{"id":450,"date":"2025-09-21T14:12:59","date_gmt":"2025-09-21T12:12:59","guid":{"rendered":"https:\/\/avlos.gr\/wpress\/?p=450"},"modified":"2025-09-21T14:16:19","modified_gmt":"2025-09-21T12:16:19","slug":"%ce%b5%ce%bb%ce%b5%ce%b3%ce%ba%cf%84%ce%ae%cf%82-pid","status":"publish","type":"post","link":"https:\/\/avlos.gr\/wpress\/%ce%b5%ce%bb%ce%b5%ce%b3%ce%ba%cf%84%ce%ae%cf%82-pid\/","title":{"rendered":"\u0395\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae\u03c2 PID"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">\u0395\u03b9\u03c3\u03b1\u03b3\u03c9\u03b3\u03ae<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u039f \u0395\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae\u03c2 PID \u03ae \u03b1\u03bb\u03bb\u03b9\u03ce\u03c2 \u03b5\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae\u03c2 \u03c4\u03c1\u03b9\u03ce\u03bd \u03cc\u03c1\u03c9\u03bd, \u03b5\u03af\u03bd\u03b1\u03b9 \u03ad\u03bd\u03b1 \u03b1\u03bd\u03b1\u03bb\u03bf\u03b3\u03b9\u03ba\u03cc &#8211; \u03bf\u03bb\u03bf\u03ba\u03bb\u03b7\u03c1\u03c9\u03c4\u03b9\u03ba\u03cc &#8211; \u03c0\u03b1\u03c1\u03ac\u03b3\u03c9\u03b3\u03bf  (Proportional\u2013Integral\u2013Derivative ) \u03c3\u03cd\u03c3\u03c4\u03b7\u03bc\u03b1 \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5. \u0395\u03af\u03bd\u03b1\u03b9 \u03ad\u03bd\u03b1\u03c2 \u03bc\u03b7\u03c7\u03b1\u03bd\u03b9\u03c3\u03bc\u03cc\u03c2 \u03b2\u03c1\u03cc\u03c7\u03bf\u03c5 \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5 \u03c0\u03bf\u03c5 \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03b5\u03af \u03b1\u03bd\u03ac\u03b4\u03c1\u03b1\u03c3\u03b7. \u03a7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03b5\u03af\u03c4\u03b1\u03b9 \u03b5\u03c5\u03c1\u03ad\u03c9\u03c2 \u03c3\u03b5 \u03b2\u03b9\u03bf\u03bc\u03b7\u03c7\u03b1\u03bd\u03b9\u03ba\u03ac \u03c3\u03c5\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1 \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5 \u03ba\u03b1\u03b9 \u03c3\u03b5 \u03bc\u03b9\u03b1 \u03c0\u03bf\u03b9\u03ba\u03b9\u03bb\u03af\u03b1 \u03ac\u03bb\u03bb\u03c9\u03bd \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ce\u03bd \u03c0\u03bf\u03c5 \u03b1\u03c0\u03b1\u03b9\u03c4\u03bf\u03cd\u03bd \u03c3\u03c5\u03bd\u03b5\u03c7\u03ce\u03c2 \u03b4\u03b9\u03b1\u03bc\u03bf\u03c1\u03c6\u03c9\u03bc\u03ad\u03bd\u03bf \u03ad\u03bb\u03b5\u03b3\u03c7\u03bf. \u0394\u03b7\u03bb\u03b1\u03b4\u03ae \u03ad\u03bd\u03b1\u03c2 \u03b5\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae\u03c2 PID \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03af\u03b6\u03b5\u03b9 \u03c3\u03c5\u03bd\u03b5\u03c7\u03ce\u03c2 \u03bc\u03b9\u03b1 \u03c4\u03b9\u03bc\u03ae \u03c3\u03c6\u03ac\u03bb\u03bc\u03b1\u03c4\u03bf\u03c2 e(t) \u03c9\u03c2 \u03c4\u03b7 \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03ac \u03bc\u03b5\u03c4\u03b1\u03be\u03cd \u03b5\u03bd\u03cc\u03c2 \u03b5\u03c0\u03b9\u03b8\u03c5\u03bc\u03b7\u03c4\u03bf\u03cd \u03c3\u03b7\u03bc\u03b5\u03af\u03bf\u03c5 \u03c1\u03cd\u03b8\u03bc\u03b9\u03c3\u03b7\u03c2 (SetPoint -SP) \u03ba\u03b1\u03b9 \u03c4\u03b7\u03c2 \u03c4\u03c1\u03ad\u03c7\u03bf\u03c5\u03c3\u03b1\u03c2 \u03c4\u03b9\u03bc\u03ae\u03c2 \u03bc\u03b9\u03b1\u03c2 \u03bc\u03b5\u03c4\u03c1\u03bf\u03cd\u03bc\u03b5\u03bd\u03b7\u03c2 \u03bc\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ae\u03c2 \u03b4\u03b9\u03b5\u03c1\u03b3\u03b1\u03c3\u03af\u03b1\u03c2 (Process Variable PV) \u03ba\u03b1\u03b9 \u03b5\u03c6\u03b1\u03c1\u03bc\u03cc\u03b6\u03b5\u03b9 \u03bc\u03b9\u03b1 \u03b4\u03b9\u03cc\u03c1\u03b8\u03c9\u03c3\u03b7 \u03c0\u03bf\u03c5 \u03b2\u03b1\u03c3\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c3\u03b5 \u03b1\u03bd\u03b1\u03bb\u03bf\u03b3\u03b9\u03ba\u03cc, \u03bf\u03bb\u03bf\u03ba\u03bb\u03b7\u03c1\u03c9\u03c4\u03b9\u03ba\u03cc \u03ba\u03b1\u03b9 \u03c0\u03b1\u03c1\u03ac\u03b3\u03c9\u03b3\u03bf \u03cc\u03c1\u03bf (\u03c0\u03bf\u03c5 \u03c3\u03c5\u03bc\u03b2\u03bf\u03bb\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03bc\u03b5 P, I \u03ba\u03b1\u03b9 D \u03b1\u03bd\u03c4\u03af\u03c3\u03c4\u03bf\u03b9\u03c7\u03b1), \u03b1\u03c0\u03cc \u03cc\u03c0\u03bf\u03c5 \u03c0\u03ae\u03c1\u03b5 \u03ba\u03b1\u03b9 \u03c4\u03bf \u03cc\u03bd\u03bf\u03bc\u03b1. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u03a0\u03c1\u03b1\u03ba\u03c4\u03b9\u03ba\u03ac, \u03b5\u03c6\u03b1\u03c1\u03bc\u03cc\u03b6\u03b5\u03b9 \u03b1\u03c5\u03c4\u03cc\u03bc\u03b1\u03c4\u03b1 \u03bc\u03b9\u03b1 \u03b1\u03ba\u03c1\u03b9\u03b2\u03ae \u03ba\u03b1\u03b9 \u03b1\u03bd\u03c4\u03b1\u03c0\u03bf\u03ba\u03c1\u03b9\u03bd\u03cc\u03bc\u03b5\u03bd\u03b7 \u03b4\u03b9\u03cc\u03c1\u03b8\u03c9\u03c3\u03b7 \u03c3\u03b5 \u03bc\u03b9\u03b1 \u03bb\u03b5\u03b9\u03c4\u03bf\u03c5\u03c1\u03b3\u03af\u03b1 \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5. \u0388\u03bd\u03b1 \u03ba\u03b1\u03b8\u03b7\u03bc\u03b5\u03c1\u03b9\u03bd\u03cc \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf <strong>cruise control<\/strong> \u03c3\u03b5 \u03ad\u03bd\u03b1 \u03c3\u03cd\u03b3\u03c7\u03c1\u03bf\u03bd\u03bf \u03b1\u03c5\u03c4\u03bf\u03ba\u03af\u03bd\u03b7\u03c4\u03bf. \u0397 \u03b1\u03bd\u03ac\u03b2\u03b1\u03c3\u03b7 \u03c3\u03b5 \u03ad\u03bd\u03b1 \u03bb\u03cc\u03c6\u03bf \u03b8\u03b1 \u03bc\u03b5\u03af\u03c9\u03bd\u03b5 \u03c4\u03b7\u03bd \u03c4\u03b1\u03c7\u03cd\u03c4\u03b7\u03c4\u03b1 \u03c4\u03bf\u03c5 \u03b1\u03c5\u03c4\u03bf\u03ba\u03b9\u03bd\u03ae\u03c4\u03bf\u03c5 \u03b5\u03ac\u03bd \u03c5\u03c0\u03ae\u03c1\u03c7\u03b5 \u03bc\u03cc\u03bd\u03bf \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ae \u03b9\u03c3\u03c7\u03cd\u03c2 \u03ba\u03b9\u03bd\u03b7\u03c4\u03ae\u03c1\u03b1. \u039f \u03b1\u03bb\u03b3\u03cc\u03c1\u03b9\u03b8\u03bc\u03bf\u03c2 PID \u03c4\u03bf\u03c5 \u03b5\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae \u03b5\u03c0\u03b1\u03bd\u03b1\u03c6\u03ad\u03c1\u03b5\u03b9 \u03c4\u03b7 \u03bc\u03b5\u03c4\u03c1\u03bf\u03cd\u03bc\u03b5\u03bd\u03b7 \u03c4\u03b1\u03c7\u03cd\u03c4\u03b7\u03c4\u03b1 \u03c3\u03c4\u03b7\u03bd \u03b5\u03c0\u03b9\u03b8\u03c5\u03bc\u03b7\u03c4\u03ae \u03c4\u03b1\u03c7\u03cd\u03c4\u03b7\u03c4\u03b1 \u03bc\u03b5 \u03b5\u03bb\u03ac\u03c7\u03b9\u03c3\u03c4\u03b7 \u03ba\u03b1\u03b8\u03c5\u03c3\u03c4\u03ad\u03c1\u03b7\u03c3\u03b7 \u03ba\u03b1\u03b9 \u03c5\u03c0\u03ad\u03c1\u03b2\u03b1\u03c3\u03b7 \u03b1\u03c5\u03be\u03ac\u03bd\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b7\u03bd \u03b9\u03c3\u03c7\u03cd \u03b5\u03be\u03cc\u03b4\u03bf\u03c5 \u03c4\u03bf\u03c5 \u03ba\u03b9\u03bd\u03b7\u03c4\u03ae\u03c1\u03b1 \u03bc\u03b5 \u03b5\u03bb\u03b5\u03b3\u03c7\u03cc\u03bc\u03b5\u03bd\u03bf \u03c4\u03c1\u03cc\u03c0\u03bf.