In this thesis is initiated a more systematic geometric exploration of energy shaping. Most of the previous results have been dealt wih particular cases and neither the existence nor the space of solutions has been discussed with any degree of generality. The geometric theory of partial differential equations originated by Goldschmidt and Spencer in late 1960s is utilized to analyze the partial differential equations in energy shaping. The energy shaping partial differential equations are described as a fibered submanifold of a $ k $-jet bundle of a fibered manifold. By revealing the nature of kinetic energy shaping, similarities are noticed between the problem of kinetic energy shaping and some well-known problems in Riemannian geometry. In particular, there is a strong similarity between kinetic energy shaping and the problem of finding a metric connection initiated by Eisenhart and Veblen. We notice that the necessary conditions for the set of so-called $ \lambda $-equation restricted to the control distribution are related to the Ricci identity, similarly to the Eisenhart and Veblen metric connection problem. Finally, the set of $ \lambda $-equations for kinetic energy shaping are coupled with the integrability results of potential energy shaping. The procedure shows how a poor design of closed-loop metric can make it impossible to achieve any flexibility in the character of the possible closed-loop potential function. The integrability results of this thesis have been used to answer some interesting questions about the energy shaping. In particular, a geometric proof is provided which shows that linear controllability is sufficient for energy shaping of linear simple mechanical systems. Furthermore, it is shown that all linearly controllable mechanical control systems with one degree of underactuation can be stabilized using energy shaping feedback. The result is geometric and completely characterizes the energy shaping problem for these systems. Using the geometric approach of this thesis, some new open problems in energy shaping are formulated. In particular, we give ideas for relating the kinetic energy shaping problem to a problem on holonomy groups. Moreover, we suggest that the so-called Fakras lemma might be used for investigating the stabilization condition of energy shaping. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2009-09-02 12:12:55.051

This dissertation deals with smooth feedback stabilization of control-affine systems via Interconnection and Damping Assignment - Passivity-Based Control (IDA-PBC). The IDA-PBC methodology is a feedback control design technique that aims to establish or manipulate a port-Hamiltonian structure of the closed-loop system. For a mechanical control system, a port-Hamiltonian system is a natural description of the dynamics, and several effective controller designs have been presented for this class of systems. In other fields of engineering, the development of such controller design is an active area of research. In particular, applications of IDA-PBC techniques prove to be difficult in practice for process control applications where the concept of energy is usually ill-defined. This thesis seeks to extend the application of the IDA-PBC methodology beyond mechanical control systems. This is achieved by following three directions of research. First, we establish conditions under which a port-Hamiltonian system can be written as a feedback interconnection of two port-Hamiltonian system. We identify such an interconnection structure for linear control systems based on their intrinsic properties. Second, as observed in application of IDA-PBC to non-mechanical systems, several additional assumptions on the structure of the desired port-Hamiltonian system can effectively reduce the complexity of the matching problem. We establish a unified approach that considers these additional assumptions. Third, we connect the matching problem to the classical feedback equivalence approach. We show that feedback equivalence between control-affine systems can be employed to construct some feasible interconnection and damping structures. / Thesis (Ph.D, Chemical Engineering) -- Queen's University, 2011-01-31 12:59:56.828

No description available.

GE-model and equations of state are used to describe and predict phase equilibria. Current models have varying capabilities and some display selectivity for certain special mixtures. While many models are superior to others in their performance, all models share a common deficiency, the inability to simultaneously describe vapour-liquid (VLE) and liquid-liquid equilibria (LLE). Current models require separate parameters to describe the two equilibria. This formed the motivation for a non-linear transformation which was formulated by Rarey (2005). The transformation was applied to the concentration space. The clear advantage of such a transformation was that it could be easily applied to any model. The flexibility of the model was drastically increased. The effects were investigated on the local composition models, in particular the UNIQUAC model resulting in the FlexQUAC model. The model was used to regress a host of VLE and LLE data sets contained in the Dortmund Data Bank (DDB). The transformation had the desired effect on the flexibility of the model and the model was now able to describe VLE and LLE. However a symmetric transformation applied to the concentration space might not be effective in the description of systems exhibiting large difference in molecular size. This is a clear disadvantage of the proposed FlexQUAC model. In order to allow the model to cater to asymmetric systems, the transformation is now applied to the surface fraction of the residual contribution of the UNIQUAC model. The Guggenheim-Staverman expression in the combinatorial part was not transformed. Both the original combinatorial term and the more suitable modification of Weidlich and Gmehling (1987) were used. The newly formed model was called the FlexQUAC-Q model. The development of the FlexQUAC-Q model, derivation of activity coefficient expressions, model implementation and its performance analysis form the basis for this research study. The activity coefficient of the new model had to be re-derived due to the application of the transformation to the residual contribution of the UNIQUAC equation. The computation of the activity coefficient was programmed in FORTRAN and integrated into the regression tool (RECVAL) of the Dortmund Data Bank (DDB). The RECVAL tool was used to regress data sets contained in the DDB. Results obtained were comparable to those obtained using the GEQUAC model. The regression was also performed in EXCEL for the three models (UNIQUAC, FlexQUAC, FlexQUAC-Q). The regression in EXCEL was more rigorous and was used for the comparison of the objective functions and to obtain a set of unique model parameters for each data set. The performance of the FlexQUAC-Q model was assessed utilizing the same data sets used to analyse the performance of the FlexQUAC model. The model's performance was assessed in the regression of 4741 binary VLE data sets, 13 ternary VLE data sets and carefully select ternary LLE cases. The minor mean relative reduction of about 3% of the objective function using FlexQUAC-Q compared to FlexQUAC was observed compared to a reduction by about 53% relative to the UNIQUAC-results. It was necessary to illustrate that the new model does not degenerate the model's existing capabilities (e.g. ability to predict multi-component mixtures from binary data) and that the model performs as well as or superior to the UNIQUAC model. FlexQUAC-Q performed similarly to FlexQUAC. However the improvement in the qualitative description of data sets exhibiting asymmetry is apparent. Herein lies the justification of such a modification and this illustrates the preference of such a model when asymmetric systems are being considered. In addition, the FLEXQUAC-Q model can be adapted to be implemented into a group contribution method, a distinct advantage over the previous model FlexQUAC. The equations for the application of a non-linear transformation to a functional group activity coefficient model, UNIFAC are also explored in this study. The resulting model is referred to as FlexFaC. / Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2007.

