{"id":753,"date":"2026-06-12T15:15:35","date_gmt":"2026-06-12T07:15:35","guid":{"rendered":"https:\/\/projectleon.net\/make\/blog\/pid-balance-imu-mpu6050-arduino-ugv-self-balancing-intro-farsi\/"},"modified":"2026-06-12T15:15:36","modified_gmt":"2026-06-12T07:15:36","slug":"pid-balance-imu-mpu6050-arduino-ugv-self-balancing-intro-farsi","status":"publish","type":"post","link":"https:\/\/projectleon.net\/make\/blog\/pid-balance-imu-mpu6050-arduino-ugv-self-balancing-intro-farsi\/","title":{"rendered":"\u062a\u0639\u0627\u062f\u0644 \u062e\u0648\u062f\u06a9\u0627\u0631 \u0628\u0627 PID \u0648 IMU: \u0622\u0645\u0648\u0632\u0634 \u067e\u0627\u06cc\u0647 \u0628\u0631\u0627\u06cc \u0631\u0628\u0627\u062a\u200c\u0647\u0627\u06cc \u0645\u062a\u0648\u0627\u0632\u0646 \u0648 UGV (\u0641\u0627\u0631\u0633\u06cc)"},"content":{"rendered":"
\n\u0631\u0628\u0627\u062a \u062e\u0648\u062f\u0645\u062a\u0648\u0627\u0632\u0646 PID MPU-6050 \u0622\u0631\u062f\u0648\u06cc\u0646\u0648\n<\/div>\n
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\u06a9\u0646\u062a\u0631\u0644 PID \u0686\u06cc\u0633\u062a \u0648 \u0686\u0631\u0627 \u0627\u06cc\u0646\u0642\u062f\u0631 \u0645\u0647\u0645 \u0627\u0633\u062a\u061f<\/h2>\n

PID<\/strong> \u0645\u062e\u0641\u0641 Proportional-Integral-Derivative \u0627\u0633\u062a \u2014 \u06cc\u06a9 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0631\u06cc\u0627\u0636\u06cc \u06a9\u0647 \u062f\u0631 \u0647\u0645\u0647 \u0686\u06cc\u0632 \u0627\u0632 \u0645\u0648\u0634\u06a9 \u062a\u0627 \u0645\u0627\u0634\u06cc\u0646 \u0644\u0628\u0627\u0633\u0634\u0648\u06cc\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0648\u0642\u062a\u06cc \u0645\u06cc\u200c\u062e\u0648\u0627\u0647\u06cc \u06cc\u06a9 \u0631\u0628\u0627\u062a \u0631\u0648\u06cc \u062f\u0648 \u0686\u0631\u062e \u062a\u0639\u0627\u062f\u0644 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f\u060c \u0647\u0631 \u0644\u062d\u0638\u0647 \u0628\u0627\u06cc\u062f \u0628\u062f\u0627\u0646\u06cc \u00ab\u0686\u0642\u062f\u0631 \u0627\u0632 \u062d\u0627\u0644\u062a \u0639\u0645\u0648\u062f\u06cc \u0645\u0646\u062d\u0631\u0641 \u0634\u062f\u0647\u200c\u0627\u0645\u061f\u00bb \u0648 \u00ab\u0686\u0642\u062f\u0631 \u0628\u0627\u06cc\u062f \u0645\u0648\u062a\u0648\u0631 \u0631\u0627 \u0628\u0686\u0631\u062e\u0627\u0646\u0645 \u062a\u0627 \u062c\u0628\u0631\u0627\u0646 \u06a9\u0646\u0645\u061f\u00bb PID \u0627\u06cc\u0646 \u0645\u062d\u0627\u0633\u0628\u0647 \u0631\u0627 \u062f\u0631 \u0647\u0631 \u06f1\u06f0ms \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u062f\u0647\u062f.<\/p>\n

