{"id":890,"date":"2020-06-05T20:56:15","date_gmt":"2020-06-05T20:56:15","guid":{"rendered":"https:\/\/garikoitz.info\/blog\/?p=890"},"modified":"2023-10-19T20:21:22","modified_gmt":"2023-10-19T20:21:22","slug":"sintonizar-pid-con-arduino-ii-balancin-simple","status":"publish","type":"post","link":"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/","title":{"rendered":"Sintonizar PID con Arduino &#8211; Balanc\u00edn simple"},"content":{"rendered":"\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">\u00cdndice<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Alternar tabla de contenidos\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#Introduccion\" >Introducci\u00f3n<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#Sistema_empleado\" >Sistema empleado<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#Componentes\" >Componentes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#Esquema_de_conexiones\" >Esquema de conexiones<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#Codigo_de_Arduino\" >C\u00f3digo de Arduino<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#Identificacion_del_sistema\" >Identificaci\u00f3n del sistema<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#Adecuando_la_senal_del_sensor\" >Adecuando la se\u00f1al del sensor<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#Recopilacion_de_datos_en_lazo_abierto\" >Recopilaci\u00f3n de datos en lazo abierto<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#Facilidad_de_control\" >Facilidad de control<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#Ajuste_y_simulacion_en_lazo_cerrado\" >Ajuste y simulaci\u00f3n en lazo cerrado<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#Resultados\" >Resultados<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#CC-25_PI\" >CC-25 (PI)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#CC-25_PI-D\" >CC-25 (PI-D)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#CC-10_PI\" >CC-10 (PI)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#CC-10_PI-D\" >CC-10 (PI-D)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#CC-10_I-P\" >CC-10 (I-P)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#CC-10_I-PD\" >CC-10 (I-PD)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#IAE-SP_PI\" >IAE-SP (PI)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#IAE-SP_PI-D\" >IAE-SP (PI-D)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#LAMBDA_PI\" >LAMBDA (PI)<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#Conclusiones\" >Conclusiones<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#Descargas\" >Descargas<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#Referencias\" >Referencias<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#Enlaces\" >Enlaces<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/#Libros_y_publicaciones\" >Libros y publicaciones<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Introduccion\"><\/span>Introducci\u00f3n<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Aqu\u00ed ten\u00e9is la segunda entrega sobre sintonizaci\u00f3n PID. <a rel=\"noreferrer noopener\" href=\"https:\/\/garikoitz.info\/blog\/?p=638\" target=\"_blank\">En la primera entrega<\/a> vimos un control de temperatura y en esta veremos un control de posici\u00f3n de un balanc\u00edn simple.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Sistema_empleado\"><\/span>Sistema empleado<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<div class=\"wp-block-media-text alignwide is-stacked-on-mobile\"><figure class=\"wp-block-media-text__media\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/06\/esquema_balanc\u00edn.png\"><img loading=\"lazy\" decoding=\"async\" width=\"426\" height=\"202\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/06\/esquema_balanc\u00edn.png\" alt=\"\" class=\"wp-image-898 size-full\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/06\/esquema_balanc\u00edn.png 426w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/06\/esquema_balanc\u00edn-300x142.png 300w\" sizes=\"auto, (max-width: 426px) 100vw, 426px\" \/><\/a><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"wp-block-paragraph\">Se trata de un balanc\u00edn simple con inclinaci\u00f3n en un solo eje,  que consta de un motor de corriente continua con h\u00e9lice y un giroscopio \/ aceler\u00f3metro que har\u00e1 de sensor para calcular la inclinaci\u00f3n.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">La maqueta est\u00e1 hecha con ca\u00f1a de bamb\u00fa y madera y consta de solo 2 componentes principales, el motor de corriente continua y el aceler\u00f3metro. El motor de corriente continua es de 5V pero necesita una fuente de alimentaci\u00f3n externa ya que consume entre 750mA y 1,8A. <\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/06\/IMG_20200605_230322-1-scaled.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/06\/IMG_20200605_230322-1-1024x768.jpg\" alt=\"\" class=\"wp-image-925\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/06\/IMG_20200605_230322-1-1024x768.jpg 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/06\/IMG_20200605_230322-1-300x225.jpg 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/06\/IMG_20200605_230322-1-768x576.jpg 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/06\/IMG_20200605_230322-1-1536x1152.jpg 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/06\/IMG_20200605_230322-1-2048x1536.jpg 2048w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/06\/IMG_20200605_230322-1-360x270.jpg 360w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">maqueta del balanc\u00edn<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">El objetivo es mediante un controlador PID situar el balanc\u00edn en el \u00e1ngulo de inclinaci\u00f3n deseado. Nos movemos en un rango de entre 30 y -30\u00ba.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/06\/Esquema_control_balanc\u00edn.png\"><img loading=\"lazy\" decoding=\"async\" width=\"423\" height=\"344\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/06\/Esquema_control_balanc\u00edn.png\" alt=\"\" class=\"wp-image-909\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/06\/Esquema_control_balanc\u00edn.png 423w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/06\/Esquema_control_balanc\u00edn-300x244.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/06\/Esquema_control_balanc\u00edn-332x270.png 332w\" sizes=\"auto, (max-width: 423px) 100vw, 423px\" \/><\/a><figcaption class=\"wp-element-caption\">Esquema de control<\/figcaption><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Componentes\"><\/span>Componentes<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a rel=\"noreferrer noopener\" href=\"https:\/\/store.arduino.cc\/arduino-uno-rev3\" target=\"_blank\">Arduino UNO R3<\/a><\/li>\n\n\n\n<li><a rel=\"noreferrer noopener\" href=\"https:\/\/www.amazon.es\/s?k=MPU6050&amp;__mk_es_ES=%C3%85M%C3%85%C5%BD%C3%95%C3%91&amp;ref=nb_sb_noss\" target=\"_blank\">Sensor acelerador + giroscopio MPU6050 (GY-521)<\/a><\/li>\n\n\n\n<li><a rel=\"noreferrer noopener\" href=\"https:\/\/www.amazon.es\/s?k=L9110&amp;__mk_es_ES=%C3%85M%C3%85%C5%BD%C3%95%C3%91&amp;ref=nb_sb_noss\" target=\"_blank\">Motor CC (L9110 Keyes)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.amazon.es\/MicroInterruptor-Soldar-Protoboard-interruptor-Unidades\/dp\/B07RCVFH4Q\/ref=sr_1_1?