This thesis presents the design, analysis, and numerical and experimental evaluation of nonlinear controllers for co-operation among several hydraulic robots operating in the presence of significant system uncertainties, non-linearities and friction. The designed controllers allow hydraulically driven manipulators to (i) co-operatively handle a rigid object (payload) following a given trajectory, (ii) share the payload and (iii) maintain an acceptable internal force on the object. A general description of the kinematic and dynamic relations for a hydraulically actuated multi-manipulator system is presented first. The entire mathematical model incorporates object dynamics, robot dynamics, hydraulic actuator functions and friction dynamics. For the purpose of simulations, a detailed numerical simulation program of such a system is also developed, in which two three-link planar robot manipulators resembling the Magnum hydraulic manipulators manufactured by ISE, interact with each other through manipulating a common object. The regulating control problem is studied next, in which the desired position of the object and the corresponding desired link displacement change step-wise. Initially, a controller is designed based on a backstepping technique, assuming that full knowledge of the dynamics and kinematics of the system is available. The assumption is then relaxed and the control system is analyzed. Based on the analysis, the controller is then modified to account for the uncertainty of the payload, robot dynamic parameters and hydraulic functions. Next, the regulating controller is extended to a tracking controller, which allows the object to follow a given trajectory and is robust against parameter uncertainties. Additionally, an observer is added to the controller to avoid the need of acceleration feedback. To investigate the effect of friction force, the above controllers are examined by introducing the most recent and complete LuGre friction model into the system dynamics. The tracking controller is then redesigned to compensate the effect of friction. Observers are designed to observe the immeasurable friction states. Based on the observed friction states and estimated friction parameters, an appropriate friction compensation scheme is designed which does not directly use velocity in order to avoid the need of acceleration feedback by the controller. Finally, the problem of “explosion of terms” coming from the backstepping method is solved by using the concept of dynamic surface control in which a low pass filter is integrated to avoid model differentiation. Simulations are carried out for analysis of the control system and verification of the developed controllers. Experimental examinations are performed on an available hydraulic system consisting of two single-axis hydraulic actuators.

No description available.

No description available.

