Takens bifurcation and give a rigorous proof for the uniqueness of limit cycles. Han, MaoanMon, 12 Nov 2018 12:11:50 GMThttps://ddd.uab.cat/record/1993632018Algebraic limit cycles in piecewise linear differential systems
https://ddd.uab.cat/record/199362
This paper is devoted to study the algebraic limit cycles of planar piecewise linear differential systems. In particular we present examples exhibiting two explicit hyperbolic algebraic limit cycles, as well as some 1-parameter families with a saddle-node bifurcation of algebraic limit cycles. We also show that all degrees for algebraic limit cycles are allowed. Buzzi, Claudio A.Mon, 12 Nov 2018 12:11:50 GMThttps://ddd.uab.cat/record/1993622018Stability of periodic orbits in the averaging theory :: applications to Lorenz and Thomas' differential systems
https://ddd.uab.cat/record/199350
We study the kind of stability of the periodic orbits provided by higher order averaging theory. We apply these results for determining the k-hyperbolicity of some periodic orbits of the Lorenz and Thoma's differential system. Cândido, Murilo R.Mon, 12 Nov 2018 12:11:50 GMThttps://ddd.uab.cat/record/1993502018On the periodic solutions of the 5–dimensional Lorenz equation modeling coupled Rosby waves and gravity waves
https://ddd.uab.cat/record/182728
de Carvalho, TiagoThu, 07 Dec 2017 14:21:34 GMThttps://ddd.uab.cat/record/1827282017Degenerate Fold–Hopf Bifurcations in a Rössler-Type System
https://ddd.uab.cat/record/182532
We study the Hopf and the fold--Hopf bifurcations of the R\"ossler--type differential system * =-y-z, =x ay, =-cz byz, * with b 0. We show that the classical Hopf bifurcation cannot be applied to this system for detecting the fold--Hopf bifurcation, which here is studied using the averaging theory. Our results show that a Hopf bifurcation takes place at the equilibrium (-ac/b,c/b,-c/b) when c=a<0. This Hopf bifurcation becomes a fold--Hopf bifurcation when c=a=0. Tigan, GheorgheTue, 28 Nov 2017 07:46:29 GMThttps://ddd.uab.cat/record/1825322017On the Homoclinic Orbits of the Lü System
https://ddd.uab.cat/record/182531
In this paper, the existence of homoclinic orbits of the equilibrium point (0, 0, 0) is demonstrated in the case of the Lu ̈ system for parameter values not reported by G. A. Leonov. In addition, some simulations are shown that agree with our theoretical analysis. Álvarez-Ramírez, MarthaTue, 28 Nov 2017 07:46:29 GMThttps://ddd.uab.cat/record/1825312017Classical Planar Algebraic Curves Realizable by Quadratic Polynomial Differential Systems
https://ddd.uab.cat/record/182525
In this paper we show examples of planar quadratic differential systems having some famous planar invariant algebraic curves. We carry out a non exhaustive classification taking into account the degree of the invariant algebraic curve. Also we pay particular attention to the Darboux integrability of the systems. García, Isaac A.Tue, 28 Nov 2017 07:46:29 GMThttps://ddd.uab.cat/record/1825252017Periodic orbits of the planar anisotropic Kepler problem
https://ddd.uab.cat/record/182514
In this paper we prove that at every energy level the anisotropic problem with small anisotropy has two periodic orbits which bifurcate from elliptic orbits of the Kepler problem with high eccentricity. Moreover we provide approximate analytic expressions for these periodic orbits. The tool for proving this result is the averaging theory. Abouelmagd, Elbaz I.Tue, 28 Nov 2017 07:46:29 GMThttps://ddd.uab.cat/record/1825142017Cooperative Multi-UAV Collision Avoidance Based on Distributed Dynamic Optimization and Causal Analysis
https://ddd.uab.cat/record/170148
A critical requirement for unmanned aerial vehicles (UAV) is the collision avoidance (CA) capability to meet safety and flexibility issues in an environment of increasing air traffic densities. This paper proposes two efficient algorithms: conflict detection (CD) algorithm and conflict resolution (CR) algorithm. These two algorithms are the key components of the cooperative multi-UAV CA system. The CD sub-module analyzes the spatial-temporal information of four dimensional (4D) Departament de Telecomunicació i Enginyeria de Sistemes trajectory to detect potential collisions. The CR sub-module calculates the minimum deviation of the planned trajectory by an objective function integrated with track adjustment, distance, and time costs, taking into account the vehicle performance, state and separation constraints. Additionally, we extend the CR sub-module with causal analysis to generate all possible solution states in order to select the optimal strategy for a multi-threat scenario, considering the potential interactions among neighboring UAVs with a global scope of a cluster. Quantitative simulation experiments are conducted to validate the feasibility and scalability of the proposed CA system, as well as to test its efficiency with variable parameters. Lao, MingruiTue, 14 Feb 2017 14:14:49 GMThttps://ddd.uab.cat/record/1701482017Topological Classification of Quadratic Polynomial Differential Systems with a Finite Semi-Elemental Triple Saddle
https://ddd.uab.cat/record/169497
The study of planar quadratic differential systems is very important not only because they appear in many areas of applied mathematics but due to their richness in structure, stability and questions concerning limit cycles, for example. Even though many papers have been written on this class of systems, a complete understanding of this family is still missing. Classical problems, and in particular Hilbert's 16th problem [Hilbert, 1900, 1902], are still open for this family. In this article, we make a global study of the family QTS of all real quadratic polynomial differential systems which have a finite semi-elemental triple saddle (triple saddle with exactly one zero eigenvalue). This family modulo the action of the affine group and time homotheties is three-dimensional and we give its bifurcation diagram with respect to a normal form, in the three-dimensional real space of the parameters of this normal form. This bifur- cation diagram yields 27 phase portraits for systems in QTS counting phase portraits with and without limit cycles. Algebraic invariants are used to construct the bifurcation set and we present the phase portraits on the Poincar ́e disk. The bifurcation set is not just algebraic due to the presence of a surface found numerically, whose points correspond to connections of separatrices. Artés, Joan CarlesMon, 23 Jan 2017 15:21:48 GMThttps://ddd.uab.cat/record/1694972016When parallels and meridians are limit cycles for polynomial vector fields on quadrics of revolution in the euclidean 3-space