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u039b\u03b5\u03b9\u03c4\u03bf\u03c5\u03c1\u03b3\u03af\u03b1 \u03c4\u03bf\u03c5 \u03b5\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u03a4\u03bf \u03c7\u03b1\u03c1\u03b1\u03ba\u03c4\u03b7\u03c1\u03b9\u03c3\u03c4\u03b9\u03ba\u03cc \u03b3\u03bd\u03ce\u03c1\u03b9\u03c3\u03bc\u03b1 \u03c4\u03bf\u03c5 \u03b5\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae PID \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03b4\u03c5\u03bd\u03b1\u03c4\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c7\u03c1\u03ae\u03c3\u03b7\u03c2 \u03c4\u03c9\u03bd \u03c4\u03c1\u03b9\u03ce\u03bd \u03cc\u03c1\u03c9\u03bd \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5 \u03c4\u03b7\u03c2 \u03b1\u03bd\u03b1\u03bb\u03bf\u03b3\u03b9\u03ba\u03ae\u03c2, \u03c4\u03b7\u03c2 \u03bf\u03bb\u03bf\u03ba\u03bb\u03b7\u03c1\u03c9\u03c4\u03b9\u03ba\u03ae\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03b7\u03c2 \u03c0\u03b1\u03c1\u03ac\u03b3\u03c9\u03b3\u03b7\u03c2 \u03b5\u03c0\u03b9\u03c1\u03c1\u03bf\u03ae\u03c2 \u03c3\u03c4\u03b7\u03bd \u03ad\u03be\u03bf\u03b4\u03bf \u03c4\u03bf\u03c5 \u03b5\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ae \u03b1\u03ba\u03c1\u03b9\u03b2\u03bf\u03cd\u03c2 \u03ba\u03b1\u03b9 \u03b2\u03ad\u03bb\u03c4\u03b9\u03c3\u03c4\u03bf\u03c5 \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5. \u03a4\u03bf \u03bc\u03c0\u03bb\u03bf\u03ba \u03b4\u03b9\u03ac\u03b3\u03c1\u03b1\u03bc\u03bc\u03b1 \u03c4\u03bf\u03c5 \u03b5\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae \u03c0\u03bf\u03c5 \u03c6\u03b1\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c0\u03b9\u03bf \u03ba\u03ac\u03c4\u03c9, \u03b4\u03b5\u03af\u03c7\u03bd\u03b5\u03b9 \u03c4\u03b9\u03c2 \u03b1\u03c1\u03c7\u03ad\u03c2 \u03c4\u03bf\u03c5 \u03c4\u03c1\u03cc\u03c0\u03bf\u03c5 \u03bc\u03b5 \u03c4\u03bf\u03bd \u03bf\u03c0\u03bf\u03af\u03bf \u03b4\u03b7\u03bc\u03b9\u03bf\u03c5\u03c1\u03b3\u03bf\u03cd\u03bd\u03c4\u03b1\u03b9 \u03ba\u03b1\u03b9 \u03b5\u03c6\u03b1\u03c1\u03bc\u03cc\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03b1\u03c5\u03c4\u03bf\u03af \u03bf\u03b9 \u03cc\u03c1\u03bf\u03b9. \u0395\u03bc\u03c6\u03b1\u03bd\u03af\u03b6\u03b5\u03b9 \u03ad\u03bd\u03b1\u03bd \u03b5\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae PID, \u03bf \u03bf\u03c0\u03bf\u03af\u03bf\u03c2 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03af\u03b6\u03b5\u03b9 \u03c3\u03c5\u03bd\u03b5\u03c7\u03ce\u03c2 \u03bc\u03b9\u03b1 \u03c4\u03b9\u03bc\u03ae \u03c3\u03c6\u03ac\u03bb\u03bc\u03b1\u03c4\u03bf\u03c2 e(t) \u03c9\u03c2 \u03c4\u03b7 \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03ac \u03bc\u03b5\u03c4\u03b1\u03be\u03cd \u03b5\u03bd\u03cc\u03c2 \u03b5\u03c0\u03b9\u03b8\u03c5\u03bc\u03b7\u03c4\u03bf\u03cd \u03c3\u03b7\u03bc\u03b5\u03af\u03bf\u03c5 \u03c1\u03cd\u03b8\u03bc\u03b9\u03c3\u03b7\u03c2 <em><strong>SP=r(t)<\/strong><\/em> \u03ba\u03b1\u03b9 \u03bc\u03b9\u03b1 \u03bc\u03b5\u03c4\u03c1\u03b7\u03bc\u03ad\u03bd\u03b7 \u03bc\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ae \u03b4\u03b9\u03b1\u03b4\u03b9\u03ba\u03b1\u03c3\u03af\u03b1\u03c2 <em><strong>PV=y(t)<\/strong><\/em> <em><strong>e(t)=r(t)-y(t) <\/strong><\/em>\u03ba\u03b1\u03b9 \u03b5\u03c6\u03b1\u03c1\u03bc\u03cc\u03b6\u03b5\u03b9 \u03bc\u03b9\u03b1 \u03b4\u03b9\u03cc\u03c1\u03b8\u03c9\u03c3\u03b7 \u03c0\u03bf\u03c5 \u03b2\u03b1\u03c3\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c3\u03b5 \u03b1\u03bd\u03b1\u03bb\u03bf\u03b3\u03b9\u03ba\u03cc, \u03bf\u03bb\u03bf\u03ba\u03bb\u03b7\u03c1\u03c9\u03c4\u03b9\u03ba\u03cc \u03ba\u03b1\u03b9 \u03c0\u03b1\u03c1\u03ac\u03b3\u03c9\u03b3\u03bf \u03cc\u03c1\u03bf. \u039f \u03b5\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae\u03c2 \u03c0\u03c1\u03bf\u03c3\u03c0\u03b1\u03b8\u03b5\u03af \u03bd\u03b1 \u03b5\u03bb\u03b1\u03c7\u03b9\u03c3\u03c4\u03bf\u03c0\u03bf\u03b9\u03ae\u03c3\u03b5\u03b9 \u03c4\u03bf \u03c3\u03c6\u03ac\u03bb\u03bc\u03b1 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03c0\u03ac\u03c1\u03bf\u03b4\u03bf \u03c4\u03bf\u03c5 \u03c7\u03c1\u03cc\u03bd\u03bf\u03c5 \u03c0\u03c1\u03bf\u03c3\u03b1\u03c1\u03bc\u03cc\u03b6\u03bf\u03bd\u03c4\u03b1\u03c2 \u03bc\u03b9\u03b1 \u03bc\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ae \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5<strong> u(t)<\/strong>, \u03cc\u03c0\u03c9\u03c2 \u03c0.\u03c7. \u03c4\u03bf \u03ac\u03bd\u03bf\u03b9\u03b3\u03bc\u03b1 \u03bc\u03b9\u03b1\u03c2 \u03b2\u03b1\u03bb\u03b2\u03af\u03b4\u03b1\u03c2 \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5, \u03c3\u03b5 \u03bc\u03b9\u03b1 \u03bd\u03ad\u03b1 \u03c4\u03b9\u03bc\u03ae \u03c0\u03bf\u03c5 \u03ba\u03b1\u03b8\u03bf\u03c1\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03ad\u03bd\u03b1 \u03c3\u03c4\u03b1\u03b8\u03bc\u03b9\u03c3\u03bc\u03ad\u03bd\u03bf \u03ac\u03b8\u03c1\u03bf\u03b9\u03c3\u03bc\u03b1 \u03c4\u03c9\u03bd \u03cc\u03c1\u03c9\u03bd \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5 .<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"363\" height=\"134\" src=\"https:\/\/avlos.gr\/wpress\/wp-content\/uploads\/2025\/09\/\u0395\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae\u03c2_PID_Opera.jpg\" alt=\"\" class=\"wp-image-454\" style=\"width:333px;height:auto\" srcset=\"https:\/\/avlos.gr\/wpress\/wp-content\/uploads\/2025\/09\/\u0395\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae\u03c2_PID_Opera.jpg 363w, https:\/\/avlos.gr\/wpress\/wp-content\/uploads\/2025\/09\/\u0395\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae\u03c2_PID_Opera-300x111.jpg 300w\" sizes=\"auto, (max-width: 363px) 100vw, 363px\" \/><figcaption class=\"wp-element-caption\">\u0395\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae\u03c2 PID<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u03a0\u03ce\u03c2 \u03b4\u03bf\u03c5\u03bb\u03b5\u03cd\u03b5\u03b9 \u03bf PID \u03b5\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae\u03c2<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u0397 \u03c3\u03c5\u03bd\u03bf\u03bb\u03b9\u03ba\u03ae \u03ad\u03be\u03bf\u03b4\u03bf\u03c2 \u03c4\u03bf\u03c5 \u03b5\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae PID \u03b5\u03af\u03bd\u03b1\u03b9 \u03ad\u03bd\u03b1\u03c2 \u03c3\u03c5\u03bd\u03b4\u03c5\u03b1\u03c3\u03bc\u03cc\u03c2 \u03c4\u03c9\u03bd \u03c4\u03c1\u03b9\u03ce\u03bd \u03cc\u03c1\u03c9\u03bd \u03cc\u03c0\u03c9\u03c2 \u03c6\u03b1\u03af\u03bd\u03bf\u03bd\u03c4\u03b1\u03b9 \u03c3\u03c4\u03bf \u03c0\u03b1\u03c1\u03b1\u03c0\u03ac\u03bd\u03c9 \u03c3\u03c7\u03ae\u03bc\u03b1, \u03c4\u03c9\u03bd : <strong>P, I <\/strong>\u03ba\u03b1\u03b9 <strong>D<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u039f \u03cc\u03c1\u03bf\u03c2 P \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03bd\u03ac\u03bb\u03bf\u03b3\u03bf\u03c2 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03c4\u03c1\u03ad\u03c7\u03bf\u03c5\u03c3\u03b1 \u03c4\u03b9\u03bc\u03ae \u03c4\u03bf\u03c5 \u03c3\u03c6\u03ac\u03bb\u03bc\u03b1\u03c4\u03bf\u03c2 SP\u2212PV = e(t).