MPU-6050<\/strong> \u06cc\u06a9 \u062a\u0631\u0627\u0634\u0647 \u0634\u062a\u0627\u0628\u200c\u0633\u0646\u062c (Accelerometer) \u0648 \u0698\u06cc\u0631\u0648\u0633\u06a9\u0648\u067e (Gyroscope) \u0633\u0647\u200c\u0645\u062d\u0648\u0631\u0647 \u0627\u0633\u062a \u06a9\u0647 \u0627\u0632 \u0637\u0631\u06cc\u0642 I2C \u0628\u0647 \u0622\u0631\u062f\u0648\u06cc\u0646\u0648 \u0648\u0635\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0634\u062a\u0627\u0628\u200c\u0633\u0646\u062c \u0632\u0627\u0648\u06cc\u0647 \u0627\u0633\u062a\u0627\u062a\u06cc\u06a9 \u0631\u0627 \u0645\u06cc\u200c\u062f\u0647\u062f \u0627\u0645\u0627 \u067e\u0631 \u0627\u0632 \u0646\u0648\u06cc\u0632 \u0627\u0633\u062a. \u0698\u06cc\u0631\u0648\u0633\u06a9\u0648\u067e \u062a\u063a\u06cc\u06cc\u0631 \u0632\u0627\u0648\u06cc\u0647 \u0631\u0627 \u062e\u06cc\u0644\u06cc \u062f\u0642\u06cc\u0642 \u0645\u06cc\u200c\u062f\u0647\u062f \u0627\u0645\u0627 drift \u062f\u0627\u0631\u062f. \u0641\u06cc\u0644\u062a\u0631 \u0645\u06a9\u0645\u0644 (Complementary Filter)<\/strong> \u0627\u06cc\u0646 \u062f\u0648 \u0631\u0627 \u0628\u0627 \u0647\u0645 \u062a\u0631\u06a9\u06cc\u0628 \u0645\u06cc\u200c\u06a9\u0646\u062f \u062a\u0627 \u0632\u0627\u0648\u06cc\u0647 \u062f\u0642\u06cc\u0642 \u0648 \u067e\u0627\u06cc\u062f\u0627\u0631 \u0628\u062f\u0633\u062a \u0628\u06cc\u0627\u06cc\u062f.<\/p>\n<\/div>\n

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🛠️ \u06a9\u0627\u0631\u062a \u067e\u0631\u0648\u0698\u0647<\/h3>\n\n\n\n\n
\u0686\u0647 \u06cc\u0627\u062f \u0645\u06cc\u200c\u06af\u06cc\u0631\u06cc\u0645\u061f<\/td>\nPID \u067e\u0627\u06cc\u0647\u060c \u062e\u0648\u0627\u0646\u062f\u0646 MPU-6050\u060c \u06a9\u062f \u0622\u0631\u062f\u0648\u06cc\u0646\u0648 \u0642\u0627\u0628\u0644 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062f\u0631 \u0647\u0645\u0647 \u067e\u0631\u0648\u0698\u0647\u200c\u0647\u0627<\/td>\n<\/tr>\n
\u0642\u0637\u0639\u0627\u062a<\/td>\nArduino Uno\/Nano + MPU-6050 (~\u06f1\u06f5\u06f0K \u062a\u0648\u0645\u0627\u0646)<\/td>\n<\/tr>\n
\u067e\u06cc\u0634\u200c\u0646\u06cc\u0627\u0632<\/td>\n\u0622\u0634\u0646\u0627\u06cc\u06cc \u067e\u0627\u06cc\u0647 \u0628\u0627 \u0622\u0631\u062f\u0648\u06cc\u0646\u0648 \u0648 C++<\/td>\n<\/tr>\n<\/table>\n<\/div>\n

BOM<\/h2>\n\n\n\n\n\n\n\n
\u0642\u0637\u0639\u0647<\/th>\n\u0645\u0634\u062e\u0635\u0627\u062a<\/th>\n\u0642\u06cc\u0645\u062a<\/th>\n<\/tr>\n<\/thead>\n
Arduino Nano<\/td>\n\u06cc\u0627 Uno<\/td>\n~\u06f1\u06f0\u06f0K<\/td>\n<\/tr>\n
MPU-6050 \u0645\u0627\u0698\u0648\u0644<\/td>\nGY-521<\/td>\n~\u06f4\u06f0K<\/td>\n<\/tr>\n
\u0633\u06cc\u0645 \u062c\u0627\u0645\u067e\u0631<\/td>\nF-M<\/td>\n~\u06f1\u06f0K<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u0627\u062a\u0635\u0627\u0644 MPU-6050 \u0628\u0647 \u0622\u0631\u062f\u0648\u06cc\u0646\u0648<\/h2>\n\n\n\n\n\n\n\n\n
MPU-6050<\/th>\nArduino Uno\/Nano<\/th>\n<\/tr>\n<\/thead>\n
VCC<\/td>\n3.3V<\/td>\n<\/tr>\n
GND<\/td>\nGND<\/td>\n<\/tr>\n
SDA<\/td>\nA4<\/td>\n<\/tr>\n
