The existence of backlash in mechanical systems provides significant challenges when attempting to control these systems to a high degree of precision. The imperfect meshing of gear or belt teeth deteriorates the performance of position controllers and tracking of small commands, producing unacceptable steady-state offsets, increased rise and settling times. Agile spacecraft often use control moment gyroscopes (CMGs) equipped with gear trains to efficiently provide torque for the fine attitude adjustments used in docking and precision stabilization maneuvers. A theoretical examination and a practical model is developed to study the effectiveness of both proportional-integral (PI) and model referencing adaptive controllers (MRAC) in overcoming the non-linearity introduced by gear lash. A Lyapunov analysis of the system’s equations of motion provides knowledge of its convergence, the tracking of ideal trajectories, and the rejections of disturbances. The objective is to create an adaptive control law that rejects the non-linearity and maintains acceptable performance with small torque commands. This control law is then validated in Simulink using a discontinuous backlash model.
","abstract_html":"<p>The existence of backlash in mechanical systems provides significant challenges when attempting to control these systems to a high degree of precision. The imperfect meshing of gear or belt teeth deteriorates the performance of position controllers and tracking of small commands, producing unacceptable steady-state offsets, increased rise and settling times. Agile spacecraft often use control moment gyroscopes (CMGs) equipped with gear trains to efficiently provide torque for the fine attitude adjustments used in docking and precision stabilization maneuvers. A theoretical examination and a practical model is developed to study the effectiveness of both proportional-integral (PI) and model referencing adaptive controllers (MRAC) in overcoming the non-linearity introduced by gear lash. A Lyapunov analysis of the system’s equations of motion provides knowledge of its convergence, the tracking of ideal trajectories, and the rejections of disturbances. The objective is to create an adaptive control law that rejects the non-linearity and maintains acceptable performance with small torque commands. This control law is then validated in Simulink using a discontinuous backlash model.</p>","abstract_has_math":false,"creators":["Bourke, Justin G."],"institution":null,"degree_name":"Master of Science in Aerospace Engineering","degree_level":"Thesis - Open Access","degree_discipline":"Aerospace Engineering","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-05-01T07:00:00Z","date_published":"2019-05-01T07:00:00Z","updated_at":"2026-07-27T19:25:29Z","subjects":["adaptive control","gyroscopes","backlash","Aerospace Engineering","Navigation, Guidance, Control and Dynamics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://commons.erau.edu/edt/443","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Bourke, Justin G."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Aerospace Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Aerospace Engineering"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["adaptive control","gyroscopes","backlash","Aerospace Engineering","Navigation, Guidance, Control and Dynamics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://commons.erau.edu/edt/443"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The existence of backlash in mechanical systems provides significant challenges when attempting to control these systems to a high degree of precision. The imperfect meshing of gear or belt teeth deteriorates the performance of position controllers and tracking of small commands, producing unacceptable steady-state offsets, increased rise and settling times. Agile spacecraft often use control moment gyroscopes (CMGs) equipped with gear trains to efficiently provide torque for the fine attitude adjustments used in docking and precision stabilization maneuvers. A theoretical examination and a practical model is developed to study the effectiveness of both proportional-integral (PI) and model referencing adaptive controllers (MRAC) in overcoming the non-linearity introduced by gear lash. A Lyapunov analysis of the system’s equations of motion provides knowledge of its convergence, the tracking of ideal trajectories, and the rejections of disturbances. The objective is to create an adaptive control law that rejects the non-linearity and maintains acceptable performance with small torque commands. This control law is then validated in Simulink using a discontinuous backlash model.
"]},{"key":"dc:title","label":"Title","values":["Adaptive Commanding of Control Moment Gyroscopes with Backlash"]}]}],"canonical_facts":{"dc:creator":["Bourke, Justin G."],"dc:description.abstract":["The existence of backlash in mechanical systems provides significant challenges when attempting to control these systems to a high degree of precision. The imperfect meshing of gear or belt teeth deteriorates the performance of position controllers and tracking of small commands, producing unacceptable steady-state offsets, increased rise and settling times. Agile spacecraft often use control moment gyroscopes (CMGs) equipped with gear trains to efficiently provide torque for the fine attitude adjustments used in docking and precision stabilization maneuvers. A theoretical examination and a practical model is developed to study the effectiveness of both proportional-integral (PI) and model referencing adaptive controllers (MRAC) in overcoming the non-linearity introduced by gear lash. A Lyapunov analysis of the system’s equations of motion provides knowledge of its convergence, the tracking of ideal trajectories, and the rejections of disturbances. The objective is to create an adaptive control law that rejects the non-linearity and maintains acceptable performance with small torque commands. This control law is then validated in Simulink using a discontinuous backlash model.
"],"dc:identifier":["https://commons.erau.edu/edt/443"],"dc:subject":["adaptive control","gyroscopes","backlash","Aerospace Engineering","Navigation, Guidance, Control and Dynamics"],"dc:title":["Adaptive Commanding of Control Moment Gyroscopes with Backlash"],"thesis:degree_discipline":["Aerospace Engineering"],"thesis:degree_level":["Thesis - Open Access"],"thesis:degree_name":["Master of Science in Aerospace Engineering"]},"updated_at":"2026-07-27T19:25:29Z"}