Nonlinear control of systems with multiple equilibria and unknown sinusoidal disturbance

In this paper, nonlinear systems having multiple equilibrium points and low order dynamics are investigated. Roll motions of ships are studied by means of modern nonlinear techniques to exemplify the behavior of such nonlinear systems in the case when they are under the influence of external sinusoidal disturbances with unknown amplitudes. The main objective is to analyze the performance of this system at different operating conditions, including those giving rise to chaos, and to design a controller with an overparameterized structure to stabilize the system at the origin. A nonlinear recursive backstepping controller is proposed and the transient performance is investigated. Lyapunov-based techniques are used to force systematic following of a reference model while introducing a nonlinear parameter estimator to guarantee adaptivity. Robustness problems as well as ways to tune the controller parameters are examined. Simulation results are submitted for the uncontrolled and controlled cases, verifying the effectiveness of the proposed controller. Finally, a discussion and conclusions are given with possible future extensions.     

(π)C—H···S, (allyl)C—H···C(π) and π···π intermolecular interactions: synthesis, characterization, and crystal structure of 2,2′-bipyridine bis(diallyldithiocarbamato)zinc(II)

A mixed-ligand Zn(II) complex formulated as [Zn(aldtc)₂(bipy)] (aldtc=diallyldithiocarbamate; bipy=2,2′-bipyridine) was synthesized and characterized by IR, ¹H and ¹³C NMR spectral measurements and X-ray crystallography. The crystal structure of this complex indicates that Zn has a distorted octahedral geometry. The Zn—N distances are invariant (2.168(2) Å), while those of the Zn—S are slightly different (2.5408(9) and 2.5440(9) Å). The N—Zn—N, S—Zn—S and N—Zn—S bond angles are in the range 75.35(13)–99.75(7)°, 70.48(3)–161.02(5)° and 95.26(7)–160.32(7)°, respectively. The crystal packing of the complex shows different motifs of supramolecularity resulting from both hydrophilic ((π)C—H···S) and hydrophobic ((allyl)C—H···C(π)) intermolecular interactions. These interactions result in a chain arrangement of molecules along crystallographic c axis and the chains are further connected via π···π stacking along with ((π)C—H···S along b axis leading to an overall crystal packing that can be regarded as layers of complexes along bc plane, which are held together through nonconventional hydrogen bonding and π···π stacking.     

Novel Synthesis of Dihydroquinoxalinylpyridazine Derivatives

Methylquinoxaline derivative 1 undergoes bromination to give bromomethyl quinoxaline 2 , which could be transferred to cyanomethyl quinoxaline 3 . The latter compound 3 readily coupled with arene diazonium salts to give hydrazone derivatives 5a‐c . Compounds 5a,b reacted with active methylene reagents to give the target ring system, quinoxalinylpyridazine derivatives 8a‐c . Compound 1 reacted with DMFDMA to give the enamine derivative 9 , which coupled with arene diazonium salts to give the aldehydic hydrazone derivatives 10a‐c . Compound 10 reacted with active methylene compounds to give quinoxalinylpyridazine derivatives. UV characterization of some of the prepared compounds was reported.     

Aspect-ratio dependent oscillatory thermocapillary convection in the floating half zone

The dependency of the critical Marangoni number on the geometrical aspect ratio of the floating half zone is essential to predict the onset of oscillatory thermocapillary convection.The experimental studies in the microgravity conditions on floating half zones of several centimeters in diameter have predicted that the critical Marangoni number increases with the increasing aspect ratio,and the terrestrial experimental studies have predicted the contradictory conclusion for floating half zones of several mil...     

Non-Gravitational Effects with Density-Matching in Evaluating the Influence of Sedimentation on Colloidal Coagulation

The method of density matching between the solid and liquid phases is often adopted to effectively eliminate the effect of sedimentation of suspensions in studies on dynamic behaviour of a colloidal system. However, the associated changes in the solvent composition may bring side effects to the properties investigated and therefore might lead to a faulty conclusion if the relevant correction is not made. To illustrate the importance of this side effect, we present an example of the sedimentation influence on the coagulation rate of suspensions of 2μm （diameter） polystyrene. The liquid mixtures, in the proper proportions of water （H2O）, deuterium oxide （D2O） and methanol （MeOH） as the liquid phase, density-matched and unmatched experiments are performed. Besides the influence of viscosity, the presence of methanol in solvent media, used to enhance the sedimentation effect, causes significant changes （reduction） in rapid coagulation rates compared to that in pure water. Without the relevant corrections for those non-gravitational factors it seems that gravitational sedimentation would retard the coagulation. The magnitude of the contribution from the non-gravitational factor is quantitatively determined, making the relevant correction possible. After necessary the influence of the sedimentation on coagulation rates at corrections for all factors, our experiments show that the initial stage of the coagulation is not observable.     

Study of nonlinear system stability using eigenvalue analysis: Gyroscopic motion

General computational multibody system (MBS) algorithms allow for the linearization of the highly nonlinear equations of motion at different points in time in order to obtain the eigenvalue solution. This eigenvalue solution of the linearized equations is often used to shed light on the system stability at different configurations that correspond to different time points. Different MBS algorithms, however, employ different sets of orientation coordinates, such as Euler angles and Euler parameters, which lead to different forms of the dynamic equations of motion. As a consequence, the forms of the linearized equations and the eigenvalue solution obtained strongly depend on the set of orientation coordinates used. This paper addresses this fundamental issue by examining the effect of the use of different orientation parameters on the linearized equations of a gyroscope. The nonlinear equations of motion of the gyroscope are formulated using two different sets of orientation parameters: Euler angles and Euler parameters. In order to obtain a set of linearized equations that can be used to define the eigenvalue solution, the algebraic equations that describe the MBS constraints are systematically eliminated leading to a nonlinear form of the equations of motion expressed in terms of the system degrees of freedom. Because in MBS applications the generalized forces can be highly nonlinear and can depend on the velocities, a state space formulation is used to solve the eigenvalue problem. It is shown in this paper that the independent state equations formulated using Euler angles and Euler parameters lead to different eigenvalue solutions. This solution is also different from the solution obtained using a form of the Newton-Euler matrix equation expressed in terms of the angular accelerations and angular velocities. A time-domain solution of the linearized equations is also presented in order to compare between the solutions obtained using two different sets of orientation parameters and also to shed light on the important issue of using the eigenvalue analysis in the study of MBS stability. The validity of using the eigenvalue analysis based on the linearization of the nonlinear equations of motion in the study of the stability of railroad vehicle systems, which have known critical speeds, is examined. It is shown that such an eigenvalue analysis can lead to wrong conclusions regarding the stability of nonlinear systems.