| dc.description.abstract | For centuries researchers have been pushing the boundaries of their respective technical domains, but it is only a few decades ago that research started taking its dig on system design theory. A system design theory encapsulates all individual components design and their simultaneous optimization, i.e., it provides a complete framework to design the structure. The approach behind this research is to make small steps in structure design, dynamic models, information architecture, and control design with some free parameters and then finally optimize those free parameters in a wholesome design approach to meet some specified performance. The author uses tensegrity design models to integrate structure and control design due to the various advantages mentioned further. This dissertation first makes three contributions to the study of tensegrity structures and then provides a system design theory to integrate structure and control design using the tensegrity paradigm.
The first part of the dissertation provides a detailed study of the minimum mass tensegrity structures under both local and global failures. The proposed research provides different approaches to design a structure based on optimizing mass, stiffness, or mechanical energy stored in a tensegrity structure. The second part of this research work provides accurate dynamic models of axially loaded members forming any general tensegrity structure. The dynamics models for novel gyroscopic tensegrity systems are also developed, which adds an extra degree of freedom to the control of the structure. A Matlab based tensegrity dynamics simulator is another outcome of this research. The third section of the dissertation discusses a model-based approach to control the shape of any general tensegrity structure. A Linear Matrix Inequality (LMI) framework is further used to calculate control gains to bound errors for five different types of control problems for given disturbance profile.
The last fragment of the dissertation starts with the derivation of the minimal-order linear model by linearizing the system about an equilibrium point and removing the modes which causes the length of the bars to change. The chapter further provides a methodology to integrate structure and control design where some parameter of the structure in the linearized dynamic model, control law and the information about the system architecture (actuator/sensor) is simultaneously optimized to achieve some desired performance for a covariance control problem. The force density in the strings (prestress) is used as the optimization variable for the structure, which appears affinely in the system matrices of the linearized tensegrity dynamics. The sub-optimal solution of this non-convex system design problem is found by iterating over an approximated convex problem through the use of a convexifying potential function, which enables convergence to a local minimum. | en |