SCL<\/td>\nA5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u06a9\u062f \u06a9\u0627\u0645\u0644: \u062e\u0648\u0627\u0646\u062f\u0646 \u0632\u0627\u0648\u06cc\u0647 \u0628\u0627 \u0641\u06cc\u0644\u062a\u0631 \u0645\u06a9\u0645\u0644<\/h2>\n
#include <Wire.h>\n#include <MPU6050.h>   \/\/ \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647: Jeff Rowberg's MPU6050\n\nMPU6050 mpu;\n\n\/\/ ===== PID \u067e\u0627\u0631\u0627\u0645\u062a\u0631\u0647\u0627 =====\nfloat Kp = 30.0;   \/\/ \u062a\u0646\u0627\u0633\u0628\u06cc \u2014 \u0648\u0627\u06a9\u0646\u0634 \u0641\u0648\u0631\u06cc\nfloat Ki = 0.5;    \/\/ \u0627\u0646\u062a\u06af\u0631\u0627\u0644\u06cc \u2014 \u062e\u0637\u0627\u06cc \u0645\u0627\u0646\u062f\u06af\u0627\u0631\nfloat Kd = 1.2;    \/\/ \u0645\u0634\u062a\u0642\u06cc \u2014 \u06a9\u0627\u0647\u0634 \u0646\u0648\u0633\u0627\u0646\n\nfloat setpoint = 0.0;   \/\/ \u0632\u0627\u0648\u06cc\u0647 \u0647\u062f\u0641 (\u0639\u0645\u0648\u062f = \u0635\u0641\u0631 \u062f\u0631\u062c\u0647)\nfloat input, output;\nfloat errSum = 0, lastErr = 0;\nunsigned long lastTime;\n\n\/\/ ===== \u0641\u06cc\u0644\u062a\u0631 \u0645\u06a9\u0645\u0644 =====\nfloat angle = 0.0;\nconst float alpha = 0.98;  \/\/ \u06f9\u06f8\u066a \u0698\u06cc\u0631\u0648 + \u06f2\u066a \u0634\u062a\u0627\u0628\u200c\u0633\u0646\u062c\n\nvoid setup() {\n  Serial.begin(115200);\n  Wire.begin();\n  mpu.initialize();\n  if (!mpu.testConnection()) Serial.println(\"MPU-6050 \u062e\u0637\u0627!\");\n  lastTime = millis();\n}\n\nvoid loop() {\n  int16_t ax, ay, az, gx, gy, gz;\n  mpu.getMotion6(&ax, &ay, &az, &gx, &gy, &gz);\n\n  \/\/ \u0632\u0627\u0648\u06cc\u0647 \u0627\u0632 \u0634\u062a\u0627\u0628\u200c\u0633\u0646\u062c (\u062f\u0631\u062c\u0647)\n  float accelAngle = atan2(ay, az) * 180.0 \/ PI;\n\n  \/\/ \u0646\u0631\u062e \u0686\u0631\u062e\u0634 \u0627\u0632 \u0698\u06cc\u0631\u0648 (\u062f\u0631\u062c\u0647\/\u062b\u0627\u0646\u06cc\u0647)\n  float gyroRate = gx \/ 131.0;\n\n  \/\/ \u0641\u06cc\u0644\u062a\u0631 \u0645\u06a9\u0645\u0644\n  unsigned long now = millis();\n  float dt = (now - lastTime) \/ 1000.0;\n  lastTime = now;\n  angle = alpha * (angle + gyroRate * dt) + (1 - alpha) * accelAngle;\n\n  \/\/ ===== \u0645\u062d\u0627\u0633\u0628\u0647 PID =====\n  float err = setpoint - angle;\n  errSum  += err * dt;\n  errSum   = constrain(errSum, -50, 50);   \/\/ Anti-windup\n  float dErr = (err - lastErr) \/ dt;\n  output = Kp*err + Ki*errSum + Kd*dErr;\n  output = constrain(output, -255, 255);\n  lastErr = err;\n\n  Serial.print(\"Angle: \"); Serial.print(angle, 2);\n  Serial.print(\"  PID out: \"); Serial.println(output, 1);\n  delay(10);\n}<\/code><\/pre>\n
\u0631\u0627\u0647\u0646\u0645\u0627\u06cc \u062a\u0646\u0638\u06cc\u0645 Kp\/Ki\/Kd<\/h2>\n\n\n\n\n\n\n\n
