M. S. Thesis Abstract
A Design Methodology for Control of a Belt-Driven Robot using Frequency Response Analysis
Robert Chad Rutherford
This thesis begins with a discussion of frequency response methods for the analysis and design of control systems. The frequency reshaped linear quadratic (FRLQ) method is introduced, and is the primary focus of the thesis. Also introduced is the motivation behind using belt-driven robots in the poultry industry. The problem with this particular type of robot design is that time-varying friction disturbances are present, due to the nature of the belt-drive. Through the use of FRLQ control, high frequency resonances, attributable from the belt-drive design, are able to be attenuated by creating a filter which shapes the input in the performance index. The filter is then added to the plant to create an augmented system, upon which standard linear quadratic methods apply. Data is taken of the robot axis actuated by the belt-drive, and the resulting transfer function of the plant is compared to one derived by using a lumped parameter model of the system. It is shown that by choosing a simple first-order filter that penalizes high frequency inputs in the performance index, a control design is able to be developed that reduces resonance-induced vibration by fifty percent over a classical method of control, PD control, and that responds in an almost identical way to the PD control when operated in the low frequency range. The same results are applicable to mathematically similar systems, systems that exhibit resonance in a certain frequency range. The modeling, analysis, and FRLQ design of the belt-driven system form a methodology that can be presented to students in the form of a multimedia instruction program, one that teaches not only the concept of FRLQ control as it applies to this system, but also illustrates the general principles of control systems design anchored in a real world problem. This form of presentation will help to bridge the gap between theory and applications and research and instruction.