&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"137\" height=\"29\" src=\"https:\/\/avlos.gr\/wpress\/wp-content\/uploads\/2025\/09\/Pout.jpg\" alt=\"\" class=\"wp-image-470\" style=\"width:222px;height:auto\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u0393\u03b9\u03b1 \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1, \u03b5\u03ac\u03bd \u03c4\u03bf \u03c3\u03c6\u03ac\u03bb\u03bc\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03b5\u03b3\u03ac\u03bb\u03bf \u03ba\u03b1\u03b9 \u03b8\u03b5\u03c4\u03b9\u03ba\u03cc, \u03b7 \u03ad\u03be\u03bf\u03b4\u03bf\u03c2 \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5 \u03b8\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03bd\u03b1\u03bb\u03bf\u03b3\u03b9\u03ba\u03ac \u03bc\u03b5\u03b3\u03ac\u03bb\u03b7 \u03ba\u03b1\u03b9 \u03b8\u03b5\u03c4\u03b9\u03ba\u03ae, \u03bb\u03b1\u03bc\u03b2\u03ac\u03bd\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c5\u03c0\u03cc\u03c8\u03b7 \u03c4\u03bf\u03bd \u03c0\u03b1\u03c1\u03ac\u03b3\u03bf\u03bd\u03c4\u03b1 \u03b1\u03c0\u03bf\u03bb\u03b1\u03b2\u03ae\u03c2 K<sub>p.<\/sub> \u039c\u03cc\u03bd\u03bf\u03bd \u03bf <strong>P \u03ad\u03bb\u03b5\u03b3\u03c7\u03bf\u03c2<\/strong> (Proportional) \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03c1\u03ba\u03b5\u03c4\u03cc\u03c2 \u03ba\u03b1\u03b9 \u03bb\u03b5\u03b9\u03c4\u03bf\u03c5\u03c1\u03b3\u03b5\u03af \u03ba\u03b1\u03bb\u03ac \u03ad\u03bd\u03b1 \u03c3\u03cd\u03c3\u03c4\u03b7\u03bc\u03b1 \u03cc\u03c4\u03b1\u03bd:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u03a4\u03bf \u03c3\u03cd\u03c3\u03c4\u03b7\u03bc\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 <strong>\u03b1\u03c0\u03bb\u03cc<\/strong> \u03ba\u03b1\u03b9 <strong>\u03b1\u03bd\u03c4\u03b1\u03c0\u03bf\u03ba\u03c1\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03b3\u03c1\u03ae\u03b3\u03bf\u03c1\u03b1<\/strong>.<\/li>\n\n\n\n<li>\u0394\u03b5\u03bd \u03b1\u03c0\u03b1\u03b9\u03c4\u03b5\u03af\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc\u03bb\u03c5\u03c4\u03b7 \u03b1\u03ba\u03c1\u03af\u03b2\u03b5\u03b9\u03b1 \u03c3\u03c4\u03bf \u03c4\u03b5\u03bb\u03b9\u03ba\u03cc \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1.<\/li>\n\n\n\n<li>\u0395\u03af\u03bd\u03b1\u03b9 \u03b1\u03c0\u03bf\u03b4\u03b5\u03ba\u03c4\u03cc \u03bd\u03b1 \u03c5\u03c0\u03ac\u03c1\u03c7\u03b5\u03b9 <strong>\u03bb\u03af\u03b3\u03bf \u03c3\u03c6\u03ac\u03bb\u03bc\u03b1<\/strong> \u03c3\u03c4\u03bf steady-state (\u03c4\u03b5\u03bb\u03b9\u03ba\u03ae \u03ba\u03b1\u03c4\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7).<\/li>\n\n\n\n<li>\u0394\u03b5\u03bd \u03ad\u03c7\u03b5\u03b9\u03c2 \u03c0\u03c1\u03cc\u03b2\u03bb\u03b7\u03bc\u03b1 \u03bc\u03b5 \u03ba\u03ac\u03c0\u03bf\u03b9\u03b1 <strong>\u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ae \u03b1\u03c0\u03cc\u03ba\u03bb\u03b9\u03c3\u03b7 \u03b1\u03c0\u03cc \u03c4\u03bf setpoint<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0388\u03c4\u03c3\u03b9, \u03cc\u03c4\u03b1\u03bd \u03c3\u03b5 \u03ad\u03bd\u03b1 \u03c3\u03cd\u03c3\u03c4\u03b7\u03bc\u03b1 \u03bb\u03b5\u03b9\u03c4\u03bf\u03c5\u03c1\u03b3\u03b5\u03af \u03bc\u03cc\u03bd\u03bf  P \u03ad\u03bb\u03b5\u03b3\u03c7\u03bf\u03c2 \u03c5\u03c0\u03ac\u03c1\u03c7\u03bf\u03c5\u03bd \u03c0\u03b5\u03c1\u03b9\u03bf\u03c1\u03b9\u03c3\u03bc\u03bf\u03af:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u039c\u03cc\u03bd\u03b9\u03bc\u03bf \u03c3\u03c6\u03ac\u03bb\u03bc\u03b1 (steady-state error):<\/strong>\n<ul class=\"wp-block-list\">\n<li>\u039f P \u03ad\u03bb\u03b5\u03b3\u03c7\u03bf\u03c2 <strong>\u03b4\u03b5\u03bd \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03b5\u03be\u03b1\u03c6\u03b1\u03bd\u03af\u03c3\u03b5\u03b9 \u03c4\u03b5\u03bb\u03b5\u03af\u03c9\u03c2 \u03c4\u03bf \u03c3\u03c6\u03ac\u03bb\u03bc\u03b1<\/strong>.<\/li>\n\n\n\n<li>\u038c\u03c3\u03bf \u03c0\u03bb\u03b7\u03c3\u03b9\u03ac\u03b6\u03b5\u03b9\u03c2 \u03c4\u03b7\u03bd \u03b5\u03c0\u03b9\u03b8\u03c5\u03bc\u03b7\u03c4\u03ae \u03c4\u03b9\u03bc\u03ae, \u03c4\u03bf \u03c3\u03c6\u03ac\u03bb\u03bc\u03b1 \u03bc\u03b9\u03ba\u03c1\u03b1\u03af\u03bd\u03b5\u03b9 \u2192 \u03ac\u03c1\u03b1 \u03ba\u03b1\u03b9 \u03b7 \u03b4\u03b9\u03cc\u03c1\u03b8\u03c9\u03c3\u03b7 \u03bc\u03b9\u03ba\u03c1\u03b1\u03af\u03bd\u03b5\u03b9 \u2192 \u03ba\u03b1\u03b9 \u03c3\u03c4\u03b1\u03bc\u03b1\u03c4\u03ac \u03c0\u03c1\u03b9\u03bd \u03c6\u03c4\u03ac\u03c3\u03b5\u03b9\u03c2 \u03b1\u03ba\u03c1\u03b9\u03b2\u03ce\u03c2 \u03c4\u03bf setpoint.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u03a0\u03b5\u03c1\u03b9\u03bf\u03c1\u03b9\u03c3\u03bc\u03cc\u03c2 \u03c3\u03c4\u03b7\u03bd \u03b9\u03c3\u03c7\u03cd:<\/strong>\n<ul class=\"wp-block-list\">\n<li>\u0391\u03bd \u03ba\u03ac\u03bd\u03b5\u03b9\u03c2 \u03c0\u03bf\u03bb\u03cd \u03bc\u03b5\u03b3\u03ac\u03bb\u03bf \u03c4\u03bf\u03bd \u03b1\u03bd\u03b1\u03bb\u03bf\u03b3\u03b9\u03ba\u03cc \u03c3\u03c5\u03bd\u03c4\u03b5\u03bb\u03b5\u03c3\u03c4\u03ae Kp\u200b, \u03b3\u03b9\u03b1 \u03bd\u03b1 &#8220;\u03c0\u03b9\u03ad\u03c3\u03b5\u03b9&#8221; \u03c0\u03b9\u03bf \u03c0\u03bf\u03bb\u03cd, \u03c4\u03cc\u03c4\u03b5:\n<ul class=\"wp-block-list\">\n<li>\u03a4\u03bf \u03c3\u03cd\u03c3\u03c4\u03b7\u03bc\u03b1 \u03b3\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 <strong>\u03b1\u03c3\u03c4\u03b1\u03b8\u03ad\u03c2<\/strong>.