__mk_es_ES=%C3%85M%C3%85%C5%BD%C3%95%C3%91&amp;dchild=1&amp;keywords=interruptor+protoboard&amp;qid=1600978444&amp;sr=8-1\" target=\"_blank\" rel=\"noreferrer noopener\">Microinterruptor<\/a>*<\/li>\n\n\n\n<li><a href=\"https:\/\/www.amazon.es\/Potenci%C3%B3metro-5Pack-100K-OHM-Terminal\/dp\/B073PQ2G82\/ref=sr_1_5?__mk_es_ES=%C3%85M%C3%85%C5%BD%C3%95%C3%91&amp;dchild=1&amp;keywords=potenciometro+10k&amp;qid=1600978530&amp;sr=8-5\" target=\"_blank\" rel=\"noreferrer noopener\">Potenci\u00f3metro de 10K<\/a>**<\/li>\n\n\n\n<li>Una resistencia de 220 ohm<\/li>\n\n\n\n<li>Una fuente externa de 5 voltios<\/li>\n\n\n\n<li>Cables dupont para el conexionado<\/li>\n\n\n\n<li>Una mini protoboard<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">* El microinterruptor nos sirve para conmutar entre Autom\u00e1tico y Manual.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">** En <strong>manual <\/strong>el potenci\u00f3metro altera la OP. En <strong>autom\u00e1tico <\/strong>altera el SP.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">El coste de los componentes es de aproximadamente 30-40\u20ac sin contar la fuente de alimentaci\u00f3n externa.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Esquema_de_conexiones\"><\/span>Esquema de conexiones<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/Esquema_conexiones_bb2.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"652\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/Esquema_conexiones_bb2-1024x652.png\" alt=\"\" class=\"wp-image-1163\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/Esquema_conexiones_bb2-1024x652.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/Esquema_conexiones_bb2-300x191.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/Esquema_conexiones_bb2-768x489.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/Esquema_conexiones_bb2-1536x977.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/Esquema_conexiones_bb2-2048x1303.png 2048w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/Esquema_conexiones_bb2-424x270.png 424w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Conexiones del sistema<\/figcaption><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Codigo_de_Arduino\"><\/span>C\u00f3digo de Arduino<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Notas:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Para evitar problemas y errores se han convertido a porcentaje todas las variables.<\/li>\n\n\n\n<li>Para la conversi\u00f3n de rangos con decimales se ha implementado la funci\u00f3n <strong>MAPF<\/strong>, ya que la funci\u00f3n <strong>MAP <\/strong>nativa de Arduino devuelve simplemente un long integer.<\/li>\n<\/ul>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"cpp\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">\/***************************************************************\n* Desarrollado por Garikoitz Mart\u00ednez [garikoitz.info] [06\/2020]\n* https:\/\/garikoitz.info\/blog\/?p=890\n***************************************************************\/\n\/***************************************************************\n* Librer\u00edas\n***************************************************************\/\n#include \"I2Cdev.h\"\n#include \"MPU6050.h\"\n#include &lt;Wire.h>\n#include &lt;PID_v1.h>\n\/***************************************************************\n* Variables\n***************************************************************\/\n  \/\/H\u00e9lice\n  const int INA = 10; \/\/Motor Forward\n  const int INB = 11; \/\/Motor Reverse\n  const int Interruptor = 12;\n  const int pot = 0;                                                                                \/\/Potenci\u00f3metro en pin A0\n  unsigned long previousMillis = 0;\n  int Ts = 100; \/\/Sample time 100ms\n  \/\/Girosc\u00f3pio\n  const int mpuAddress = 0x68;  \/\/Puede ser 0x68 o 0x69\n  MPU6050 mpu(mpuAddress);\n  \/\/Offsets de calibraci\u00f3n\n  #define MPU6050_ACCEL_OFFSET_X -2936\n  #define MPU6050_ACCEL_OFFSET_Y 1412\n  #define MPU6050_ACCEL_OFFSET_Z 962\n  #define MPU6050_GYRO_OFFSET_X  58\n  #define MPU6050_GYRO_OFFSET_Y  85\n  #define MPU6050_GYRO_OFFSET_Z  15\n  int ax, ay, az;\n  int gx, gy, gz;\n  float ang_x, ang_y;\n  float ang_x_prev, ang_y_prev;\n  long tiempo_prev;\n  float dt;\n  \/\/Control PID\n  boolean modo = false; \/\/false=auto true=manual\n  float tmp = 0;\n  float tmp_ant = 0;\n  float OP = 0;\n  double SetpointP, InputP, OutputP;\n  double Kp=6, Ki=3, Kd=2;\n  PID myPID(&amp;InputP, &amp;OutputP, &amp;SetpointP, Kp, Ki, Kd,P_ON_E, DIRECT);    \/\/PI-D\n  \/\/PID myPID(&amp;InputP, &amp;OutputP, &amp;SetpointP, Kp, Ki, Kd,P_ON_M, DIRECT);  \/\/I-PD\n\/***************************************************************\n* SETUP\n***************************************************************\/\nvoid setup() \n{ \n  \/\/H\u00e9lice\n  pinMode(INA,OUTPUT); \n  pinMode(INB,OUTPUT); \n  pinMode(Interruptor, INPUT);\n  \/\/PID \n  myPID.SetSampleTime(50);        \/\/PID calcula cada 50ms. Por defecto es cada 100ms.\n  myPID.SetOutputLimits(0, 100);\n  myPID.SetMode(MANUAL);\n  \/\/Girosc\u00f3pio\n  mpu.initialize();\n  \/\/Calibraci\u00f3n\n  mpu.setXAccelOffset(MPU6050_ACCEL_OFFSET_X);\n  mpu.setYAccelOffset(MPU6050_ACCEL_OFFSET_Y);\n  mpu.setZAccelOffset(MPU6050_ACCEL_OFFSET_Z);\n  mpu.setXGyroOffset(MPU6050_GYRO_OFFSET_X);\n  mpu.setYGyroOffset(MPU6050_GYRO_OFFSET_Y);\n  mpu.setZGyroOffset(MPU6050_GYRO_OFFSET_Z);\n  Serial.println(mpu.testConnection() ? F(\"IMU iniciado correctamente\") : F(\"Error al iniciar IMU\"));\n  Serial.begin(9600);\n}\n\/***************************************************************\n* BUCLE PRINCIPAL\n***************************************************************\/\nvoid loop() \n{\n  if (millis() - previousMillis > Ts) \n  {\n    previousMillis = millis();\n    if (digitalRead(12) == HIGH){\n      modo=true;\/\/Manual\n      myPID.SetMode(MANUAL);\n    }else{\n      digitalWrite(INB ,LOW);\n      analogWrite(INA,OP);   \/\/Forward\n      modo=false;\/\/Autom\u00e1tico\n      myPID.SetMode(AUTOMATIC);\n    }\n    mpu.getAcceleration(&amp;ax, &amp;ay, &amp;az);\n    mpu.getRotation(&amp;gx, &amp;gy, &amp;gz);\n    \/\/Calcular los \u00e1ngulos con acelerometro\n    double accel_ang_x=atan(ay\/sqrt(pow(ax,2) + pow(az,2)))*(180.0\/3.14);\n    double accel_ang_y=atan(-ax\/sqrt(pow(ay,2) + pow(az,2)))*(180.0\/3.14);\n    dt = (millis()-tiempo_prev)\/1000.0;\n    tiempo_prev=millis();\n    \/\/\u00c1ngulo de rotaci\u00f3n y filtro complementario \n    ang_x = 0.98*(ang_x_prev+(gx\/131)*dt) + 0.02*accel_ang_x;\n    ang_x_prev=ang_x;\n    \/\/\n    \/***************************************************************\n    * Modo MANUAL - Potenci\u00f3metro ---> PWM Motor CC\n    ***************************************************************\/\n    