Energy-oriented Modeling And Control of Robotic Systems

This research focuses on the energy-oriented control of robotic systems using an ultracapacitor as the energy source. The primary objective is to simultaneously achieve the motion task objective and to increase energy efficiency through energy regeneration. To achieve this objective, three aims have been introduced and studied: brushless DC motors (BLDC) control by achieving optimum current in the motor, such that the motion task is achieved, and the energy consumption is minimized. A proof-ofconcept study to design a BLDC motor driver which has superiority compare to an off-the-shelf driver in terms of energy regeneration, and finally, the third aim is to develop a framework to study energy-oriented control in cooperative robots. The first aim is achieved by introducing an analytical solution which finds the optimal currents based on the desired torque generated by a virtual. Furthermore, it is shown that the well-known choice of a zero direct current component in the direct-quadrature frame is sub-optimal relative to our energy optimization objective. The second aim is achieved by introducing a novel BLDC motor driver, composed of three independent regenerative drives. To run the motor, the control law is obtained by specifying an outer-loop torque controller followed by minimization of power consumption via online constrained quadratic optimization. An experiment is conducted to assess the performance of the proposed concept against an off-the-shelf driver. It is shown that, in terms of energy regeneration and consumption, the developed driver has better performance, and a reduction of 15% energy consumption is achieved. v For the third aim, an impedance-based control scheme is introduced for cooperative manipulators grasping a rigid object. The position and orientation of the payload are to be maintained close to a desired trajectory, trading off tracking accuracy by low energy consumption and maintaining stability. To this end, an optimization problem is formulated using energy balance equations. The optimization finds the damping and stiffness gains of the impedance relation such that the energy consumption is minimized. Furthermore, L2 stability techniques are used to allow for time-varying damping and stiffness in the desired impedance. A numerical example is provided to demonstrate the results

Rationality of the spectral action for Robertson-Walker metrics and the geometry of the determinant line bundle for the noncommutative two torus

In noncommutative geometry, the geometry of a space is given via a spectral triple $(\mathcal{A,H},D)$. Geometric information, in this approach, is encoded in the spectrum of $D$ and to extract them, one should study spectral functions such as the heat trace \Tr (e^{-tD^2}), the spectral zeta function \Tr(|D|^{-s}) and the spectral action functional, \Tr f(D/\Lambda). The main focus of this thesis is on the methods and tools that can be used to extract the spectral information. Applying the pseudodifferential calculus and the heat trace techniques, in addition to computing the newer terms, we prove the rationality of the spectral action of the Robertson-Walker metrics, which was conjectured by Chamseddine and Connes. In the second part, we define the canonical trace for Connes\u27 pseudodifferential calculus on the noncommutative torus and use it to compute the curvature of the determinant line bundle for the noncommutative torus. In the last chapter, the Euler-Maclaurin summation formula is used to compute the spectral action of a Dirac operator (with torsion) on the Berger spheres $\mathbb{S}^3(T)$

Experimental characterization and crystal plasticity modeling of mechanical properties and microstructure evolution of additively manufactured Inconel 718 superalloy

In this thesis, the mechanical behavior of the additively manufactured (AM) IN718 nickel-based superalloy and their correlations with the evolution of microstructure are studied comprehensively. The effects of manufacturing parameters, build orientations, and post processing procedures, i.e. standard heat treatment and hot isostatic pressing (HIP), on various mechanical properties including monotonic compression and tension strength, low cyclic fatigue performance, high cyclic fatigue behaviour, and fatigue crack growth behavior are investigated. Due to the high temperature applications of the IN718 alloy, elevated temperature properties are examined as well. Electron Backscattered Diffraction (EBSD) technique is employed to measure the initial and deformed textures. In addition, an elasto-plastic self-consistent polycrystal plasticity model is developed to interpret the deformation behavior of the alloy in room temperature and high temperatures. The model incorporates the contributions of solid solution, precipitates shearing, and grain size and shape effects into the initial slip resistance. For activating the slip systems, the non-Schmid effects and backstress are implemented in the model. The crystal plasticity model is capable of simulating the monotonic and large-strain load reversal cycles of the material with pole figure difference (PFD) values no more than 0.2

Modeling and Control of a Smart Single-Layer Graphene Sheet

In this study, a smart single-layer graphene sheet (SLGS) is analytically modeled and its buckling is controlled using coupled polyvinylidene fluoride (PVDF) nanoplates. A voltage is applied to the PVDF nanoplate in thickness direction in order to control the critical load of the SLGS. Electric potential distribution is assumed as a combination of a half-cosine and linear variation in order to satisfy the Maxwell equation. The exact analysis is performed for the case when all four ends are simply supported and in free electrical boundary condition. The nonlocal governing equations are derived through Hamilton’s principle and energy method based on a nonlocal Mindlin plate theory. The detailed mathematical derivations are presented and numerical investigations are performed, while the emphasis is placed on investigating the effect of several parameters such as small-scale coefficient, stiffness of the internal elastic medium, graphene length, mode number, and external electric voltage on the buckling smart control of the SLGS in detail. It is explicitly shown that the imposed external voltage is an effective controlling parameter for buckling of the SLGS. Numerical results are presented to serve as benchmarks for design and smart control of nanodevices