Thesis (M.S.)--University of Wisconsin--Madison, 1965. / eContent provider-neutral record in process. Description based on print version record. Bibliography: l. 79-82.

Systematic numerical and graphical techniques have been developed for analysing,and to some extent synthesizing,linear or linearized multiple input-output (multivariable) feedback control systems. A class of multivariable systems is studied which can be considered to consist of two parts. The first part of the system consists of the system configuration and certain elements characteristic to the system, i.e. the interaction or the system dynamics, which are considered to be unalterable. The other part of the system consists of elements which the designer may modify to ensure a satisfactory system performance. These have been called the variable elements, consisting usually of power amplifying devices and compensating networks. The variable elements are represented by one common variable element. This allows the unalterable part of the system dynamics to be represented independently of the variable elements. This method is suitable for automatic high speed computing and plotting facilities, or it may serve as a guide while simulating multivariable systems on analog computers. Sets of curves can be computed which represent the critical behaviour of the unalterable part of the system, for example its instability and null response, with respect to the elements whose influence on the system is being studied (the variable elements). Thus, when the stability of the system is being studied, the corresponding critical curves behave as the -1 point in the study of single-variable control systems. Hence the concepts developed for single-variable systems, such as the Nyquist and Nichols plots and root-locus methods, may be extended to the study of multivariable systems. The curves representing system instability are the eigenvalues of the loop-matrix in the system, and those representing null response have been called "eigenzeros". Any transfer function in the system may then be represented graphically in terms of the loci of the eigenvalues and the eigenzeros (which represent the unalterable elements), and the locus representing the elements whose influence on the system is being determined (the variable elements). Analogously to single-variable systems, compensation for improved stability and frequency response consists of modifying the locus of the variable elements with respect to the loci representing the fixed part of the system. Furthermore, additional compensation techniques exist which transform the entire eigenvalue spectrum, but leave the locus of the variable elements unchanged. In the synthesis of linear multivariable feedback control systems, it is often difficult to obtain stable elements, i.e. elements with only left-half s-plane poles, when the overall system response is given. For certain classes of multivariable systems,eigenvalue techniques may be used to predict the stability of the elements in certain configurations before the values for the elements have been calculated. As a special case, the stability of two-variable systems (systems with two inputs and outputs) have been formulated so that the -1 point of single-variable systems transforms to one critical locus. Numerous examples are used to illustrate the theory and its applications. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

This thesis deals with the design of simple circuits to realize the optimum second order contactor type servo. The analysis is based on the generation of a switching function so that torque reversal will occur at the point where the generated function g(t) intersects the error function e(t). The conventional treatment differs from the above method in that the required switching boundary relationship, f(ė), between e and e^° is obtained so that voltage proportional to e-f(e^°) is used as the switching signal. Using a d-c shunt motor or an induction motor, analysis and design of optimum systems based on the generated function treatment had been carried out taking into account the actual motor characteristics and relay time delay. An optimum relay servo for a 1/50 h.p. Ford induction motor was constructed on this principle and tested. The simplicity of the circuits involved makes this design highly practical. The optimization of a second order contactor servo can also be accomplished by approximating the optimum switching boundary with a simple lead network. A servo system using the same 1/50 h.p. induction motor was built according to this method. This approach results in a simpler circuit than the former; however, it has a larger dead zone and is only applicable with an a-c servo motor. A brief discussion of the possiblity of employing the generated function technique to the analysis of a 3rd order system was also made. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