if (modo==true){\n      SetpointP=0;\n      \/\/Leo el sensor\n      InputP = mapf(ang_x, -30, 30, 0, 100);          \/\/Filtro complementario\n      \/\/Leo el potenci\u00f3metro\n      \/\/Evitar saltos del 0.85% al leer el potenci\u00f3metro\n      tmp = analogRead(pot);\n      tmp = mapf(tmp, 0, 1023, 0, 100);\n      if(abs(tmp-tmp_ant)>0.85){\n        OP = tmp;\n      }\n      tmp_ant=OP;\n      digitalWrite(INB ,LOW);\n      analogWrite(INA,OP\/0.392156);   \/\/FORWARD 0-100 a 0-255 para PWM\n      \/***************************************************************\n      * DEBUG PUERTO SERIE (Para Arduino COM Plotter)\n      ***************************************************************\/\n      Serial.print(\"#\");             \/\/Char inicio\n      Serial.print(SetpointP,0);     \/\/SP\n      Serial.write(\" \");             \/\/Char separador\n      Serial.print(InputP,3);        \/\/PV\n      Serial.write(\" \");             \/\/Char separador\n      Serial.print(OP,0);            \/\/OP\n      Serial.println();\n    }\n    \/***************************************************************\n    * Modo AUTOM\u00c1TICO - PID\n    ***************************************************************\/\n    if (modo==false){\n      tmp = analogRead(pot);\n      tmp = mapf(tmp, 0, 1023, 0, 100);\n      \/\/Evitar saltos del 0.85% al leer el potenci\u00f3metro\n      if(abs(tmp-tmp_ant)>0.85){\n        SetpointP = tmp;\n      }\n      tmp_ant=SetpointP;\n      InputP = mapf(ang_x, -30, 30, 0, 100);\n      myPID.Compute();\n      digitalWrite(INB ,LOW);\n      analogWrite(INA,OutputP\/0.392156); \/\/FORWARD 0-100 a 0-255 para PWM\n      \/***************************************************************\n      * DEBUG PUERTO SERIE (Para Arduino COM Plotter)\n      ***************************************************************\/\n      Serial.print(\"#\");                \/\/Char inicio\n      Serial.print(SetpointP,0);        \/\/SP\n      Serial.write(\" \");                \/\/Char separador\n      Serial.print(InputP,3);           \/\/PV\n      Serial.write(\" \");                \/\/Char separador\n      Serial.print(OutputP,0);          \/\/OP\n      Serial.println();\n    }\n  }\n}\n\/***************************************************************\n* FUNCIONES\n***************************************************************\/\n\/\/Funci\u00f3n MAP adaptada a punto flotante.\ndouble mapf(double val, double in_min, double in_max, double out_min, double out_max) {\n    return (val - in_min) * (out_max - out_min) \/ (in_max - in_min) + out_min;\n}<\/pre>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Identificacion_del_sistema\"><\/span>Identificaci\u00f3n del sistema<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Adecuando_la_senal_del_sensor\"><\/span>Adecuando la se\u00f1al del sensor<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Del sensor recibimos 6 medidas, 3 aceleraciones y 3 velocidades angulares. Nosotros nos centraremos en las aceleraciones y en concreto en el \u00e1ngulo theta del eje X. No me explayo m\u00e1s ya que este sensor da para una entrada del blog completa, os dejo en referencias unos art\u00edculos para que juzgu\u00e9is vosotros mismos e indagu\u00e9is todas las posibilidades.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/Ang_balancin-1.png\"><img decoding=\"async\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/Ang_balancin-1.png\" alt=\"\" class=\"wp-image-1183\" style=\"width:350px;height:339px\"\/><\/a><figcaption class=\"wp-element-caption\">C\u00e1lculo del \u00e1ngulo Theta del eje x<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Las medidas resultantes del sensor son muy oscilantes y adem\u00e1s debemos tener en cuenta el \u00abdrift\u00bb generado al integrar la velocidad angular con respecto del tiempo para hallar el \u00e1ngulo deseado. La forma m\u00e1s sencilla de <em>minimizar <\/em>el drift es con un <a rel=\"noreferrer noopener\" href=\"https:\/\/sites.google.com\/site\/myimuestimationexperience\/filters\/complementary-filter\" target=\"_blank\">filtro complementario<\/a> y la m\u00e1s elegante con un <a rel=\"noreferrer noopener\" href=\"https:\/\/quantdare.com\/filtro-kalman\/\" target=\"_blank\">filtro de Kalman<\/a>. El filtro complementario combina el \u00e1ngulo calculado por el giroscopio con el \u00e1ngulo calculado por el aceler\u00f3metro pudiendo dar m\u00e1s peso a uno o a otro dependiendo de nuestras necesidades. El filtro de Kalman es mucho m\u00e1s complejo pero a cambio el resultado es bastante mejor. En la imagen inferior vemos que ambos filtros hacen bien su trabajo pero que el filtro de Kalman est\u00e1 afectando a la respuesta del sistema por lo que habr\u00eda que retocar los par\u00e1metros hasta encontrar los id\u00f3neos.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/Comparativa-filtros.png\"><img loading=\"lazy\" decoding=\"async\" width=\"986\" height=\"1024\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/Comparativa-filtros-986x1024.png\" alt=\"\" class=\"wp-image-1176\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/Comparativa-filtros-986x1024.png 986w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/Comparativa-filtros-289x300.png 289w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/Comparativa-filtros-768x798.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/Comparativa-filtros-1478x1536.png 1478w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/Comparativa-filtros-260x270.png 260w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/Comparativa-filtros.avif 1871w\" sizes=\"auto, (max-width: 986px) 100vw, 986px\" \/><\/a><figcaption class=\"wp-element-caption\"> Se\u00f1al RAW VS Filtro complementario VS Filtro de Kalman<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Hay que tener cierta precauci\u00f3n al utilizar filtros de cualquier tipo si lo que te planteas es hacer control con la se\u00f1al filtrada. El filtro nos da una se\u00f1al \u00ablimpia\u00bb pero a cambio el tiempo de respuesta es alterado. En resumen, cada caso requiere una reflexi\u00f3n que afectar\u00e1 a la sinton\u00eda de control.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por sencillez implementar\u00e9 un filtro complementario con la ecuaci\u00f3n 1 y con los par\u00e1metros \u03b1=0.98 y \u03b2=0.02.<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\begin{align}\n&amp; X = \\alpha \\left ( \\left (X-1  \\right )+\\omega_{giroscopio} \\ast dt  \\right )+\\beta\\left ( \\measuredangle \\hspace{0.1cm} acelerometro \\right )\\\\\n&amp; \\alpha +\\beta =1\n\\end{align}<\/pre><\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Recopilacion_de_datos_en_lazo_abierto\"><\/span>Recopilaci\u00f3n de datos en lazo abierto<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Con el interruptor en modo manual realizamos una serie de escalones para ver como reacciona el sensor con la ayuda de <a rel=\"noreferrer noopener\" href=\"https:\/\/garikoitz.info\/blog\/?p=674\" target=\"_blank\">ACP<\/a>.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_28_09_2020_23_32_15.