\u067e\u0627\u0631\u0627\u0645\u062a\u0631<\/th>\n\u0627\u0641\u0632\u0627\u06cc\u0634 \u0622\u0646<\/th>\n\u06a9\u0627\u0647\u0634 \u0622\u0646<\/th>\n\u0634\u0631\u0648\u0639 \u0628\u0627<\/th>\n<\/tr>\n<\/thead>\n
Kp<\/td>\n\u0648\u0627\u06a9\u0646\u0634 \u0633\u0631\u06cc\u0639\u200c\u062a\u0631\u060c \u0646\u0648\u0633\u0627\u0646 \u0628\u06cc\u0634\u062a\u0631<\/td>\n\u06a9\u0646\u062f \u0648 \u0628\u06cc\u200c\u062a\u0641\u0627\u0648\u062a<\/td>\n10\u201340<\/td>\n<\/tr>\n
Ki<\/td>\n\u062e\u0637\u0627 \u0628\u0647 \u0635\u0641\u0631 \u0645\u06cc\u200c\u0631\u0633\u062f\u060c \u0644\u0631\u0632\u0634<\/td>\n\u062e\u0637\u0627\u06cc \u0645\u0627\u0646\u062f\u06af\u0627\u0631<\/td>\n0.0\u20131.0<\/td>\n<\/tr>\n
Kd<\/td>\n\u0646\u0648\u0633\u0627\u0646 \u06a9\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f<\/td>\n\u0628\u06cc\u0634 \u0627\u0632 \u062d\u062f \u06a9\u0645\u06a9 \u0646\u0645\u06cc\u200c\u06a9\u0646\u062f<\/td>\n0.5\u20133.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\u0631\u0648\u0634 Ziegler\u2013Nichols \u0633\u0627\u062f\u0647:<\/strong> \u0627\u0628\u062a\u062f\u0627 Ki=0, Kd=0 \u0628\u06af\u0630\u0627\u0631. Kp \u0631\u0627 \u0622\u0631\u0627\u0645 \u0628\u0627\u0644\u0627 \u0628\u0628\u0631 \u062a\u0627 \u0631\u0628\u0627\u062a \u0634\u0631\u0648\u0639 \u0628\u0647 \u0646\u0648\u0633\u0627\u0646 \u0628\u0627 \u062f\u0627\u0645\u0646\u0647 \u062b\u0627\u0628\u062a \u06a9\u0646\u062f. \u0622\u0646 \u0631\u0627 Ku<\/em> \u0628\u0646\u0627\u0645. \u0633\u067e\u0633: Kp = 0.6\u00d7Ku\u060c Ki = 1.2\u00d7Ku\/Tu\u060c Kd = 0.075\u00d7Ku\u00d7Tu (Tu = \u062f\u0648\u0631\u0647 \u062a\u0646\u0627\u0648\u0628 \u0646\u0648\u0633\u0627\u0646).<\/p>\n
\u0686\u06a9\u200c\u0644\u06cc\u0633\u062a<\/h2>\n\n\n\n\n\n\n\n\n
\u0645\u0631\u062d\u0644\u0647<\/th>\n\u0646\u062a\u06cc\u062c\u0647 \u0645\u0648\u0631\u062f \u0627\u0646\u062a\u0638\u0627\u0631<\/th>\n\u2713<\/th>\n<\/tr>\n<\/thead>\n
MPU-6050 detect \u0645\u06cc\u200c\u0634\u0648\u062f<\/td>\nSerial: \u00ab\u062e\u0637\u0627\u00bb \u0646\u0634\u0627\u0646 \u0646\u0645\u06cc\u200c\u062f\u0647\u062f<\/td>\n⬜<\/td>\n<\/tr>\n
\u0632\u0627\u0648\u06cc\u0647 \u0635\u0641\u062d\u0647 \u0627\u0641\u0642\u06cc \u2248 \u06f0\u00b0<\/td>\nSerial Monitor \u0632\u0627\u0648\u06cc\u0647 \u0646\u0632\u062f\u06cc\u06a9 \u0635\u0641\u0631<\/td>\n⬜<\/td>\n<\/tr>\n
\u06a9\u062c \u06a9\u0631\u062f\u0646 \u06f4\u06f5\u00b0 \u2192 \u2248\u06f4\u06f5\u00b0<\/td>\n\u0632\u0627\u0648\u06cc\u0647 \u062f\u0631\u0633\u062a \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f<\/td>\n⬜<\/td>\n<\/tr>\n
PID output \u0645\u0646\u0637\u0642\u06cc \u0627\u0633\u062a<\/td>\n\u06a9\u062c \u06a9\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc output \u0628\u0632\u0631\u06af \u0645\u06cc\u200c\u0634\u0648\u062f<\/td>\n⬜<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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