{"id":40,"date":"2012-03-06T09:16:00","date_gmt":"2012-03-06T15:16:00","guid":{"rendered":"http:\/\/charles-oneill.com\/blog\/?p=40"},"modified":"2014-07-31T11:17:14","modified_gmt":"2014-07-31T16:17:14","slug":"optimal-control-project-ball-and-beam-optimal-control","status":"publish","type":"post","link":"https:\/\/charles-oneill.com\/blog\/optimal-control-project-ball-and-beam-optimal-control\/","title":{"rendered":"Optimal Control Project: Ball and Beam Optimal Control"},"content":{"rendered":"<div style=\"text-align: center;\">Optimal Control &nbsp;5413 Project:<\/div>\n<div style=\"text-align: center;\">Ball and Beam Optimal Control<\/div>\n<div style=\"text-align: center;\">Charles O\u2019Neill<\/div>\n<div style=\"text-align: center;\">7 May 2004<\/div>\n<p>This design project simulates and controls a beam and ball system. A ball rolls on a pivoting beam. The beam is connected through DC motor through a linkage arm. The objective is to create an output feedback control system. The project simulates the system using&nbsp;Matlab and Simulink.<\/p>\n<table align=\"center\" cellpadding=\"0\" cellspacing=\"0\" style=\"margin-left: auto; margin-right: auto; text-align: center;\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><a href=\"http:\/\/charles-oneill.com\/blog\/wp-content\/uploads\/2012\/03\/beamangle.png\" style=\"margin-left: auto; margin-right: auto;\"><img loading=\"lazy\" decoding=\"async\" border=\"0\" height=\"276\" src=\"http:\/\/charles-oneill.com\/blog\/wp-content\/uploads\/2012\/03\/beamangle-300x259.png\" width=\"320\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">Ball and beam geometry<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The physical system consists of coupled linkages and a free-to-roll ball. The linkage motion is nonlinearly coupled to the gear angle. The beam has a length of 1 meter. The gear arm has a radius of 0.03 meters, and the linking arm has a length of 0.2 meters. The ball is steel with a radius of 15 millimeters. The system has 2 energy storage components: beam inertia and ball inertia. System control is allowed through a voltage input into the DC motor, which provides a torque applied at the gear arm. The gear arm motion is harmonic; the gear can go past topdead-center in the straight up and down positions.<\/p>\n<p>The document is available&nbsp;<a href=\"http:\/\/charles-oneill.com\/projects\/ballbeam.pdf\">here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Optimal Control &nbsp;5413 Project: Ball and Beam Optimal Control Charles O\u2019Neill 7 May 2004 This design project simulates and controls a beam and ball system. A ball rolls on a pivoting beam. The beam is connected through DC motor through a linkage arm. The objective is to create an output feedback control system. The project [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":67,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/posts\/40"}],"collection":[{"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/comments?post=40"}],"version-history":[{"count":0,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/posts\/40\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/media\/67"}],"wp:attachment":[{"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/media?parent=40"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/categories?post=40"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/tags?post=40"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}