<p>Assessment of left ventricular (LV) deformation is essential for clinical evaluation of LV function and cardiac images are frequently used to evaluate the LV motion and function. By combining the images with mathematical models more information may be extracted from the images. The work presented in this thesis has focused on using the finite element (FE) method to describe the LV and its deformation and combining this method with images of the heart to extract more information about the deformation.</p><p>We developed a method that estimated the LV deformation by manually tracking distinct anatomical landmarks (fiducial markers) through the cardiac cycle in 3 dimensional (3D) images of the heart. The motion of the nodal parameters of an FE mesh shaped to the geometry of the LV was fitted to the motion of the fiducial markers and thus provided a means to describe the motion. The sparsity of the fiducial markers made the fitting problem under-constrained so a parameter distribution model (PDM) of likely motions were constructed from a historical database of cases where FE meshes had been fitted to the motion of magnetic resonance (MR) tagged data. The estimated deformation from the fiducial marker fitting was filtered through the PDM and the resulting deformation corresponded well when compared to the deformation obtained from MR tagging in 13 normal subjects.</p><p>A method that decomposed the LV deformation into different deformation modes such as longitudinal shortening, wall thickening, and twisting was developed. The nodes of a subject’s LV FE mesh were displaced according to each deformation mode and the relative contribution of each mode to the total deformation measured by MR tagging was quantified by calculating a coefficient for each mode. A study that compared 13 young normal subjects with 13 older diabetes patients showed that the patients had a significantly lower degree of longitudinal shortening and wall thickening but a higher degree of longitudinal twist.</p><p>The LV deformation is influenced by cardiac disease via the material properties of the myocardium. We investigated the effects of the material parameter values on the LV deformation in a simulation study using an FE model of the LV. A description of the myocardial microstructure and a passive and active constitutive law was included in the model. The cardiac cycle was simulated from the beginning of diastasis through to the end of ejection by applying appropriate boundary conditions. The different deformation modes between end diastole and end systole were extracted and quantified for different sets of material parameters. We found that stiffer material properties particularly in the myocardial sheet direction impaired longitudinal shortening and wall thickening.</p><p>A sensitivity analysis was carried out to look at the various material parameters’ influence on LV wall strains during passive inflation. The analysis showed a high degree of coupling of the parameters in the constitutive law, which indicated an overparameterization of the law. A parameter estimation study revealed the same problem. Most of the parameters were set to constant values and only one parameter in each of the three microstructural directions were estimated during the passive inflation phase using synthetic strain data as measurements. This still gave good estimates of the stress-strain relationships in the fiber and sheet directions.</p> / Papers I and II reprinted with kind permission of Elsevier, ScienceDirect

Assessment of left ventricular (LV) deformation is essential for clinical evaluation of LV function and cardiac images are frequently used to evaluate the LV motion and function. By combining the images with mathematical models more information may be extracted from the images. The work presented in this thesis has focused on using the finite element (FE) method to describe the LV and its deformation and combining this method with images of the heart to extract more information about the deformation. We developed a method that estimated the LV deformation by manually tracking distinct anatomical landmarks (fiducial markers) through the cardiac cycle in 3 dimensional (3D) images of the heart. The motion of the nodal parameters of an FE mesh shaped to the geometry of the LV was fitted to the motion of the fiducial markers and thus provided a means to describe the motion. The sparsity of the fiducial markers made the fitting problem under-constrained so a parameter distribution model (PDM) of likely motions were constructed from a historical database of cases where FE meshes had been fitted to the motion of magnetic resonance (MR) tagged data. The estimated deformation from the fiducial marker fitting was filtered through the PDM and the resulting deformation corresponded well when compared to the deformation obtained from MR tagging in 13 normal subjects. A method that decomposed the LV deformation into different deformation modes such as longitudinal shortening, wall thickening, and twisting was developed. The nodes of a subject’s LV FE mesh were displaced according to each deformation mode and the relative contribution of each mode to the total deformation measured by MR tagging was quantified by calculating a coefficient for each mode. A study that compared 13 young normal subjects with 13 older diabetes patients showed that the patients had a significantly lower degree of longitudinal shortening and wall thickening but a higher degree of longitudinal twist. The LV deformation is influenced by cardiac disease via the material properties of the myocardium. We investigated the effects of the material parameter values on the LV deformation in a simulation study using an FE model of the LV. A description of the myocardial microstructure and a passive and active constitutive law was included in the model. The cardiac cycle was simulated from the beginning of diastasis through to the end of ejection by applying appropriate boundary conditions. The different deformation modes between end diastole and end systole were extracted and quantified for different sets of material parameters. We found that stiffer material properties particularly in the myocardial sheet direction impaired longitudinal shortening and wall thickening. A sensitivity analysis was carried out to look at the various material parameters’ influence on LV wall strains during passive inflation. The analysis showed a high degree of coupling of the parameters in the constitutive law, which indicated an overparameterization of the law. A parameter estimation study revealed the same problem. Most of the parameters were set to constant values and only one parameter in each of the three microstructural directions were estimated during the passive inflation phase using synthetic strain data as measurements. This still gave good estimates of the stress-strain relationships in the fiber and sheet directions. / Papers I and II reprinted with kind permission of Elsevier, ScienceDirect

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Thesis (M.S.)--University of Wisconsin--Madison, 1965. / eContent provider-neutral record in process. Description based on print version record. Bibliography: l. 79-81.

Thesis (M.S.)--University of Wisconsin--Madison, 1968. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (M.S.)--University of Wisconsin--Madison, 1966. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (M.S.)--University of Wisconsin--Madison, 1965. / eContent provider-neutral record in process. Description based on print version record. Bibliography: l. 59-61.