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"298\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_28_09_2020_23_32_15-1024x298.png\" alt=\"\" class=\"wp-image-1191\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_28_09_2020_23_32_15-1024x298.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_28_09_2020_23_32_15-300x87.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_28_09_2020_23_32_15-768x224.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_28_09_2020_23_32_15-1536x447.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_28_09_2020_23_32_15-604x176.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_28_09_2020_23_32_15.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Step Test<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Introduciendo los datos en <a rel=\"noreferrer noopener\" href=\"https:\/\/garikoitz.info\/blog\/?p=674\" target=\"_blank\">ACP<\/a> de un escal\u00f3n representativo obtenemos las constantes del sistema que nos ayudar\u00e1n a simular y a ajustar nuestro controlador.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/2020-09-28_233115.png\"><img decoding=\"async\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/2020-09-28_233115.png\" alt=\"\" class=\"wp-image-1190\" style=\"width:296px;height:293px\"\/><\/a><figcaption class=\"wp-element-caption\">Constantes del sistema obtenidas con ACP<\/figcaption><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Facilidad_de_control\"><\/span>Facilidad de control<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">El cociente entre T0 y Tp nos sugiere la facilidad de control de un sistema. En este caso estamos en la zona f\u00e1cil ya que 1\/1,5=0,66.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/Facilidad_control_balancin.png\"><img decoding=\"async\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/Facilidad_control_balancin.png\" alt=\"\" class=\"wp-image-1257\"\/><\/a><figcaption class=\"wp-element-caption\">Facilidad de control<\/figcaption><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ajuste_y_simulacion_en_lazo_cerrado\"><\/span>Ajuste y simulaci\u00f3n en lazo cerrado<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">En la siguiente tabla tenemos las sinton\u00edas calculadas por ACP. ACP nos da Ti y Td pero la librer\u00eda de arduino utiliza Ki y Kd por lo que hay que realizar la siguiente conversi\u00f3n:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\begin{align}\n&amp; K_{i}=\\frac{K_{c}}{T_{i}} \\hspace{0.2cm};\\hspace{0.2cm} K_{d}={K_{c}}\\times {T_{d}}\n\\end{align}<\/pre><\/div>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/tabla-1.png\"><img decoding=\"async\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/tabla-1.png\" alt=\"\" class=\"wp-image-1243\"\/><\/a><figcaption class=\"wp-element-caption\">Sinton\u00edas calculadas por ACP<\/figcaption><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading has-text-align-left\"><span class=\"ez-toc-section\" id=\"Resultados\"><\/span>Resultados<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A continuaci\u00f3n veamos la respuesta de unas cuantas sinton\u00edas. El tiempo de muestreo es de 100ms.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"CC-25_PI\"><\/span>CC-25 (PI)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Como se aprecia en la imagen, un peque\u00f1o cambio en el punto de consigna hace que entre en oscilaci\u00f3n continua. Posiblemente en esta maqueta, un sobre pasamiento del 25% con una estrategia PI no sea adecuado.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_24_33.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"298\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_24_33-1024x298.png\" alt=\"\" class=\"wp-image-1201\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_24_33-1024x298.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_24_33-300x87.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_24_33-768x224.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_24_33-1536x447.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_24_33-604x176.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_24_33.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Respuesta real<\/figcaption><\/figure>\n<\/div>\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_11_23_31.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"276\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_11_23_31-1024x276.png\" alt=\"\" class=\"wp-image-1202\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_11_23_31-1024x276.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_11_23_31-300x81.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_11_23_31-768x207.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_11_23_31-1536x414.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_11_23_31-604x163.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_11_23_31.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Simulaci\u00f3n en lazo cerrado<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"CC-25_PI-D\"><\/span>CC-25 (PI-D)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Al incluir el t\u00e9rmino derivativo ganamos en estabilidad. Ya no entra en oscilaci\u00f3n continua aunque variemos el punto de consigna &gt;10%.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_52_34.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"298\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_52_34-1024x298.png\" alt=\"\" class=\"wp-image-1206\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_52_34-1024x298.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_52_34-300x87.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_52_34-768x224.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_52_34-1536x447.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_52_34-604x176.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_52_34.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Respuesta real<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_50_40.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"298\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_50_40-1024x298.png\" alt=\"\" class=\"wp-image-1204\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_50_40-1024x298.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_50_40-300x87.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_50_40-768x224.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_50_40-1536x447.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_50_40-604x176.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_11_50_40.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Respuesta real &#8211; Detalle de un cambio en el SP del 10%<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_11_51_26.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"276\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_11_51_26-1024x276.png\" alt=\"\" class=\"wp-image-1207\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_11_51_26-1024x276.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_11_51_26-300x81.