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Brigham Young University

1. Hakala, Tim. Settling-Time Improvements in Positioning Machines Subject to Nonlinear Friction Using Adaptive Impulse Control.

Degree: PhD, 2006, Brigham Young University

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.

Subjects/Keywords: 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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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Hakala, T. (2006). Settling-Time Improvements in Positioning Machines Subject to Nonlinear Friction Using Adaptive Impulse Control. (Doctoral Dissertation). Brigham Young University. Retrieved from https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=2060&context=etd

Chicago Manual of Style (16th Edition):

Hakala, Tim. “Settling-Time Improvements in Positioning Machines Subject to Nonlinear Friction Using Adaptive Impulse Control.” 2006. Doctoral Dissertation, Brigham Young University. Accessed October 28, 2020. https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=2060&context=etd.

MLA Handbook (7th Edition):

Hakala, Tim. “Settling-Time Improvements in Positioning Machines Subject to Nonlinear Friction Using Adaptive Impulse Control.” 2006. Web. 28 Oct 2020.

Vancouver:

Hakala T. Settling-Time Improvements in Positioning Machines Subject to Nonlinear Friction Using Adaptive Impulse Control. [Internet] [Doctoral dissertation]. Brigham Young University; 2006. [cited 2020 Oct 28]. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=2060&context=etd.

Council of Science Editors:

Hakala T. Settling-Time Improvements in Positioning Machines Subject to Nonlinear Friction Using Adaptive Impulse Control. [Doctoral Dissertation]. Brigham Young University; 2006. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=2060&context=etd

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