<\/li>\n\n\n\n<li>\u038a\u03c3\u03c9\u03c2 \u03ad\u03c7\u03b5\u03b9\u03c2 <strong>\u03c4\u03b1\u03bb\u03b1\u03bd\u03c4\u03ce\u03c3\u03b5\u03b9\u03c2<\/strong> \u03ae <strong>\u03c5\u03c0\u03b5\u03c1\u03b2\u03bf\u03bb\u03b9\u03ba\u03ae \u03b1\u03c0\u03cc\u03ba\u03c1\u03b9\u03c3\u03b7 (overshoot)<\/strong>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u039a\u03b1\u03ba\u03ae \u03c3\u03c5\u03bc\u03c0\u03b5\u03c1\u03b9\u03c6\u03bf\u03c1\u03ac \u03c3\u03b5 \u03b1\u03c1\u03b3\u03ac \u03ae \u03c0\u03bf\u03bb\u03cd\u03c0\u03bb\u03bf\u03ba\u03b1 \u03c3\u03c5\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1:<\/strong>\n<ul class=\"wp-block-list\">\n<li>\u03a3\u03b5 \u03c3\u03c5\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1 \u03bc\u03b5 \u03b1\u03b4\u03c1\u03ac\u03bd\u03b5\u03b9\u03b1 (\u03cc\u03c0\u03c9\u03c2 \u03b8\u03b5\u03c1\u03bc\u03b9\u03ba\u03ac \u03ae \u03bc\u03b7\u03c7\u03b1\u03bd\u03b9\u03ba\u03ac), \u03bf P \u03ad\u03bb\u03b5\u03b3\u03c7\u03bf\u03c2 \u03bc\u03cc\u03bd\u03bf\u03c2 \u03c4\u03bf\u03c5 <strong>\u03b4\u03b5\u03bd \u03c0\u03c1\u03bf\u03bb\u03b1\u03b2\u03b1\u03af\u03bd\u03b5\u03b9<\/strong> \u03ae <strong>\u03ba\u03b1\u03b8\u03c5\u03c3\u03c4\u03b5\u03c1\u03b5\u03af<\/strong> \u03bd\u03b1 \u03b1\u03bd\u03c4\u03b9\u03b4\u03c1\u03ac\u03c3\u03b5\u03b9 \u03c3\u03c9\u03c3\u03c4\u03ac.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u0393\u03b9\u03b1 \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1 \u03b1\u03c2 \u03c0\u03bf\u03cd\u03bc\u03b5 \u03cc\u03c4\u03b9 \u03b5\u03bb\u03ad\u03b3\u03c7\u03b5\u03b9\u03c2 \u03ad\u03bd\u03b1\u03bd \u03ba\u03b9\u03bd\u03b7\u03c4\u03ae\u03c1\u03b1 \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03c6\u03c4\u03ac\u03c3\u03b5\u03b9 \u03c3\u03b5 \u03c3\u03c5\u03b3\u03ba\u03b5\u03ba\u03c1\u03b9\u03bc\u03ad\u03bd\u03b7 \u03c4\u03b1\u03c7\u03cd\u03c4\u03b7\u03c4\u03b1.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u039c\u03b5 <strong>P \u03bc\u03cc\u03bd\u03bf<\/strong>, \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03c6\u03c4\u03ac\u03c3\u03b5\u03b9 \u03ba\u03bf\u03bd\u03c4\u03ac \u03c3\u03c4\u03bf\u03bd \u03c3\u03c4\u03cc\u03c7\u03bf, \u03b1\u03bb\u03bb\u03ac:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u039c\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03c3\u03c4\u03b1\u03bc\u03b1\u03c4\u03ae\u03c3\u03b5\u03b9 \u03c3\u03c4\u03bf <strong>98%<\/strong> \u03c4\u03bf\u03c5 \u03c3\u03c4\u03cc\u03c7\u03bf\u03c5 \u03ba\u03b1\u03b9 \u03bd\u03b1 \u03bc\u03b7 \u03c0\u03ac\u03b5\u03b9 \u03c0\u03bf\u03c4\u03ad \u03b1\u03ba\u03c1\u03b9\u03b2\u03ce\u03c2 \u03c3\u03c4\u03bf 100%.<\/li>\n\n\n\n<li>\u0391\u03bd \u03b1\u03c5\u03be\u03ae\u03c3\u03b5\u03b9\u03c2 \u03c4\u03bf\u03bd Kp\u200b, \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03c4\u03b1\u03bb\u03b1\u03bd\u03c4\u03ce\u03bd\u03b5\u03c4\u03b1\u03b9 \u03b3\u03cd\u03c1\u03c9 \u03b1\u03c0\u03cc \u03c4\u03bf 100% (overshoot \u2192 undershoot \u2192 overshoot&#8230;).<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u039f \u03cc\u03c1\u03bf\u03c2<strong> I <\/strong>\u03bb\u03b1\u03bc\u03b2\u03ac\u03bd\u03b5\u03b9 \u03c5\u03c0\u03cc\u03c8\u03b7 \u03c4\u03b9\u03c2 \u03c0\u03c1\u03bf\u03b7\u03b3\u03bf\u03cd\u03bc\u03b5\u03bd\u03b5\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03c4\u03bf\u03c5 \u03c3\u03c6\u03ac\u03bb\u03bc\u03b1\u03c4\u03bf\u03c2 SP\u2212PV<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"133\" height=\"39\" src=\"https:\/\/avlos.gr\/wpress\/wp-content\/uploads\/2025\/09\/Iout.jpg\" alt=\"\" class=\"wp-image-469\" style=\"width:184px;height:auto\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u03ba\u03b1\u03b9 \u03c4\u03b9\u03c2 \u03b5\u03bd\u03c3\u03c9\u03bc\u03b1\u03c4\u03ce\u03bd\u03b5\u03b9 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03c0\u03ac\u03c1\u03bf\u03b4\u03bf \u03c4\u03bf\u03c5 \u03c7\u03c1\u03cc\u03bd\u03bf\u03c5 \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03c0\u03b1\u03c1\u03ac\u03b3\u03b5\u03b9 \u03c4\u03bf\u03bd \u03cc\u03c1\u03bf I. \u0393\u03b9\u03b1 \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1, \u03b5\u03ac\u03bd \u03c5\u03c0\u03ac\u03c1\u03c7\u03b5\u03b9 \u03ad\u03bd\u03b1 \u03c5\u03c0\u03bf\u03bb\u03b5\u03b9\u03c0\u03cc\u03bc\u03b5\u03bd\u03bf \u03c3\u03c6\u03ac\u03bb\u03bc\u03b1 SP\u2212PV \u03bc\u03b5\u03c4\u03ac \u03c4\u03b7\u03bd \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ae \u03c4\u03bf\u03c5 \u03b1\u03bd\u03b1\u03bb\u03bf\u03b3\u03b9\u03ba\u03bf\u03cd \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5, \u03bf \u03bf\u03bb\u03bf\u03ba\u03bb\u03b7\u03c1\u03c9\u03c4\u03b9\u03ba\u03cc\u03c2 \u03cc\u03c1\u03bf\u03c2 \u03b5\u03c0\u03b9\u03b4\u03b9\u03ce\u03ba\u03b5\u03b9 \u03bd\u03b1 \u03b5\u03be\u03b1\u03bb\u03b5\u03af\u03c8\u03b5\u03b9 \u03c4\u03bf \u03c5\u03c0\u03bf\u03bb\u03b5\u03b9\u03c0\u03cc\u03bc\u03b5\u03bd\u03bf \u03c3\u03c6\u03ac\u03bb\u03bc\u03b1 \u03c0\u03c1\u03bf\u03c3\u03b8\u03ad\u03c4\u03bf\u03bd\u03c4\u03b1\u03c2 \u03ad\u03bd\u03b1 \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5, \u03bc\u03b5 \u03b2\u03b1\u03c1\u03cd\u03c4\u03b7\u03c4\u03b1 K<sub>i&nbsp;<\/sub>,&nbsp;\u03bb\u03cc\u03b3\u03c9 \u03c4\u03b7\u03c2 \u03b9\u03c3\u03c4\u03bf\u03c1\u03b9\u03ba\u03ae\u03c2 \u03b1\u03b8\u03c1\u03bf\u03b9\u03c3\u03c4\u03b9\u03ba\u03ae\u03c2 \u03c4\u03b9\u03bc\u03ae\u03c2 \u03c4\u03bf\u03c5 \u03c3\u03c6\u03ac\u03bb\u03bc\u03b1\u03c4\u03bf\u03c2. \u038c\u03c4\u03b1\u03bd \u03b5\u03be\u03b1\u03bb\u03b5\u03b9\u03c6\u03b8\u03b5\u03af \u03c4\u03bf \u03c3\u03c6\u03ac\u03bb\u03bc\u03b1, \u03bf \u03bf\u03bb\u03bf\u03ba\u03bb\u03b7\u03c1\u03c9\u03c4\u03b9\u03ba\u03cc\u03c2 \u03cc\u03c1\u03bf\u03c2 \u03b8\u03b1 \u03c0\u03ac\u03c8\u03b5\u03b9 \u03bd\u03b1 \u03b1\u03c5\u03be\u03ac\u03bd\u03b5\u03c4\u03b1\u03b9. \u0391\u03c5\u03c4\u03cc \u03b8\u03b1 \u03ad\u03c7\u03b5\u03b9 \u03c9\u03c2 \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03c4\u03b7 \u03bc\u03b5\u03af\u03c9\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03b1\u03bd\u03b1\u03bb\u03bf\u03b3\u03b9\u03ba\u03bf\u03cd \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03ad\u03c3\u03bc\u03b1\u03c4\u03bf\u03c2 \u03ba\u03b1\u03b8\u03ce\u03c2 \u03bc\u03b5\u03b9\u03ce\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c4\u03bf \u03c3\u03c6\u03ac\u03bb\u03bc\u03b1, \u03b1\u03bb\u03bb\u03ac \u03b1\u03c5\u03c4\u03cc \u03b1\u03bd\u03c4\u03b9\u03c3\u03c4\u03b1\u03b8\u03bc\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03bf \u03b1\u03c5\u03be\u03b1\u03bd\u03cc\u03bc\u03b5\u03bd\u03bf \u03bf\u03bb\u03bf\u03ba\u03bb\u03b7\u03c1\u03c9\u03c4\u03b9\u03ba\u03cc \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u039f \u03cc\u03c1\u03bf\u03c2 D \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03ba\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03b7 \u03b5\u03ba\u03c4\u03af\u03bc\u03b7\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03bc\u03b5\u03bb\u03bb\u03bf\u03bd\u03c4\u03b9\u03ba\u03ae\u03c2 \u03c4\u03ac\u03c3\u03b7\u03c2 \u03c4\u03bf\u03c5 \u03c3\u03c6\u03ac\u03bb\u03bc\u03b1\u03c4\u03bf\u03c2 SP\u2212PV,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"130\" height=\"44\" src=\"https:\/\/avlos.gr\/wpress\/wp-content\/uploads\/2025\/09\/Dout.jpg\" alt=\"\" class=\"wp-image-468\" style=\"width:192px;height:auto\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u03bc\u03b5 \u03b2\u03ac\u03c3\u03b7 \u03c4\u03bf\u03bd \u03c4\u03c1\u03ad\u03c7\u03bf\u03bd\u03c4\u03b1 \u03c1\u03c5\u03b8\u03bc\u03cc \u03bc\u03b5\u03c4\u03b1\u03b2\u03bf\u03bb\u03ae\u03c2 \u03c4\u03bf\u03c5. \u039c\u03b5\u03c1\u03b9\u03ba\u03ad\u03c2 \u03c6\u03bf\u03c1\u03ad\u03c2 \u03b1\u03c0\u03bf\u03ba\u03b1\u03bb\u03b5\u03af\u03c4\u03b1\u03b9 \u00ab\u03c0\u03c1\u03bf\u03bb\u03b7\u03c0\u03c4\u03b9\u03ba\u03cc\u03c2 \u03ad\u03bb\u03b5\u03b3\u03c7\u03bf\u03c2\u00bb, \u03ba\u03b1\u03b8\u03ce\u03c2 \u03b5\u03c0\u03b9\u03b4\u03b9\u03ce\u03ba\u03b5\u03b9 \u03bf\u03c5\u03c3\u03b9\u03b1\u03c3\u03c4\u03b9\u03ba\u03ac \u03bd\u03b1 \u03bc\u03b5\u03b9\u03ce\u03c3\u03b5\u03b9 \u03c4\u03b7\u03bd \u03b5\u03c0\u03af\u03b4\u03c1\u03b1\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03c3\u03c6\u03ac\u03bb\u03bc\u03b1\u03c4\u03bf\u03c2 SP\u2212PV \u03b1\u03c3\u03ba\u03ce\u03bd\u03c4\u03b1\u03c2 \u03bc\u03b9\u03b1 \u03b5\u03c0\u03b9\u03c1\u03c1\u03bf\u03ae \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5 \u03c0\u03bf\u03c5 \u03b4\u03b7\u03bc\u03b9\u03bf\u03c5\u03c1\u03b3\u03b5\u03af\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd \u03c1\u03c5\u03b8\u03bc\u03cc \u03bc\u03b5\u03c4\u03b1\u03b2\u03bf\u03bb\u03ae\u03c2 \u03c4\u03bf\u03c5 \u03c3\u03c6\u03ac\u03bb\u03bc\u03b1\u03c4\u03bf\u03c2. \u038c\u03c3\u03bf \u03c0\u03b9\u03bf \u03b3\u03c1\u03ae\u03b3\u03bf\u03c1\u03b7 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03b1\u03bb\u03bb\u03b1\u03b3\u03ae, \u03c4\u03cc\u03c3\u03bf \u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5 \u03ae \u03b1\u03c0\u03cc\u03c3\u03b2\u03b5\u03c3\u03b7\u03c2. \u03a3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03cc\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf \u03c1\u03cc\u03bb\u03bf\u03c2 \u03c4\u03b7\u03c2 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac\u03c2 K<sub>d&nbsp;<\/sub>\u03c3\u03c4\u03bf\u03bd \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03cc \u03c4\u03b7\u03c2 \u03b4\u03b9\u03cc\u03c1\u03b8\u03c9\u03c3\u03b7\u03c2 D.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u0395\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ae \u03b5\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae PID \u03c3\u03c4\u03bf\u03bd \u039a\u03ce\u03b4\u03b9\u03ba\u03b1<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u0393\u03b9\u03b1 \u03bd\u03b1 \u03b5\u03c6\u03b1\u03c1\u03bc\u03cc\u03c3\u03b5\u03c4\u03b5 \u03ad\u03bd\u03b1\u03bd \u03b5\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae PID \u03c3\u03b5 \u03ba\u03ce\u03b4\u03b9\u03ba\u03b1 \u03ae \u03c3\u03b5 \u03ad\u03bd\u03b1 \u03c0\u03c1\u03cc\u03b3\u03c1\u03b1\u03bc\u03bc\u03b1 Arduino, \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b3\u03bd\u03c9\u03c3\u03c4\u03ad\u03c2 \u03c0\u03ad\u03bd\u03c4\u03b5 \u03c0\u03b1\u03c1\u03ac\u03bc\u03b5\u03c4\u03c1\u03bf\u03b9:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u03b1\u03bd\u03b1\u03bb\u03bf\u03b3\u03b9\u03ba\u03ae \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac K<sub>p<\/sub><\/li>\n\n\n\n<li>\u03bf\u03bb\u03bf\u03ba\u03bb\u03b7\u03c1\u03c9\u03c4\u03b9\u03ba\u03ae \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac K<sub>i<\/sub><\/li>\n\n\n\n<li>\u03ba\u03b1\u03b9 \u03c0\u03b1\u03c1\u03ac\u03b3\u03c9\u03b3\u03b7 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac K<sub>d<\/sub><\/li>\n\n\n\n<li>\u03c4\u03b9\u03bc\u03ae \u03b5\u03b9\u03c3\u03cc\u03b4\u03bf\u03c5 (PV)<\/li>\n\n\n\n<li>\u03ba\u03b1\u03b9 \u03c4\u03b9\u03bc\u03ae \u03c3\u03b7\u03bc\u03b5\u03af\u03bf\u03c5 \u03c1\u03cd\u03b8\u03bc\u03b9\u03c3\u03b7\u03c2 (SP)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><br>\u039f \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03cc\u03c2 PID \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03b2\u03c1\u03af\u03c3\u03ba\u03b5\u03c4\u03b1\u03b9 \u03bc\u03ad\u03c3\u03b1 \u03c3\u03b5 \u03bc\u03b9\u03b1 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7 \u03b2\u03c1\u03cc\u03c7\u03bf\u03c5. \u03a4\u03bf \u03c0\u03c1\u03ce\u03c4\u03bf \u03bc\u03ad\u03c1\u03bf\u03c2 \u03c4\u03b7\u03c2 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7\u03c2 \u03b8\u03b1 \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf \u03ba\u03b1\u03b8\u03bf\u03c1\u03b9\u03c3\u03bc\u03cc\u03c2 \u03c4\u03bf\u03c5 \u03c7\u03c1\u03cc\u03bd\u03bf\u03c5 \u03c0\u03bf\u03c5 \u03ad\u03c7\u03b5\u03b9 \u03c0\u03b1\u03c1\u03ad\u03bb\u03b8\u03b5\u03b9.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u03a3\u03c4\u03bf Arduino, \u03b7 \u03c4\u03c1\u03ad\u03c7\u03bf\u03c5\u03c3\u03b1 \u03ce\u03c1\u03b1 \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03c0\u03c1\u03bf\u03c3\u03b4\u03b9\u03bf\u03c1\u03b9\u03c3\u03c4\u03b5\u03af \u03bc\u03b5 \u03c4\u03b7 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7 millis() \u03ba\u03b1\u03b9 \u03bf \u03c7\u03c1\u03cc\u03bd\u03bf\u03c2 \u03c0\u03bf\u03c5 \u03ad\u03c7\u03b5\u03b9 \u03c0\u03b1\u03c1\u03ad\u03bb\u03b8\u03b5\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03c0\u03bb\u03ce\u03c2:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">currentTime = millis();<br>elapsedTime = currentTime &#8211; previousTime;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u03a3\u03c4\u03b7 \u03c3\u03c5\u03bd\u03ad\u03c7\u03b5\u03b9\u03b1, \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03c0\u03c1\u03bf\u03c3\u03b4\u03b9\u03bf\u03c1\u03b9\u03c3\u03c4\u03b5\u03af \u03c4\u03bf \u03c3\u03c6\u03ac\u03bb\u03bc\u03b1:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">error = setPoint \u2013 input;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u03a0\u03c1\u03bf\u03b3\u03c1\u03b1\u03bc\u03bc\u03b1\u03c4\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c3\u03b5 Arduino \u03bf\u03b9 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03bf\u03af \u03b1\u03c0\u03bb\u03bf\u03c0\u03bf\u03b9\u03bf\u03cd\u03bd\u03c4\u03b1\u03b9 \u03c0\u03ac\u03c1\u03b1 \u03c0\u03bf\u03bb\u03cd \u03bc\u03b5 \u03c4\u03b7 \u03c7\u03c1\u03ae\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03b2\u03b9\u03b2\u03bb\u03b9\u03bf\u03b8\u03ae\u03ba\u03b7\u03c2 PID_v1. \u03a3\u03c4\u03bf \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1 \u03c0\u03bf\u03c5 \u03c3\u03b1\u03c2 \u03c0\u03b1\u03c1\u03b1\u03b8\u03ad\u03c4\u03c9 \u03ad\u03ba\u03b1\u03bd\u03b1 \u03c7\u03c1\u03ae\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03b2\u03b9\u03b2\u03bb\u03b9\u03bf\u03b8\u03ae\u03ba\u03b7\u03c2 PID_v1.