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_11_51_26-768x207.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_11_51_26-1536x414.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_11_51_26-604x163.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_11_51_26.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Simulaci\u00f3n en lazo cerrado<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"CC-10_PI\"><\/span>CC-10 (PI)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">En esta ocasi\u00f3n con un sobrepasamiento del 10% la estrategia PI consigue mantenerse estable aunque la respuesta no es igual a la simulaci\u00f3n.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_06_57.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"298\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_06_57-1024x298.png\" alt=\"\" class=\"wp-image-1209\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_06_57-1024x298.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_06_57-300x87.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_06_57-768x224.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_06_57-1536x447.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_06_57-604x176.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_06_57.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Respuesta real<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_08_47.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"298\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_08_47-1024x298.png\" alt=\"\" class=\"wp-image-1210\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_08_47-1024x298.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_08_47-300x87.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_08_47-768x224.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_08_47-1536x447.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_08_47-604x176.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_08_47.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Respuesta real &#8211; Detalle de un cambio en el SP del 5%<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_12_08_50.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"276\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_12_08_50-1024x276.png\" alt=\"\" class=\"wp-image-1211\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_12_08_50-1024x276.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_12_08_50-300x81.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_12_08_50-768x207.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_12_08_50-1536x414.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_12_08_50-604x163.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_12_08_50.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Simulaci\u00f3n en lazo cerrado<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"CC-10_PI-D\"><\/span>CC-10 (PI-D)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">De nuevo al incorporar el t\u00e9rmino derivativo se gana en estabilidad.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_19_48.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"298\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_19_48-1024x298.png\" alt=\"\" class=\"wp-image-1212\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_19_48-1024x298.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_19_48-300x87.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_19_48-768x224.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_19_48-1536x447.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_19_48-604x176.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_19_48.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Respuesta real<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_39_01.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"298\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_39_01-1024x298.png\" alt=\"\" class=\"wp-image-1214\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_39_01-1024x298.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_39_01-300x87.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_39_01-768x224.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_39_01-1536x447.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_39_01-604x176.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_39_01.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Respuesta real &#8211; Detalle de un cambio en el SP del 11%<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_12_38_53.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"276\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_12_38_53-1024x276.png\" alt=\"\" class=\"wp-image-1215\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_12_38_53-1024x276.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_12_38_53-300x81.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_12_38_53-768x207.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_12_38_53-1536x414.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_12_38_53-604x163.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_12_38_53.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Simulaci\u00f3n en lazo cerrado<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"CC-10_I-P\"><\/span>CC-10 (I-P)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Al utilizar un algoritmo I-P la respuesta del sistema se vuelve similar a una sinton\u00eda lambda o cualquier otra que utilice el par\u00e1metro \u00abTf\u00bb. Esto es debido a que el algoritmo utiliza la PV en lugar del error en la constante proporcional suavizando la respuesta considerablemente.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_07_27.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"308\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_07_27-1024x308.png\" alt=\"\" class=\"wp-image-1247\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_07_27-1024x308.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_07_27-300x90.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_07_27-768x231.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_07_27-1536x462.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_07_27-604x182.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_07_27.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Respuesta real<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_12_13.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"308\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_12_13-1024x308.png\" alt=\"\" class=\"wp-image-1248\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_12_13-1024x308.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_12_13-300x90.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_12_13-768x231.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_12_13-1536x462.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_12_13-604x182.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_12_13.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Respuesta real &#8211; Detalle de un cambio en el SP del 9%<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_23_12_11.