The performance of manufacturing machines of all sorts depends upon precise control of the position of some sort of end-effector. Mechanical friction has forever been the thorn in the side of the developers of such machines. A 1988 publication by researchers at the University of California at Berkeley describes a remarkably effective algorithm for point-to-point control of the position of the end-effector of a rigid-body plant that is subject to mechanical friction, including stiction. This Pulse Width Control (PWC) algorithm is applied only when the end-effector is close enough to its desired position that stiction forces come into play. The algorithm applies a series of fixed-height rectangular force pulses in a feedback fashion to move the end-effector to its desired position. For point-to-point position control, the algorithm guarantees limit-cycle-free operation and zero steady-state error, even when the plant parameters, including the stiction and Coulomb friction levels, are not known exactly. This project's Principle Investigators have investigated PWC applied to flexible-body plants. They have shown that when the Berkeley PWC algorithm is applied to a flexible-body plant, the result can be a position-error limit cycle. They have furthermore shown that this limit cycle can be avoided, and zero steady-state position error can be achieved, by use of a piecewise-linear-gain PWC law. In this project a methodology for designing adaptive piecewise-linear-gain PWC laws will be developed. This methology will be applicable to the design of end-effector position control laws for industrial robots and machine tools in bona fide industrial settings. Intellectual Merit: The idea of PWC with piecewise-linear-gain PWC laws was pioneered by this project's Principal Investigators. The adaptive piecewise-linear-gain PWC law design methodology that will be developed in this project will constitute a unique and significant contribution to the control systems design community. The significance of this contribution will grow as the number of applications of the methodology to the design of end-effector position control laws for industrial robots and machine tools in bona fide industrial settings grows. Broader Impacts: In our society today, the expectation is unmistakably that, as time marches on, manufacturing machines will be capable of manufacturing parts to ever more exacting standards. The only hope for meeting this expectation is for manufacturing machines to take advantage of the rate of innovation that is evident today in two areas, namely instrumentation and computing. This project will ultimately result in dramatic demonstrations of what can be accomplished when the latest in instrumentation, control system design methodology, and computing technology are simultaneously focused on the task of dramatically improving the accuracy of end-effector position control in industrial robots and machine tools. The broader impacts of this project will be significantly enhanced by the fact that it will be performed by a team of researchers from a predominantly undergraduate institution (Bucknell University) and Research I institution (University of Washington).
