Realization-Preserving Simplification and Reduction of Dynamic System Models at the Graph Level.

The literature deems a model “proper”, if it is only as complex as necessary to fulfill its purpose. Ensuring the properness of models is critical to efficient and successful design, analysis, and control of engineering systems, but it requires much time and expertise as systems become more complex. Thus, there is a growing need for proper-modeling tools for complex systems. Existing tools are inadequate in terms of applicability to nonlinear systems at the graph level, accounting for the scenarios of interest explicitly, preserving the realization, and considering the model structure. This dissertation is aimed to address this gap within the scope of lumped parameter models of nonlinear energetic deterministic systems. Building on the “activity” concept from the literature, a structural simplification algorithm is developed. This algorithm removes from the model structure those elements that do not contribute to the energetic behavior of the system in the considered scenario, thereby simplifying the model without affecting its predictive ability for that scenario. To complement the simplification algorithm, a coordinate frame reorientation algorithm is developed to better orient body-fixed coordinate frames in multibody systems to render the model more conducive to simplification. This Karhunen-Loève-expansion-based algorithm detects the existence of and finds the transformation into coordinate frames preferred for simplification. To reduce models further, a new metric is proposed to evaluate the relative contributions of various system parts to the system behavior. This metric uniquely considers the correlations between the energy-flow patterns throughout the system, and allows for the assessment of system components and their interactions. Based on this metric, a reduction algorithm is proposed. This algorithm reduces not only the model order, but also the model structure for the scenario of interest. The proper modeling of the HMMWV is presented as a case study. The multibody dynamics of the HMMWV is modeled through a modular approach first. This “full” model is then simplified and reduced for three different scenarios: a two-double-lane-change maneuver, a shaker table setup, and driving straight. Thus, three different proper models of the HMMWV are obtained for the respective scenarios, illustrating the benefits of the proposed algorithms.Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/57603/2/tersal_1.pd

A mathematical model for incorporating biofeedback into human postural control

<p>Abstract</p> <p>Background</p> <p>Biofeedback of body motion can serve as a balance aid and rehabilitation tool. To date, mathematical models considering the integration of biofeedback into postural control have represented this integration as a sensory addition and limited their application to a single degree-of-freedom representation of the body. This study has two objectives: 1) to develop a scalable method for incorporating biofeedback into postural control that is independent of the model’s degrees of freedom, how it handles sensory integration, and the modeling of its postural controller; and 2) to validate this new model using multidirectional perturbation experimental results.</p> <p>Methods</p> <p>Biofeedback was modeled as an additional torque to the postural controller torque. For validation, this biofeedback modeling approach was applied to a vibrotactile biofeedback device and incorporated into a two-link multibody model with full-state-feedback control that represents the dynamics of bipedal stance. Average response trajectories of body sway and center of pressure (COP) to multidirectional surface perturbations of subjects with vestibular deficits were used for model parameterization and validation in multiple perturbation directions and for multiple display resolutions. The quality of fit was quantified using average error and cross-correlation values.</p> <p>Results</p> <p>The mean of the average errors across all tactor configurations and perturbations was 0.24° for body sway and 0.39 cm for COP. The mean of the cross-correlation value was 0.97 for both body sway and COP.</p> <p>Conclusions</p> <p>The biofeedback model developed in this study is capable of capturing experimental response trajectory shapes with low average errors and high cross-correlation values in both the anterior-posterior and medial-lateral directions for all perturbation directions and spatial resolution display configurations considered. The results validate that biofeedback can be modeled as an additional torque to the postural controller without a need for sensory reweighting. This novel approach is scalable and applicable to a wide range of movement conditions within the fields of balance and balance rehabilitation. The model confirms experimental results that increased display resolution does not necessarily lead to reduced body sway. To our knowledge, this is the first theoretical confirmation that a spatial display resolution of 180° can be as effective as a spatial resolution of 22.5°.</p

Time delay systems: theory, numerics, applications, and experiments

This volume collects contributions related to selected presentations from the 12th IFAC Workshop on Time Delay Systems, Ann Arbor, June 28-30, 2015. The included papers present novel techniques and new results of delayed dynamical systems. The topical spectrum covers control theory, numerical analysis, engineering and biological applications as well as experiments and case studies. The target audience primarily comprises research experts in the field of time delay systems, but the book may also be beneficial for graduate students alike.