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"266\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_23_12_11-1024x266.png\" alt=\"\" class=\"wp-image-1249\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_23_12_11-1024x266.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_23_12_11-300x78.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_23_12_11-768x199.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_23_12_11-1536x399.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_23_12_11-604x157.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_23_12_11.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Simulaci\u00f3n en lazo cerrado<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"CC-10_I-PD\"><\/span>CC-10 (I-PD)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">La respuesta es similar a la respuesta I-P pero al incluir el t\u00e9rmino derivativo, la salida se ha vuelto m\u00e1s oscilante.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_24_16.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"308\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_24_16-1024x308.png\" alt=\"\" class=\"wp-image-1250\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_24_16-1024x308.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_24_16-300x90.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_24_16-768x231.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_24_16-1536x462.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_24_16-604x182.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_24_16.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Respuesta real<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_27_22.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"308\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_27_22-1024x308.png\" alt=\"\" class=\"wp-image-1251\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_27_22-1024x308.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_27_22-300x90.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_27_22-768x231.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_27_22-1536x462.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_27_22-604x182.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_23_27_22.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Respuesta real &#8211; Detalle de un cambio en el SP del 13%<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_23_26_29.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"266\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_23_26_29-1024x266.png\" alt=\"\" class=\"wp-image-1252\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_23_26_29-1024x266.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_23_26_29-300x78.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_23_26_29-768x199.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_23_26_29-1536x399.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_23_26_29-604x157.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_23_26_29.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Simulaci\u00f3n en lazo cerrado<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"IAE-SP_PI\"><\/span>IAE-SP (PI)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Inicialmente aunque con m\u00e1s oscilaciones de las esperadas el control se mantiene estable, pero finalmente entra en oscilaci\u00f3n continua tras una perturbaci\u00f3n no medida.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_25_53.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"308\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_25_53-1024x308.png\" alt=\"\" class=\"wp-image-1221\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_25_53-1024x308.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_25_53-300x90.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_25_53-768x231.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_25_53-1536x462.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_25_53-604x182.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_25_53.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Respuesta real<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_29_09.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"308\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_29_09-1024x308.png\" alt=\"\" class=\"wp-image-1222\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_29_09-1024x308.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_29_09-300x90.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_29_09-768x231.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_29_09-1536x462.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_29_09-604x182.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_29_09.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Respuesta real &#8211; Detalle de un cambio en el SP del 7%<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_16_29_10.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"266\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_16_29_10-1024x266.png\" alt=\"\" class=\"wp-image-1223\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_16_29_10-1024x266.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_16_29_10-300x78.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_16_29_10-768x199.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_16_29_10-1536x399.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_16_29_10-604x157.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_16_29_10.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Simulaci\u00f3n en lazo cerrado<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"IAE-SP_PI-D\"><\/span>IAE-SP (PI-D)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">El t\u00e9rmino derivativo da estabilidad incluso con cambios en el punto de consigna del 15%.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_38_26.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"308\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_38_26-1024x308.png\" alt=\"\" class=\"wp-image-1225\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_38_26-1024x308.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_38_26-300x90.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_38_26-768x231.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_38_26-1536x462.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_38_26-604x182.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_38_26.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Respuesta real<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_45_48.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"308\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_45_48-1024x308.png\" alt=\"\" class=\"wp-image-1226\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_45_48-1024x308.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_45_48-300x90.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_45_48-768x231.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_45_48-1536x462.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_45_48-604x182.