<br>\u03a3\u03b5 \u03ba\u03ac\u03b8\u03b5 \u03c0\u03b5\u03c1\u03af\u03c0\u03c4\u03c9\u03c3\u03b7 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03bd\u03b1\u03b3\u03ba\u03b1\u03af\u03bf\u03c2 \u03bf \u03c0\u03c1\u03bf\u03c3\u03b4\u03b9\u03bf\u03c1\u03b9\u03c3\u03bc\u03cc\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03b9\u03c2 \u03c4\u03c1\u03b5\u03b9\u03c2 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ad\u03c2 P, I, D. \u0391\u03c5\u03c4\u03cc\u03c2 \u03bf \u03c0\u03c1\u03bf\u03c3\u03b4\u03b9\u03bf\u03c1\u03b9\u03c3\u03bc\u03cc\u03c2 \u03b3\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c3\u03c5\u03bd\u03ae\u03b8\u03c9\u03c2 \u03c0\u03b5\u03b9\u03c1\u03b1\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03ba\u03b1\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03b9\u03b1 \u03b5\u03c0\u03af\u03c0\u03bf\u03bd\u03b7 \u03b4\u03b9\u03b1\u03b4\u03b9\u03ba\u03b1\u03c3\u03af\u03b1.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">&nbsp;\u039a\u03b1\u03c4\u03b1\u03c3\u03ba\u03b5\u03c5\u03ae<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u0397 \u03ba\u03b1\u03c4\u03b1\u03c3\u03ba\u03b5\u03c5\u03ae \u03b1\u03c5\u03c4\u03ae \u03b5\u03af\u03bd\u03b1\u03b9 \u03c3\u03c5\u03bd\u03ad\u03c7\u03b5\u03b9\u03b1 \u03c4\u03b7\u03c2 \u03c0\u03c1\u03bf\u03b7\u03b3\u03bf\u03cd\u03bc\u03b5\u03bd\u03b7\u03c2 \u03c0\u03bf\u03c5 \u03ad\u03ba\u03b1\u03bd\u03b1 \u03bc\u03b5 \u03c4\u03bf\u03c5\u03c2 \u03b4\u03cd\u03bf \u03c3\u03b5\u03c1\u03b2\u03bf\u03ba\u03b9\u03bd\u03b7\u03c4\u03ae\u03c1\u03b5\u03c2. \u03a3\u03b5 \u03b1\u03c5\u03c4\u03ae \u03c4\u03b7\u03bd \u03ba\u03b1\u03c4\u03b1\u03c3\u03ba\u03b5\u03c5\u03ae \u03ad\u03c7\u03c9 \u03c0\u03c1\u03bf\u03c3\u03b8\u03ad\u03c3\u03b5\u03b9 \u03c4\u03bf\u03bd \u03b1\u03b9\u03c3\u03b8\u03b7\u03c4\u03ae\u03c1\u03b1 MPU-9250 \u03bf \u03bf\u03c0\u03bf\u03af\u03bf\u03c2 \u03b8\u03b1 &#8220;\u03bf\u03b4\u03b7\u03b3\u03b5\u03af&#8221; \u03c4\u03bf\u03c5\u03c2 \u03c3\u03b5\u03c1\u03b2\u03bf\u03ba\u03b9\u03bd\u03b7\u03c4\u03ae\u03c1\u03b5\u03c2. \u0392\u03bb\u03ad\u03c0\u03b5 \u03c3\u03c7\u03b5\u03c4\u03b9\u03ba\u03ac&nbsp;<a href=\"https:\/\/avlos.gr\/wpress\/\u03b1\u03b9\u03c3\u03b8\u03b7\u03c4\u03ae\u03c1\u03b1\u03c2-\u03ba\u03af\u03bd\u03b7\u03c3\u03b7\u03c2\" target=\"_blank\" rel=\"noreferrer noopener\">\u03b5\u03b4\u03ce.&nbsp;<\/a><br>\u03a4\u03bf \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03cc\u03c4\u03b5\u03c1\u03bf \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03ba\u03b1\u03c4\u03b1\u03c3\u03ba\u03b5\u03c5\u03ae \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf <strong>\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03b9\u03ba\u03cc <\/strong>\u03c0\u03bf\u03c5 \u03b8\u03b1 \u03b3\u03c1\u03ac\u03c8\u03bf\u03c5\u03bc\u03b5 \u03ad\u03c4\u03c3\u03b9 \u03ce\u03c3\u03c4\u03b5 \u03b7 \u03ba\u03af\u03bd\u03b7\u03c3\u03b7 \u03c3\u03c4\u03bf\u03c5\u03c2 \u03c3\u03b5\u03c1\u03b2\u03bf\u03ba\u03b9\u03bd\u03b7\u03c4\u03ae\u03c1\u03b5\u03c2 \u03bd\u03b1 \u03b5\u03bb\u03ad\u03b3\u03c7\u03b5\u03c4\u03b1\u03b9 \u03c0\u03bb\u03ad\u03bf\u03bd \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd \u03b1\u03b9\u03c3\u03b8\u03b7\u03c4\u03ae\u03c1\u03b1 \u03ba\u03b1\u03b9 \u03bd\u03b1 \u03b3\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03bf\u03bc\u03b1\u03bb\u03ac, \u03c7\u03c9\u03c1\u03af\u03c2 \u03c4\u03b1\u03bb\u03b1\u03bd\u03c4\u03ce\u03c3\u03b5\u03b9\u03c2 \u03ba\u03b1\u03b9 \u03bd\u03b1 \u03c6\u03ad\u03c1\u03bd\u03b5\u03b9 \u03c4\u03bf \u03c3\u03cd\u03c3\u03c4\u03b7\u03bc\u03b1 \u03c3\u03c4\u03b7\u03bd \u03b5\u03c0\u03b9\u03b8\u03c5\u03bc\u03b7\u03c4\u03ae (\u03bf\u03c1\u03b9\u03b6\u03cc\u03bd\u03c4\u03b9\u03b1) \u03b8\u03ad\u03c3\u03b7.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u03a4\u03bf\u03bd \u03ba\u03ce\u03b4\u03b9\u03ba\u03b1 \u03c4\u03b7\u03c2 \u03ba\u03b1\u03c4\u03b1\u03c3\u03ba\u03b5\u03c5\u03ae\u03c2 \u03b3\u03b9\u03b1 Arduino UNO \u03c4\u03bf\u03bd \u03b2\u03bb\u03ad\u03c0\u03b5\u03c4\u03b5 \u03c3\u03c4\u03b7 \u03c3\u03c5\u03bd\u03ad\u03c7\u03b5\u03b9\u03b1 \u03ba\u03b1\u03b9 \u03bc\u03c0\u03bf\u03c1\u03b5\u03af\u03c4\u03b1\u03b9 \u03bd\u03b1 \u03c4\u03bf \u03ba\u03b1\u03c4\u03b5\u03b2\u03ac\u03c3\u03b5\u03c4\u03b5 \u03b1\u03c0\u03cc\u00a0<a href=\"https:\/\/avlos.gr\/wpress\/download\/\u03b5\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae\u03c2-pid-\u03c3\u03b5-\u03c3\u03b5\u03c1\u03b2\u03bf\u03ba\u03b9\u03bd\u03b7\u03c4\u03ae\u03c1\u03b5\u03c2\" target=\"_blank\" rel=\"noreferrer noopener\">\u03b5\u03b4\u03ce<\/a>.<\/p>\n\n\n\n<pre class=\"wp-block-code has-small-font-size\"><code>\/********************************************************\n* Author : Manolis Aristovoulidis\n* \u03a4\u03bf \u03c0\u03c1\u03cc\u03b3\u03c1\u03b1\u03bc\u03bc\u03b1 \u03b1\u03c5\u03c4\u03cc \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03b5\u03af \u03ad\u03bd\u03b1\u03bd \u03b1\u03b9\u03c3\u03b8\u03b7\u03c4\u03ae\u03c1\u03b1 \u03ba\u03af\u03bd\u03b7\u03c3\u03b7\u03c2 MPU-9250, \n* \u03b4\u03cd\u03bf \u03c3\u03b5\u03c1\u03b2\u03bf\u03ba\u03b9\u03bd\u03b7\u03c4\u03ae\u03c1\u03b5\u03c2 \u03ba\u03b1\u03b9 \u03ad\u03bb\u03b5\u03b3\u03c7\u03bf PID \u03c3\u03c4\u03b7\u03bd \u03ba\u03af\u03bd\u03b7\u03c3\u03b7 \u03c4\u03c9\u03bd \u03c3\u03b5\u03c1\u03b2\u03bf\u03ba\u03b9\u03bd\u03b7\u03c4\u03ae\u03c1\u03c9\u03bd.