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1	Scaling a Prismatic Revolute Joint (Pr) Manipulator Using Similitude and Buckingham Pi Techniques Gilbert, Gregory S. Jr. 01 April 1998 (has links) This thesis presents scaling methods for sizing a prototype micro prismatic revolute (PR) manipulator actuated by permanent magnet (PM) direct current (d.c.) gearmotors. Dimensional analysis was the principle tool used in this investigation, and addressed the problems of scaling a trajectory planner, control law, and gearmotors that exhibit internal nonlinear friction. Similitude methods were used to develop a scaleable two degree-of-freedom trajectory planner from a third order polynomial. Scaling laws were developed from Buckingham's Pi theorem to facilitate the selection process of gearmotors. Nondimensional, nonlinear, differential equations were developed to describe viscous, Coulomb and static friction in comparative PM d.c. motors. From the insights gained through dimensional analysis, a scaleable controller based on the computed torque method was developed and implemented with a cubic trajectory planner. Model and prototype PR manipulator systems were simulated using a hybrid Matlab/Simulink simulation scheme. Experimental systems were constructed with dissimilar model and prototype motors. Control was provided by an AT class PC equipped with 12-bit A/D, D/A cards operating at a sample rate of 100 Hz. The control algorithm was written in Borland 3.1 C for DOS. Results from the experimental testing showed excellent agreement between the test and simulated data and verified the viability of the scaling laws. The techniques presented in this thesis are expected to be applicable to any application that involves scaling PM d.c. micro gearmotors that have significant internal friction terms. These simple, practical tools should be especially beneficial to designers of micro robotic systems. / Master of Science Dimensional Analysis Buckingham Pi Theorem Similitude Scaling Brushed DC Permanent Magnet Motors Coulomb Viscous Static Nonlinear Friction Computed Torque Control
2	A micromechanical model for the nonlinearity of microcracks in random distributions and their effect on higher harmonic Rayleigh wave generation Oberhardt, Tobias 07 January 2016 (has links) This research investigates the modeling of randomly distributed surface-breaking microcracks and their effects on higher harmonic generation in Rayleigh surface waves. The modeling is based on micromechanical considerations of rough surface contact. The nonlinear behavior of a single microcrack is described by a hyperelastic effective stress-strain relationship. Finite element simulations of nonlinear wave propagation in a solid with distributed microcracks are performed. The evolution of fundamental and second harmonic amplitudes along the propagation distance is studied and the acoustic nonlinearity parameter is calculated. The results show that the nonlinearity parameter increases with crack density and root mean square roughness of the crack faces. While, for a dilute concentration of microcracks, the increase in acoustic nonlinearity is proportional to the crack density, this is not valid for higher crack densities, as the microcracks start to interact. Finally, it is shown that odd higher harmonic generation in Rayleigh surface waves due to sliding crack faces introduces a friction nonlinearity. Surface-breaking microcracks Acoustic nonlinearity parameter Contact mechanics Hyperelasticity model Nonlinear Rayleigh waves Nonlinear friction mechanism Stick-slip mechanism Finite element simulation Contact acoustic nonlinearity (CAN)
3	Settling-Time Improvements in Positioning Machines Subject to Nonlinear Friction Using Adaptive Impulse Control Hakala, Tim 31 January 2006 (has links) (PDF) A new method of adaptive impulse control is developed to precisely and quickly control the position of machine components subject to friction. Friction dominates the forces affecting fine positioning dynamics. Friction can depend on payload, velocity, step size, path, initial position, temperature, and other variables. Control problems such as steady-state error and limit cycles often arise when applying conventional control techniques to the position control problem. Studies in the last few decades have shown that impulsive control can produce repeatable displacements as small as ten nanometers without limit cycles or steady-state error in machines subject to dry sliding friction. These displacements are achieved through the application of short duration, high intensity pulses. The relationship between pulse duration and displacement is seldom a simple function. The most dependable practical methods for control are self-tuning; they learn from online experience by adapting an internal control parameter until precise position control is achieved. To date, the best known adaptive pulse control methods adapt a single control parameter. While effective, the single parameter methods suffer from sub-optimal settling times and poor parameter convergence. To improve performance while maintaining the capacity for ultimate precision, a new control method referred to as Adaptive Impulse Control (AIC) has been developed. To better fit the nonlinear relationship between pulses and displacements, AIC adaptively tunes a set of parameters. Each parameter affects a different range of displacements. Online updates depend on the residual control error following each pulse, an estimate of pulse sensitivity, and a learning gain. After an update is calculated, it is distributed among the parameters that were used to calculate the most recent pulse. As the stored relationship converges to the actual relationship of the machine, pulses become more accurate and fewer pulses are needed to reach each desired destination. When fewer pulses are needed, settling time improves and efficiency increases. AIC is experimentally compared to conventional PID control and other adaptive pulse control methods on a rotary system with a position measurement resolution of 16000 encoder counts per revolution of the load wheel. The friction in the test system is nonlinear and irregular with a position dependent break-away torque that varies by a factor of more than 1.8 to 1. AIC is shown to improve settling times by as much as a factor of two when compared to other adaptive pulse control methods while maintaining precise control tolerances. control position adaptive impulsive settling-time nonlinear friction pulses displacements precise tolerances log-spaced update distributed learning Coulomb Stribeck Tomizuka Yang AIC PID MRAC STR RTAI Linux FreeBSD kernel modules microcontroller convergence practical self-tuning methods techniques limit-cycles steady-state error zero stable stability bound envelope partitioned scheme lookup-table multi-point adaptation repeatable mean servo motor exponential square-law rise-time real-time log-log interpolation pro-forma curve-fit sensitivity compliance variable static dynamic response torque acceleration velocity optical encoder parameters evolution fixed-law enhanced split weighting initialization trajectory layered processes Mechanical Engineering

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