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_16_45_48.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Respuesta real &#8211; Detalle de un cambio en el SP del 10%<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_16_45_49.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"266\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_16_45_49-1024x266.png\" alt=\"\" class=\"wp-image-1227\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_16_45_49-1024x266.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_16_45_49-300x78.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_16_45_49-768x199.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_16_45_49-1536x399.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_16_45_49-604x157.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_16_45_49.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Simulaci\u00f3n en lazo cerrado<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"LAMBDA_PI\"><\/span>LAMBDA (PI)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Con este m\u00e9todo podemos ajustar mediante el par\u00e1metro Tf cuando queremos que la PV se iguale al SP. En este caso se ha utilizado un Tf = 5 por lo que la PV igualar\u00e1 al SP en 5 unidades de tiempo. <\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_49_52.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"298\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_49_52-1024x298.png\" alt=\"\" class=\"wp-image-1216\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_49_52-1024x298.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_49_52-300x87.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_49_52-768x224.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_49_52-1536x447.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_49_52-604x176.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_12_49_52.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Respuesta real<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Haciendo un c\u00e1lculo r\u00e1pido tenemos que la PV y el SP se deber\u00edan igualar en el segundo 5&#215;5+67,7 = 92,7. Como vemos, en la respuesta real hay un ligero sobrepasamiento inicial igual\u00e1ndose unos segundos m\u00e1s tarde, aunque dado que existe ruido en la PV se puede considerar se asemeja bastante con la simulaci\u00f3n.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_14_44_33.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"298\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_14_44_33-1024x298.png\" alt=\"\" class=\"wp-image-1217\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_14_44_33-1024x298.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_14_44_33-300x87.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_14_44_33-768x224.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_14_44_33-1536x447.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_14_44_33-604x176.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_29_09_2020_14_44_33.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Respuesta real &#8211; Detalle de un cambio en el SP del 8%<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_14_43_30.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"276\" src=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_14_43_30-1024x276.png\" alt=\"\" class=\"wp-image-1218\" srcset=\"https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_14_43_30-1024x276.png 1024w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_14_43_30-300x81.png 300w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_14_43_30-768x207.png 768w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_14_43_30-1536x414.png 1536w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_14_43_30-604x163.png 604w, https:\/\/garikoitz.info\/blog\/wp-content\/uploads\/2020\/09\/ACP_sim_29_09_2020_14_43_30.avif 1549w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Simulaci\u00f3n en lazo cerrado<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Conclusiones\"><\/span>Conclusiones<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Maqueta sencilla y control relativamente sencillo. Una vez identificado, todo depende de la respuesta que estemos buscando. Si buscamos una respuesta r\u00e1pida nos decantaremos por m\u00e9todos cl\u00e1sicos o m\u00e9todos que busquen minimizar el \u00edndice de error. Si lo que buscamos es una respuesta suave podemos decantarnos por cualquier m\u00e9todo afectado por el par\u00e1metro \u00abTf\u00bb o usar un algoritmo I-P \/ I-PD para suavizar la respuesta del sistema. As\u00ed mismo, si nos empe\u00f1amos en utilizar un algoritmo PI nos vemos obligados a recurrir a sinton\u00edas que utilizan el par\u00e1metro \u00abTf\u00bb o bien usar un algoritmo I-P. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Casi todos los m\u00e9todos obtienen una respuesta adecuada y bastante fiel a la simulaci\u00f3n y me reitero, la simulaci\u00f3n debe ser similar a la respuesta real, de lo contrario algo falla.<\/p>\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube aligncenter wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"lyte-wrapper fourthree\" style=\"width:420px;max-width:100%;margin:5px;\"><div class=\"lyMe\" id=\"WYL_zTvhxIlqtEM\"><div id=\"lyte_zTvhxIlqtEM\" data-src=\"\/\/i.ytimg.com\/vi\/zTvhxIlqtEM\/hqdefault.jpg\" class=\"pL\"><div class=\"tC\"><div class=\"tT\"><\/div><\/div><div class=\"play\"><\/div><div class=\"ctrl\"><div class=\"Lctrl\"><\/div><div class=\"Rctrl\"><\/div><\/div><\/div><noscript><a href=\"https:\/\/youtu.be\/zTvhxIlqtEM\" rel=\"nofollow\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i.ytimg.com\/vi\/zTvhxIlqtEM\/0.jpg\" alt=\"YouTube video thumbnail\" width=\"420\" height=\"295\" \/><br \/>Ver este v\u00eddeo en YouTube<\/a><\/noscript><\/div><\/div><div class=\"lL\" style=\"max-width:100%;width:420px;margin:5px;\"><\/div><figcaption>Balanc\u00edn simple con sinton\u00eda CC-10<\/figcaption><\/figure>\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Descargas\"><\/span>Descargas<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/garikoitz.info\/blog\/?p=674#Descarga\" target=\"_blank\" rel=\"noreferrer noopener\">Arduino COM Plotter<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/garikoitz.info\/blog\/descargas\/Balancin_ACP_files.zip\">Archivos de Arduino COM Plotter<\/a><\/li>\n\n\n\n<li><a rel=\"noreferrer noopener\" href=\"https:\/\/github.com\/jrowberg\/i2cdevlib\/tree\/master\/Arduino\/I2Cdev\" target=\"_blank\">Librer\u00eda I2CDev by Jeff Rowberg<\/a> [Github]<\/li>\n\n\n\n<li><a rel=\"noreferrer noopener\" href=\"https:\/\/github.com\/jrowberg\/i2cdevlib\/tree\/master\/Arduino\/MPU6050\" target=\"_blank\">Librer\u00eda MPU650 by Jeff Rowberg<\/a> [Github]<\/li>\n\n\n\n<li><a rel=\"noreferrer noopener\" href=\"https:\/\/github.com\/denyssene\/SimpleKalmanFilter\" target=\"_blank\">Simple Kalman Filter by Denys Sene<\/a> [Github]<\/li>\n\n\n\n<li><a rel=\"noreferrer noopener\" href=\"https:\/\/github.com\/br3ttb\/Arduino-PID-Library\" target=\"_blank\">Librer\u00eda PID by Brett