{"id":768,"date":"2026-06-12T15:16:47","date_gmt":"2026-06-12T07:16:47","guid":{"rendered":"https:\/\/projectleon.net\/make\/blog\/pid-tuning-calibration-self-balancing-vehicle-practical-guide-farsi\/"},"modified":"2026-06-12T15:16:48","modified_gmt":"2026-06-12T07:16:48","slug":"pid-tuning-calibration-self-balancing-vehicle-practical-guide-farsi","status":"publish","type":"post","link":"https:\/\/projectleon.net\/make\/blog\/pid-tuning-calibration-self-balancing-vehicle-practical-guide-farsi\/","title":{"rendered":"\u06a9\u0627\u0644\u06cc\u0628\u0631\u0627\u0633\u06cc\u0648\u0646 \u0648 \u062a\u06cc\u0648\u0646\u06cc\u0646\u06af PID \u0628\u0631\u0627\u06cc \u0648\u0633\u0627\u06cc\u0644 \u0646\u0642\u0644\u06cc\u0647 \u062e\u0648\u062f\u0645\u062a\u0648\u0627\u0632\u0646 \u2014 \u0631\u0627\u0647\u0646\u0645\u0627\u06cc \u0639\u0645\u0644\u06cc (\u0641\u0627\u0631\u0633\u06cc)"},"content":{"rendered":"
\n\u062a\u06cc\u0648\u0646\u06cc\u0646\u06af PID \u0631\u0628\u0627\u062a \u062e\u0648\u062f\u0645\u062a\u0648\u0627\u0632\u0646 Serial Plotter\n<\/div>\n
\n

\u0686\u0631\u0627 PID \u0628\u0647 \u062a\u0646\u0638\u06cc\u0645 \u062f\u0642\u06cc\u0642 \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u062f\u061f<\/h2>\n

\u0641\u0631\u0645\u0648\u0644 PID \u0633\u0647 \u0639\u062f\u062f \u062f\u0627\u0631\u062f: Kp\u060c Ki\u060c Kd. \u0647\u06cc\u0686 \u0645\u0642\u062f\u0627\u0631 \u00ab\u062c\u0627\u062f\u0648\u06cc\u06cc\u00bb \u0628\u0631\u0627\u06cc \u0647\u0645\u0647 \u0631\u0628\u0627\u062a\u200c\u0647\u0627 \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f \u2014 \u0647\u0631 \u0633\u06cc\u0633\u062a\u0645 \u0628\u0633\u062a\u0647 \u0628\u0647 \u062c\u0631\u0645\u060c \u0627\u0631\u062a\u0641\u0627\u0639 \u0645\u0631\u06a9\u0632 \u062c\u0631\u0645\u060c \u0642\u062f\u0631\u062a \u0645\u0648\u062a\u0648\u0631 \u0648 \u0633\u0631\u0639\u062a \u062d\u0644\u0642\u0647 \u06a9\u0646\u062a\u0631\u0644\u060c \u0627\u0639\u062f\u0627\u062f \u0645\u062a\u0641\u0627\u0648\u062a\u06cc \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u062f. \u062a\u0646\u0638\u06cc\u0645 \u062f\u0633\u062a\u06cc \u06cc\u0627\u062f \u06af\u0631\u0641\u062a\u0646\u06cc \u0627\u0633\u062a \u0627\u0645\u0627 \u0646\u06cc\u0627\u0632 \u0628\u0647 \u0631\u0648\u0634 \u0648 \u0635\u0628\u0631 \u062f\u0627\u0631\u062f. \u062f\u0631 \u0627\u06cc\u0646 \u067e\u0633\u062a \u06cc\u0627\u062f \u0645\u06cc\u200c\u06af\u06cc\u0631\u06cc\u0645 \u0686\u0637\u0648\u0631 \u0628\u0627 \u0627\u0628\u0632\u0627\u0631\u0647\u0627\u06cc \u0631\u0627\u06cc\u06af\u0627\u0646 \u0622\u0631\u062f\u0648\u06cc\u0646\u0648 PID \u0631\u0627 \u0628\u0647\u06cc\u0646\u0647 \u06a9\u0646\u06cc\u0645.<\/p>\n<\/div>\n

\n

🛠️ \u0627\u0628\u0632\u0627\u0631\u0647\u0627\u06cc \u0644\u0627\u0632\u0645<\/h3>\n\n\n\n
\u0646\u0631\u0645\u200c\u0627\u0641\u0632\u0627\u0631<\/td>\nArduino IDE \u2192 Serial Plotter (\u0631\u0627\u06cc\u06af\u0627\u0646)<\/td>\n<\/tr>\n
\u0633\u062e\u062a\u200c\u0627\u0641\u0632\u0627\u0631<\/td>\n\u0631\u0628\u0627\u062a\/\u0627\u0633\u06a9\u0648\u062a\u0631 \u0622\u0645\u0627\u062f\u0647 \u0627\u0632 \u067e\u0633\u062a\u200c\u0647\u0627\u06cc \u0642\u0628\u0644<\/td>\n<\/tr>\n<\/table>\n<\/div>\n