\n* \u039c\u03b5 \u03c4\u03b7 \u03bb\u03b5\u03b9\u03c4\u03bf\u03c5\u03c1\u03b3\u03af\u03b1 \u03c4\u03bf\u03c5 \u03c0\u03c1\u03bf\u03b3\u03c1\u03ac\u03bc\u03bc\u03b1\u03c4\u03bf\u03c2 \u03bf\u03b9\u03c3\u03b5\u03c1\u03b2\u03bf\u03ba\u03b9\u03bd\u03b7\u03c4\u03ae\u03c1\u03b5\u03c2 \u03ba\u03c1\u03b1\u03c4\u03bf\u03c5\u03bd \u03c0\u03ac\u03bd\u03c4\u03b1 \u03c3\u03b5\n* \u03bf\u03c1\u03b9\u03b6\u03cc\u03bd\u03c4\u03b9\u03b1 \u03b8\u03ad\u03c3\u03b7 \u03c4\u03bf\u03bd \u03b1\u03b9\u03c3\u03b8\u03b7\u03c4\u03ae\u03c1\u03b1 \u03cc\u03c0\u03c9\u03c2 \u03ba\u03b1\u03b9 \u03bd\u03b1 \u03c0\u03b5\u03c1\u03b9\u03c3\u03c4\u03c1\u03ad\u03c8\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b7 \u03b2\u03ac\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03ba\u03b1\u03c4\u03b1\u03c3\u03ba\u03b5\u03c5\u03ae\u03c2\n* \n* This program uses an MPU-9250 motion sensor,\n* two servomotors and PID control in servomotors.\n* With the operation of the program, motors always keep on\n* position the sensor horizontally as well as rotate the base of the construction\n* Date : 27\/11\/2021\n* \n ********************************************************\/\n#include &lt;Wire.h&gt;\n#include &lt;MPU9250.h&gt;\n#include &lt;Servo.h&gt;\n#include &lt;PID_v1.h&gt;\n\nServo servo_x;      \/\/ \u03b4\u03b7\u03bc\u03b9\u03bf\u03c5\u03c1\u03b3\u03af\u03b1 \u03b5\u03bd\u03cc\u03c2 servo object \u03b3\u03b9\u03b1 \u03c4\u03bf\u03bd \u03ad\u03bb\u03b5\u03b3\u03c7\u03bf \u03c4\u03bf\u03c5 servo\nServo servo_y;      \/\/ creating a servo object to control the servo\n\nint val_x = 100;     \/\/ \u0391\u03c1\u03c7\u03b9\u03ba\u03ae \u03b3\u03c9\u03bd\u03b9\u03b1 \u03b3\u03b9\u03b1 \u03c4\u03bf servo_x    Home corner for servo_x\nint val_y = 100;    \/\/ \u0391\u03c1\u03c7\u03b9\u03ba\u03ae \u03b3\u03c9\u03bd\u03b9\u03b1 \u03b3\u03b9\u03b1 \u03c4\u03bf servo_y    Home corner for servo_y\n\n \/\/ an MPU9250 object with the MPU-9250 sensor on I2C bus 0 with address 0x68\n MPU9250 IMU(Wire,0x68);\n \nint status;\n\n \/\/Acc Variables\n\nfloat rad_to_deg = 180\/3.141592654;           \/\/\u0391\u03c5\u03c4\u03ae \u03b7 \u03c4\u03b9\u03bc\u03ae \u03b5\u03af\u03bd\u03b1\u03b9 \u03b3\u03b9\u03b1 \u03c4\u03b7 \u03bc\u03b5\u03c4\u03b1\u03c4\u03c1\u03bf\u03c0\u03ae \u03b1\u03ba\u03c4\u03b9\u03bd\u03af\u03c9\u03bd \u03c3\u03b5 \u03bc\u03bf\u03af\u03c1\u03b5\u03c2\nfloat Acc_rawX, Acc_rawY, Acc_rawZ;           \/\/\u0395\u03b4\u03ce \u03b1\u03c0\u03bf\u03b8\u03b7\u03ba\u03b5\u03cd\u03bf\u03c5\u03bc\u03b5 \u03b1\u03bd\u03b5\u03c0\u03b5\u03be\u03ad\u03c1\u03b3\u03b1\u03c3\u03c4\u03b1 \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03b1 \u03b1\u03c0\u03cc \u03c4\u03bf \u03b5\u03c0\u03b9\u03c4\u03b1\u03c7\u03c5\u03bd\u03c3\u03b9\u03cc\u03bc\u03b5\u03c4\u03c1\u03bf\nfloat Acc_angle_x, Acc_angle_y;               \/\/\u0395\u03b4\u03ce \u03b1\u03c0\u03bf\u03b8\u03b7\u03ba\u03b5\u03cd\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b9\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03b3\u03c9\u03bd\u03af\u03b1\u03c2 \u03c0\u03bf\u03c5 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03af\u03c3\u03b1\u03bc\u03b5 \u03b3\u03b9\u03b1 \u03c4\u03bf \u03b5\u03c0\u03b9\u03c4\u03b1\u03c7\u03c5\u03bd\u03c3\u03b9\u03cc\u03bc\u03b5\u03c4\u03c1\u03bf\nfloat SUp_Acc_angle_x, SUp_Acc_angle_y;        \/\/SetUp angles\nfloat Gyr_rawX, Gyr_rawY, Gyr_rawZ;           \/\/\u0395\u03b4\u03ce \u03b1\u03c0\u03bf\u03b8\u03b7\u03ba\u03b5\u03cd\u03bf\u03c5\u03bc\u03b5 \u03b1\u03bd\u03b5\u03c0\u03b5\u03be\u03ad\u03c1\u03b3\u03b1\u03c3\u03c4\u03b1 \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03b1 \u03b1\u03c0\u03cc \u03c4\u03bf \u03b3\u03c5\u03c1\u03bf\u03c3\u03ba\u03cc\u03c0\u03b9\u03bf\nfloat Gyro_angle_x, Gyro_angle_y;             \/\/\u0395\u03b4\u03ce \u03b1\u03c0\u03bf\u03b8\u03b7\u03ba\u03b5\u03cd\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b9\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03b3\u03c9\u03bd\u03af\u03b1\u03c2 \u03c0\u03bf\u03c5 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03af\u03c3\u03b1\u03bc\u03b5 \u03b3\u03b9\u03b1 \u03c4\u03bf \u03b3\u03c5\u03c1\u03bf\u03c3\u03ba\u03cc\u03c0\u03b9\u03bf\n\nfloat Total_angle_x, Total_angle_y;           \/\/\u0395\u03b4\u03ce \u03b1\u03c0\u03bf\u03b8\u03b7\u03ba\u03b5\u03cd\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b9\u03c2 \u03c4\u03b5\u03bb\u03b9\u03ba\u03b5\u03c2 \u03bf\u03bb\u03b9\u03ba\u03ad\u03c2 \u03b3\u03c9\u03bd\u03af\u03b5\u03c2\nfloat elapsedTime, timeNow, timePrev;         \/\/\u039c\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ad\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03bf\u03bd \u03ad\u03bb\u03b5\u03b3\u03c7\u03bf \u03c7\u03c1\u03cc\u03bd\u03bf\u03c5\n\n\n\/\/\u039a\u03b1\u03b8\u03bf\u03c1\u03af\u03b6\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b9\u03c2 \u03bc\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ad\u03c2 \u03c0\u03bf\u03c5 \u03b8\u03b1 \u03c3\u03c5\u03bd\u03b4\u03b5\u03b8\u03bf\u03cd\u03bd \u03bc\u03b5 \u03c4\u03b1 \u03b1\u03bd\u03c4\u03b9\u03ba\u03b5\u03af\u03bc\u03b5\u03bd\u03b1 PID_x \u03ba\u03b1\u03b9 PID_y\ndouble Setpoint_x, Input_x, Output_x;\ndouble Setpoint_y, Input_y, Output_y;\n\n\/\/\u039a\u03b1\u03b8\u03bf\u03c1\u03af\u03b6\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b9\u03c2 \u03b1\u03c1\u03c7\u03b9\u03ba\u03ad\u03c2 \u03c0\u03b1\u03c1\u03b1\u03bc\u03ad\u03c4\u03c1\u03bf\u03c5\u03c2 \u03c3\u03c5\u03bd\u03c4\u03bf\u03bd\u03b9\u03c3\u03bc\u03bf\u03cd\ndouble x_Kp=2.0, x_Ki=0.5, x_Kd=0.01;\ndouble y_Kp=2.0, y_Ki=0.5, y_Kd=0.01;\n\n\/\/\u0394\u03b7\u03bc\u03b9\u03bf\u03c5\u03c1\u03b3\u03bf\u03cd\u03bc\u03b5 \u03c4\u03b1 \u03b1\u03bd\u03c4\u03b9\u03ba\u03b5\u03af\u03bc\u03b5\u03bd\u03b1 PID\nPID PID_x(&amp;Input_x, &amp;Output_x, &amp;Setpoint_x, x_Kp, x_Ki, x_Kd, DIRECT);\nPID PID_y(&amp;Input_y, &amp;Output_y, &amp;Setpoint_y, y_Kp, y_Ki, y_Kd, DIRECT);\n\nvoid setup()\n{\n  Serial.begin(115200);\n  while(!Serial) {}\n\n    servo_x.attach(4);    \/\/\u03ba\u03ac\u03bd\u03b5\u03b9 \u03c0\u03c1\u03bf\u03c3\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7 \u03c4\u03bf\u03c5 servo \u03c3\u03c4\u03bf pin 4 \u03c4\u03bf\u03c5 servo object \/\/ attachs the servo to pin 4 of the servo object\n    servo_y.attach(5);    \/\/\u03ba\u03ac\u03bd\u03b5\u03b9 \u03c0\u03c1\u03bf\u03c3\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7 \u03c4\u03bf\u03c5 servo \u03c3\u03c4\u03bf pin 5 \u03c4\u03bf\u03c5 servo object \/\/ attachs the servo to pin 5 of the servo object\n  \n    \/\/\u03c0\u03b5\u03c1\u03b9\u03c3\u03c4\u03bf\u03c6\u03ae \u03c4\u03c9\u03bd \u03c3\u03b5\u03c1\u03b2\u03bf\u03ba\u03b9\u03bd\u03b7\u03c4\u03ae\u03c1\u03c9\u03bd\n    servo_x.write(val_x);   \/\/\u039c\u03b5\u03c4\u03ac \u03b1\u03c0\u03cc \u03c0\u03b5\u03b9\u03c1\u03b1\u03bc\u03b1\u03c4\u03b9\u03c3\u03bc\u03bf\u03cd\u03c2 \u03b1\u03c5\u03c4\u03ae \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7      \/\/After experimentation this is\n    servo_y.write(val_y);   \/\/\u03bf\u03c1\u03b9\u03b6\u03cc\u03bd\u03c4\u03b9\u03b1 \u03b8\u03ad\u03c3\u03b7 \u03b3\u03b9\u03b1 \u03c4\u03b7 \u03b2\u03ac\u03c3\u03b7 \u03c4\u03bf\u03c5 MPU9250    \/\/ horizontal position for the MPU9250 base\n\n    delay(1000);\n\n    \/\/ start communication with IMU\n    status = IMU.begin();\n    if (status &lt; 0) {\n      Serial.println(\"IMU initialization unsuccessful\");\n      Serial.println(\"Check IMU wiring or try cycling power\");\n      Serial.print(\"Status: \");\n      Serial.println(status);\n      while(1) {}\n    }\n  \/* Default values of MPU9250\n   * accel range to 16G as default \n   * gyro range to 2000DPS as default\n   * bandwidth to 184Hz as default\n   * sample rate divider to 0 as default\n   *\n   *\/\n   delay(3000);\n\n    IMU.readSensor();\n    Acc_rawX = IMU.getAccelX_mss();\n    Acc_rawY = IMU.getAccelY_mss();\n    Acc_rawZ = IMU.getAccelZ_mss();\n\n    \n      \n    \/*---Y---*\/\n    SUp_Acc_angle_x = (atan((Acc_rawY)\/sqrt(pow((Acc_rawX),2) + pow((Acc_rawZ),2)))*rad_to_deg) ;\n    \/*---Y---*\/\n    SUp_Acc_angle_y = (atan(-1*(Acc_rawX)\/sqrt(pow((Acc_rawY),2) + pow((Acc_rawZ),2)))*rad_to_deg) ;  \n  \n  \/\/Input_x = 0.0;\n  Input_x = SUp_Acc_angle_x;\n  Setpoint_x = SUp_Acc_angle_x;\n  \/\/Setpoint_x = 0.0;\n\n  \/\/Input_y = 0.0;\n  \/\/Setpoint_y = 0.0;\n  Input_y = SUp_Acc_angle_y;\n  Setpoint_y = SUp_Acc_angle_y;\n\n  double mini = -90;\n  double maxi = 90;\n  PID_x.SetOutputLimits(mini, maxi);  \/\/\u03bf\u03c1\u03af\u03b6\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b1 \u03cc\u03c1\u03b9\u03b1 \u03b5\u03bb\u03ac\u03c7\u03b9\u03c3\u03c4\u03b7\u03c2 - \u03bc\u03ad\u03b3\u03b9\u03c3\u03c4\u03b7\u03c2 \u03c4\u03b9\u03bc\u03ae\u03c2 \u03c0\u03bf\u03c5 \n  PID_y.SetOutputLimits(mini, maxi);  \/\/\u03b8\u03b1 \u03bc\u03b1\u03c2 \u03b5\u03c0\u03b9\u03c3\u03c4\u03c1\u03ad\u03c6\u03b5\u03b9 \u03bf \u03bc\u03b7\u03c7\u03b1\u03bd\u03b9\u03c3\u03bc\u03cc\u03c2 \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5 PID\n  \/\/turn the PID on\n  PID_x.SetMode(AUTOMATIC);\n  PID_y.SetMode(AUTOMATIC);\n}\n\nvoid loop()\n{\n  timePrev = timeNow;  \/\/ \u03b7 \u03c0\u03c1\u03bf\u03b7\u03b3\u03bf\u03cd\u03bc\u03b5\u03bd\u03b7 \u03ce\u03c1\u03b1 \u03b1\u03c0\u03bf\u03b8\u03b7\u03ba\u03b5\u03cd\u03b5\u03c4\u03b1\u03b9 \u03c0\u03c1\u03b9\u03bd \u03b4\u03b9\u03b1\u03b2\u03ac\u03c3\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b7\u03bd \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03ce\u03c1\u03b1\n  timeNow = millis();  \/\/ \u0391\u03bd\u03ac\u03b3\u03bd\u03c9\u03c3\u03b7 \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae\u03c2 \u03ce\u03c1\u03b1\u03c2\n  elapsedTime = (timeNow - timePrev) \/ 1000;  \n  \n  IMU.readSensor();\n  Acc_rawX = IMU.getAccelX_mss();\n  Acc_rawY = IMU.getAccelY_mss();\n  Acc_rawZ = IMU.getAccelZ_mss();\n\n  Gyr_rawX=IMU.getGyroX_rads();     \n  Gyr_rawY=IMU.getGyroY_rads();\n\n  \/*---Y---*\/\n  Acc_angle_x = (atan((Acc_rawY)\/sqrt(pow((Acc_rawX),2) + pow((Acc_rawZ),2)))*rad_to_deg) ;\n  \/*---Y---*\/\n  Acc_angle_y = (atan(-1*(Acc_rawX)\/sqrt(pow((Acc_rawY),2) + pow((Acc_rawZ),2)))*rad_to_deg) ;  \n\n  Gyro_angle_x = Gyr_rawX*elapsedTime;\n  \/*---X---*\/\n  Gyro_angle_y = Gyr_rawY*elapsedTime;\n\n  \n  Total_angle_x = 0.98 *(Total_angle_x + Gyro_angle_x) + 0.02*Acc_angle_x;\n  Total_angle_y = 0.98 *(Total_angle_y + Gyro_angle_y) + 0.02*Acc_angle_y;\n  \n  Input_x = Total_angle_x;\n  Input_y = Total_angle_y;\n     \n  PID_x.Compute();\n  PID_y.Compute();\n  \n  servo_x.write(Output_x + val_x );        \/\/ \u03c1\u03c5\u03b8\u03bc\u03af\u03b6\u03b5\u03b9 \u03c4\u03b7 \u03b8\u03ad\u03c3\u03b7 \u03c4\u03bf\u03c5 servo \u03c3\u03c4\u03b7\u03bd \u03c4\u03b9\u03bc\u03ae \u03c4\u03b7\u03c2 \u03ba\u03bb\u03af\u03bc\u03b1\u03ba\u03b1\u03c2\n  servo_y.write(val_y - Output_y); \n  \/\/Serial.print(Input_x);                   \/\/ \u03b5\u03ba\u03c4\u03c5\u03c0\u03ce\u03c3\u03b5\u03b9\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03c0\u03b1\u03c1\u03b1\u03ba\u03bf\u03bb\u03bf\u03cd\u03b8\u03b7\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03bc\u03b7\u03c7\u03b1\u03bd\u03b9\u03c3\u03bc\u03bf\u03cd \u03c3\u03b5 \u03bb\u03b5\u03b9\u03c4\u03bf\u03c5\u03c1\u03b3\u03af\u03b1 \n  \/\/Serial.print(\",\");\n  \/\/Serial.println(Input_y);\n  delay(40);\n}\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>\u0395\u03b9\u03c3\u03b1\u03b3\u03c9\u03b3\u03ae \u039f \u0395\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae\u03c2 PID \u03ae \u03b1\u03bb\u03bb\u03b9\u03ce\u03c2 \u03b5\u03bb\u03b5\u03b3\u03ba\u03c4\u03ae\u03c2 \u03c4\u03c1\u03b9\u03ce\u03bd \u03cc\u03c1\u03c9\u03bd, \u03b5\u03af\u03bd\u03b1\u03b9 \u03ad\u03bd\u03b1 \u03b1\u03bd\u03b1\u03bb\u03bf\u03b3\u03b9\u03ba\u03cc &#8211; \u03bf\u03bb\u03bf\u03ba\u03bb\u03b7\u03c1\u03c9\u03c4\u03b9\u03ba\u03cc &#8211; \u03c0\u03b1\u03c1\u03ac\u03b3\u03c9\u03b3\u03bf (Proportional\u2013Integral\u2013Derivative ) \u03c3\u03cd\u03c3\u03c4\u03b7\u03bc\u03b1 \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5. \u0395\u03af\u03bd\u03b1\u03b9 \u03ad\u03bd\u03b1\u03c2 \u03bc\u03b7\u03c7\u03b1\u03bd\u03b9\u03c3\u03bc\u03cc\u03c2 \u03b2\u03c1\u03cc\u03c7\u03bf\u03c5 \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5 \u03c0\u03bf\u03c5 \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03b5\u03af \u03b1\u03bd\u03ac\u03b4\u03c1\u03b1\u03c3\u03b7. \u03a7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03b5\u03af\u03c4\u03b1\u03b9 \u03b5\u03c5\u03c1\u03ad\u03c9\u03c2 \u03c3\u03b5 \u03b2\u03b9\u03bf\u03bc\u03b7\u03c7\u03b1\u03bd\u03b9\u03ba\u03ac \u03c3\u03c5\u03c3\u03c4\u03ae\u03bc\u03b1\u03c4\u03b1 \u03b5\u03bb\u03ad\u03b3\u03c7\u03bf\u03c5 \u03ba\u03b1\u03b9 \u03c3\u03b5 \u03bc\u03b9\u03b1 \u03c0\u03bf\u03b9\u03ba\u03b9\u03bb\u03af\u03b1 \u03ac\u03bb\u03bb\u03c9\u03bd \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ce\u03bd&hellip; 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