https://ddd.uab.cat/record/169483
We study polynomial vector fields of arbitrary degree in R^3 with an invariant quadric of revolution. We characterize all the possible configurations of invariant meridians and parallels that these vector fields can exhibit. Furthermore we analyze when these invariant meridians and parallels can be limit cycles. Dias, Fabio ScalcoMon, 23 Jan 2017 15:21:47 GMThttps://ddd.uab.cat/record/1694832016Centers: their integrability and relations with the divergence
https://ddd.uab.cat/record/169477
This is a brief survey on the centers of the analytic differential systems in R^2. First we consider the kind of integrability of the different types of centers, and after we analyze the focus--center problem, i. e. how to distinguish a center from a focus. This is a difficult problem which is not completely solved. We shall present some recent results using the divergence of the differential system. Llibre, JaumeMon, 23 Jan 2017 15:21:47 GMThttps://ddd.uab.cat/record/1694772016Heteroclinic, homoclinic and closed orbits in the Chen system
https://ddd.uab.cat/record/169472
Bounded orbits such as closed, homoclinic and heteroclinic orbits are discussed in this work for a Lorenz- like 3D nonlinear system. For a large spectrum of the parameters the system has neither closed nor homoclinic orbits but has exactly two heteroclinic orbits, while under other constraints the system has symmetrical homoclinic orbits. Tigan, GheorgheMon, 23 Jan 2017 15:21:47 GMThttps://ddd.uab.cat/record/1694722016Asymptotic expansion of the heteroclinic bifurcation for the planar normal form of the 1:2 resonance
https://ddd.uab.cat/record/169464
We consider the family of planar differential systems depending on two real parameters \[ x =y, y = _1 x _2 y x^3-x^2y. \] This system corresponds to the normal form for the 1:2 resonance which exhibits a heteroclinic connection. The phase portrait of the system has a limit cycle which disappears in the heteroclinic connection for the parameter values on the curve _2=c(_1)=-15_1 O(_1^2), _1<0. We significantly improve the knowledge of this curve in a neighborhood of the origin. Roberto, Lucy AnyMon, 23 Jan 2017 15:21:46 GMThttps://ddd.uab.cat/record/1694642016Global phase portraits of Kukles differential systems with homogenous polynomial nonlinearities of degree 5 having a center and their small limit cycles
https://ddd.uab.cat/record/169460
We provide the nine topological global phase portraits in the Poincaré disk of the family of the centers of Kukles polynomial differential systems of the form x = -y, y= x ax^5y bx^3y^3 cxy^5, where x,y\R and a,b,c are real parameters satisfying a^2 b^2 c^2 0. Using averaging theory up to sixth order we determine the number of limit cycles which bifurcate from the origin when we perturb this system first inside the class of all homogeneous polynomial differential systems of degree 6, and second inside the class of all polynomial differential systems of degree 6. Llibre, JaumeMon, 23 Jan 2017 15:21:46 GMThttps://ddd.uab.cat/record/1694602016The geometry of quadratic polynomial differential systems with a finite and an infinite saddle-node (C)
https://ddd.uab.cat/record/169436
Planar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and in particular, Hilbert's 16th problem [Hilbert, 1900, Hilbert, 1902], are still open for this family. Our goal is to make a global study of the family QsnSN of all real quadratic polynomial differential systems which have a finite semi–elemental saddle–node and an infinite saddle–node formed by the collision of two infinite singular points. This family can be divided into three different subfamilies, all of them with the finite saddle–node in the origin of the plane with the eigenvectors on the axes and with the eigenvector associated with the zero eigenvalue on the horizontal axis and (A) with the infinite saddle–node in the horizontal axis, (B) with the infinite saddle–node in the vertical axis and (C) with the infinite saddle–node in the bisector of the first and third quadrants. These three subfamilies modulo the action of the affine group and time homotheties are three–dimensional and we give the bifurcation diagram of their closure with respect to specific normal forms, in the three–dimensional real projective space. The subfamilies (A) and (B) have already been studied [Artés et al. , 2013b] and in this paper we provide the complete study of the geometry of the last family (C). The bifurcation diagram for the subfamily (C) yields 371 topologically distinct phase portraits with and without limit cycles for systems in the closure QsnSN(C) within the representatives of QsnSN(C) given by a chosen normal form. Algebraic invariants are used to construct the bifurcation set. The phase portraits are represented on the Poincaré disk. The bifurcation set of QsnSN(C) is not only algebraic due to the presence of some surfaces found numerically. All points in these surfaces correspond to either connections of separatrices, or the presence of a double limit cycle. Artés, Joan CarlesMon, 23 Jan 2017 15:21:45 GMThttps://ddd.uab.cat/record/1694362015Periodic solutions of a periodic FitzHugh-Nagumo differential system
https://ddd.uab.cat/record/169428
Recently some interest has appeared for the periodic FitzHugh–Nagumo differential systems. Here, we provide sufficient conditions for the existence of periodic solutions in such differential systems. Llibre, JaumeMon, 23 Jan 2017 15:21:44 GMThttps://ddd.uab.cat/record/1694282015