Loudspeakers were invented over 150 years ago, but the loudspeakers used todayare still based on the same ideas. Traditionally, good sound quality has been obtainedby using expensive materials in the loudspeakers and by allowing themto be big. However, nowadays loudspeakers are wanted in applications such asmobile phones and tablets where size and weight are very limited and there is aconstant desire to decrease production costs. Special small loudspeakers, knownas micro loudspeakers, have been developed for this purpose but due to the severerestrictions in size and manufacturing costs, the sound quality in the microloudspeakers is relatively poor. One problem is that the nonlinearities of thesystem, present in any loudspeaker, become more evident in the case of microloudspeakers and cause noticeable distortion of the sound.This master’s thesis has been performed in cooperation with Opalum (formerlyActiwave), a company specializing in using digital signal processing to improvethe sound in loudspeakers with poor acoustic properties. The objective of thethesis is to investigate ways to increase the sound quality in micro loudspeakersby using nonlinear control. Focus has been on frequencies below the resonancefrequency since the distortion is more noticeable at low frequencies. First, a nonlinearmodel of the micro loudspeaker has been obtained using system identificationstrategies. The model describes the relationship between the voltage overthe voice-coil and the diaphragm displacement. Subsequently, input-output linearisationhas been used to design a controller for the system and the effect onthe distortion has been investigated through experiments. Two different modelstructures have been tested, a physical model based on the Thiele-Small modeland a black-box model with a Hammerstein-Wiener structure. In both cases, thenonlinearities were modelled as polynomials. The controller was then extendedwith an updating algorithm, making it adaptive.The efficiency of the controllers has been proved by experiments, where distortionwas decreased by up to 60 % compared to the case without control. The effectwas largest for low frequencies, around one third of the resonance frequency,but improvements were noted up to about two thirds of the resonance frequency,depending on the loudspeaker unit. The approach using a physical model andthat using a black-box model have shown similar results. / Högtalaren uppfanns för över 150 år sedan men de högtalare som används idagbygger till stora delar på samma teknik. Högkvalitativt ljud har traditionellt uppnåttsgenom att ge högtalaren goda akustiska egenskaper genom att tillåta den attvara stor och tillverkad av dyra material. Utmaningen idag ligger i att högtalarefinns inbyggda i exempelvis mobiltelefoner, vilket innebär att de behöver görassmå, lätta och billiga att producera. För att möta dessa krav har kompromisserkrävts vilket gör att dessa små högtalare, kallade mikrohögtalare, har sämre ljudkvalitet.Ett problem är att de olinjäriteter som finns i alla högtalare blir extraframträdande i små högtalare vilket leder till distorsion och övertoner i ljudsignalen.Detta examensarbete är gjort i samarbete med Opalum (tidigare Actiwave), vilketär ett företag som specialiserar sig på att med hjälp av digital signalbehandlingförbättra ljudkvaliteten för högtalare med akustiskt dåliga egenskaper. Syftetmed examensarbetet har varit att minska distorsionen i en mikrohögtalaremed hjälp av olinjär reglering. Fokus har legat på den lägre delen av frekvensbandet,under resonansfrekvensen, eftersom det är där distorsionen är mest märkbar.Först har en olinjär modell av högtalaren tagits fram genom systemidentifiering.Modellen förklarar sambandet mellan spänningen över högtalarens talspole ochmembranets utslag. I ett nästa steg har en regulator designats utifrån modellenoch regulatorns effekt på distorsionen har utvärderats genom experiment. Två olikamodellstrukturer har undersökts, dels en fysikalisk modell baserad på Thiele-Smallmodellen och dels en svartlådemodell med Hammerstein-Wienerstruktur.I båda fallen har olinjäriteterna modellerats som polynom. Regulatorn har sedanutökats med en uppdateringsalgoritm som gör den adaptiv.Experiment har visat att regleringen bidrog till att minska distorsionen med upptill 60 % jämfört med då systemet kördes utan reglering. Effekten har varit störstför låga frekvenser, kring en tredjedel av resonsnsfrekvensen, men förbättringarhar kunnat ses upp till frekvenser kring två tredjedelar av resonansfrekvensen.Både metoden med en fysikalisk modellstruktur och med en svartlådestrukturhar visat likartade resultat.

This thesis presents the design, analysis, and numerical and experimental evaluation of nonlinear controllers for co-operation among several hydraulic robots operating in the presence of significant system uncertainties, non-linearities and friction. The designed controllers allow hydraulically driven manipulators to (i) co-operatively handle a rigid object (payload) following a given trajectory, (ii) share the payload and (iii) maintain an acceptable internal force on the object. A general description of the kinematic and dynamic relations for a hydraulically actuated multi-manipulator system is presented first. The entire mathematical model incorporates object dynamics, robot dynamics, hydraulic actuator functions and friction dynamics. For the purpose of simulations, a detailed numerical simulation program of such a system is also developed, in which two three-link planar robot manipulators resembling the Magnum hydraulic manipulators manufactured by ISE, interact with each other through manipulating a common object. The regulating control problem is studied next, in which the desired position of the object and the corresponding desired link displacement change step-wise. Initially, a controller is designed based on a backstepping technique, assuming that full knowledge of the dynamics and kinematics of the system is available. The assumption is then relaxed and the control system is analyzed. Based on the analysis, the controller is then modified to account for the uncertainty of the payload, robot dynamic parameters and hydraulic functions. Next, the regulating controller is extended to a tracking controller, which allows the object to follow a given trajectory and is robust against parameter uncertainties. Additionally, an observer is added to the controller to avoid the need of acceleration feedback. To investigate the effect of friction force, the above controllers are examined by introducing the most recent and complete LuGre friction model into the system dynamics. The tracking controller is then redesigned to compensate the effect of friction. Observers are designed to observe the immeasurable friction states. Based on the observed friction states and estimated friction parameters, an appropriate friction compensation scheme is designed which does not directly use velocity in order to avoid the need of acceleration feedback by the controller. Finally, the problem of “explosion of terms” coming from the backstepping method is solved by using the concept of dynamic surface control in which a low pass filter is integrated to avoid model differentiation. Simulations are carried out for analysis of the control system and verification of the developed controllers. Experimental examinations are performed on an available hydraulic system consisting of two single-axis hydraulic actuators.

Thesis (M.S.)--Ohio University, March, 1999. / Title from PDF t.p.