Beauregard<\/a> [Github]<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Referencias\"><\/span>Referencias<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Enlaces\"><\/span>Enlaces<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a rel=\"noreferrer noopener\" href=\"https:\/\/es.wikipedia.org\/wiki\/Filtro_de_Kalman\" target=\"_blank\">Filtro de Kalman<\/a> [Wikipedia]<\/li>\n\n\n\n<li><a rel=\"noreferrer noopener\" href=\"https:\/\/sites.google.com\/site\/myimuestimationexperience\/filters\/complementary-filter\" target=\"_blank\">Filtro complementario<\/a> (ingl\u00e9s)<\/li>\n\n\n\n<li><a rel=\"noreferrer noopener\" href=\"https:\/\/www.diarioelectronicohoy.com\/blog\/configurar-el-mpu6050\" target=\"_blank\">Configurar el MPU6050<\/a> [diarioelectronicohoy]<\/li>\n\n\n\n<li><a rel=\"noreferrer noopener\" href=\"https:\/\/garikoitz.info\/blog\/?p=1566\" target=\"_blank\">Introducci\u00f3n al algoritmo PID y su implementaci\u00f3n en Arduino<\/a><\/li>\n\n\n\n<li><a rel=\"noreferrer noopener\" href=\"https:\/\/naylampmechatronics.com\/blog\/45_Tutorial-MPU6050-Aceler%C3%B3metro-y-Giroscopio.html\" target=\"_blank\">Tutorial MPU6050, Aceler\u00f3metro y Giroscopio<\/a> [naylampmechatronics]<\/li>\n\n\n\n<li><a rel=\"noreferrer noopener\" href=\"https:\/\/www.luisllamas.es\/arduino-orientacion-imu-mpu-6050\/\" target=\"_blank\">Determinar la orientaci\u00f3n con Arduino y el IMU MPU-6050<\/a> [Luis Llamas]<\/li>\n\n\n\n<li><a rel=\"noreferrer noopener\" href=\"https:\/\/www.luisllamas.es\/medir-la-inclinacion-imu-arduino-filtro-complementario\/\" target=\"_blank\">Medir la inclinaci\u00f3n con IMU, Arduino y filtro complementario<\/a> [Luis Llamas]<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Libros_y_publicaciones\"><\/span>Libros y publicaciones<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">[1] Aidan O\u2019Dwyer. Handbook of PI and PID controller tuning rules, 3rd edition, Imperial College Press. ISBN: 978-1-84816-242-6<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[2] Karl J. Astrom, Tore Hagglund. Control PID avanzado, Pearson, ISBN: 978-84-8322-511-0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[3] Daniel Chuck. Los sistemas de primer orden y los controladores PID, edici\u00f3n 2012. [<a rel=\"noreferrer noopener\" href=\"https:\/\/garikoitz.info\/blog\/descargas\/ControladoresPID.pdf\" target=\"_blank\">Link<\/a>] [<a rel=\"noreferrer noopener\" href=\"http:\/\/dea.unsj.edu.ar\/control2\/ControladoresPID.pdf\" target=\"_blank\">Link2<\/a>]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[4] J.G. Ziegler, N.B. Nichols. Optimum Settings For Automatic Controllers, 1942 edition, American Society of Mechanical Engineers. [<a rel=\"noreferrer noopener\" href=\"https:\/\/garikoitz.info\/blog\/descargas\/Z-N.pdf\" target=\"_blank\">Link<\/a>]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[5] G.H. Cohen, G.A. Coon. Theoretical Consideration of Retarded Control, 1953 edition, American Society of Mechanical Engineers. [<a rel=\"noreferrer noopener\" href=\"https:\/\/garikoitz.info\/blog\/descargas\/Cohen_Coon.pdf\" target=\"_blank\">Link<\/a>] [<a rel=\"noreferrer noopener\" href=\"http:\/\/folk.ntnu.no\/skoge\/puublications_others\/Cohen%20and%20Coon%20(1953)%20-%20Theoretical%20Consideration%20of%20Retarded%20Control.pdf\" target=\"_blank\">Link2<\/a>]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[6] Daniel E. Rivera. Internal Model Control: A Comprehensive View, 1999 edition, College of Engineering and Applied Sciences. [<a rel=\"noreferrer noopener\" href=\"https:\/\/garikoitz.info\/blog\/descargas\/IMC_(Rivera).pdf\" target=\"_blank\">Link<\/a>]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[7] R. Vilanova, A. Visioli. PID Control in the Third Millennium. Chapter 5, The SIMC Method for smooth PID Controller Tuning, Springer. ISBN: 978-1-4471-2424-5.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[8] Chriss Grimholt, Sigurd Skogestad. The improved SIMC method for PI controller tuning, IFAC-conference PID\u201912, Brescia, Italy, March 2012. [<a href=\"http:\/\/npcw17.imm.dtu.dk\/Proceedings\/Session%207%20Control%20Theory\/The%20improved%20SIMC%20method%20for%20PI%20controller%20tuning.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Link<\/a>]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[9] Guillermo J. Silva, Aniruddha Datta, S.P. Bhattacharyya. PID Controllers for Time-Delay Systems. Chapter 10, Analysis of Some PID Tunning Techniques. Birkh\u00e4user. ISBN: 0-8176-4266-8<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introducci&oacute;n Aqu&iacute; ten&eacute;is la segunda entrega sobre sintonizaci&oacute;n PID. En la primera entrega vimos un control de temperatura y en esta veremos un control de posici&oacute;n de un balanc&iacute;n simple. Sistema empleado Se trata de un balanc&iacute;n simple con inclinaci&oacute;n en un solo eje, que consta de un motor de corriente continua con h&eacute;lice y un giroscopio \/ aceler&oacute;metro que har&aacute; de sensor para calcular la inclinaci&oacute;n. La maqueta est&aacute; hecha con ca&ntilde;a de bamb&uacute; y madera y consta de&#8230;<\/p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https:\/\/garikoitz.info\/blog\/2020\/06\/sintonizar-pid-con-arduino-ii-balancin-simple\/\"> Leer m\u00e1s<span class=\"screen-reader-text\">  Leer m\u00e1s<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":892,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","wpupg_custom_link":[],"wpupg_custom_link_behaviour":[],"wpupg_custom_link_nofollow":[],"wpupg_custom_image":[],"wpupg_custom_image_id":[],"footnotes":""},"categories":[15],"tags":[94,16,95,107,103,96,104,97,106,98],"class_list":["post-890","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-arduino","tag-acp","tag-arduino","tag-arduino-com-plotter","tag-filtro-de-kalman","tag-gy-521","tag-identificacion-de-procesos","tag-l9110-keyes","tag-modelado-de-procesos","tag-mpu6050","tag-sintonizacion-pid"],"_links":{"self":[{"href":"https:\/\/garikoitz.info\/blog\/wp-json\/wp\/v2\/posts\/890","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/garikoitz.info\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/garikoitz.info\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/garikoitz.info\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/garikoitz.info\/blog\/wp-json\/wp\/v2\/comments?post=890"}],"version-history":[{"count":164,"href":"https:\/\/garikoitz.info\/blog\/wp-json\/wp\/v2\/posts\/890\/revisions"}],"predecessor-version":[{"id":2159,"href":"https:\/\/garikoitz.info\/blog\/wp-json\/wp\/v2\/posts\/890\/revisions\/2159"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/garikoitz.info\/blog\/wp-json\/wp\/v2\/media\/892"}],"wp:attachment":[{"href":"https:\/\/garikoitz.info\/blog\/wp-json\/wp\/v2\/media?parent=890"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/garikoitz.info\/blog\/wp-json\/wp\/v2\/categories?post=890"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/garikoitz.info\/blog\/wp-json\/wp\/v2\/tags?post=890"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}