\u0631\u0648\u0634 \u062a\u0646\u0638\u06cc\u0645 \u062f\u0633\u062a\u06cc \u06af\u0627\u0645 \u0628\u0647 \u06af\u0627\u0645<\/h2>\n\n\n\n\n\n\n\n\n\n
\u0645\u0631\u062d\u0644\u0647<\/th>\n\u06a9\u0627\u0631<\/th>\n\u0646\u062a\u06cc\u062c\u0647 \u0645\u0648\u0631\u062f \u0627\u0646\u062a\u0638\u0627\u0631<\/th>\n<\/tr>\n<\/thead>\n
\u06f1<\/td>\nKi=0, Kd=0 \u2014 \u0641\u0642\u0637 Kp \u0631\u0627 \u0628\u0627\u0644\u0627 \u0628\u0628\u0631<\/td>\n\u0631\u0628\u0627\u062a \u0648\u0627\u06a9\u0646\u0634 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f \u0627\u0645\u0627 \u0646\u0648\u0633\u0627\u0646 \u062f\u0627\u0631\u062f<\/td>\n<\/tr>\n
\u06f2<\/td>\nKp \u0631\u0627 \u062a\u0627 \u0646\u0648\u0633\u0627\u0646 \u067e\u0627\u06cc\u062f\u0627\u0631 \u0628\u0627\u0644\u0627 \u0628\u0628\u0631 (Ku)<\/td>\n\u0646\u0648\u0633\u0627\u0646 \u062b\u0627\u0628\u062a \u0628\u0627 \u062f\u0627\u0645\u0646\u0647 \u0645\u0634\u062e\u0635 (Tu \u0631\u0627 \u0627\u0646\u062f\u0627\u0632\u0647 \u0628\u06af\u06cc\u0631)<\/td>\n<\/tr>\n
\u06f3<\/td>\nKp=0.6\u00d7Ku\u060c Kd=0.075\u00d7Ku\u00d7Tu \u0627\u0636\u0627\u0641\u0647 \u06a9\u0646<\/td>\n\u0646\u0648\u0633\u0627\u0646 \u06a9\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f<\/td>\n<\/tr>\n
\u06f4<\/td>\nKi=1.2\u00d7Ku\/Tu \u0627\u0636\u0627\u0641\u0647 \u06a9\u0646<\/td>\n\u062e\u0637\u0627\u06cc \u0645\u0627\u0646\u062f\u06af\u0627\u0631 \u0627\u0632 \u0628\u06cc\u0646 \u0645\u06cc\u200c\u0631\u0648\u062f<\/td>\n<\/tr>\n
\u06f5<\/td>\n\u062f\u0633\u062a\u200c\u062a\u0646\u0638\u06cc\u0645 \u0638\u0631\u06cc\u0641 \u0628\u0627 Serial Plotter<\/td>\n\u067e\u0627\u0633\u062e \u0646\u0631\u0645 \u0648 \u0633\u0631\u06cc\u0639<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u06a9\u062f \u0628\u0627 Serial Plotter output<\/h2>\n
\/\/ \u0627\u0641\u0632\u0648\u062f\u0646 \u0628\u0647 loop() \u0628\u0631\u0627\u06cc \u0646\u0645\u0627\u06cc\u0634 \u062f\u0631 Serial Plotter:\nSerial.print(\"Setpoint:\"); Serial.print(setpoint);\nSerial.print(\",Angle:\");   Serial.print(angle);\nSerial.print(\",Output:\");  Serial.println(output);\n\/\/ \u062f\u0631 Serial Plotter \u0633\u0647 \u062e\u0637 \u0631\u0646\u06af\u06cc \u0645\u06cc\u200c\u0628\u06cc\u0646\u06cc\n\/\/ \u0647\u062f\u0641: Angle \u0631\u0648\u06cc Setpoint \u0628\u0645\u0627\u0646\u062f \u0648 Output \u0622\u0631\u0627\u0645 \u0628\u0627\u0634\u062f<\/code><\/pre>\n
\u06a9\u0627\u0644\u06cc\u0628\u0631\u0627\u0633\u06cc\u0648\u0646 \u0622\u0641\u0633\u062a IMU<\/h2>\n
\/\/ \u0642\u0628\u0644 \u0627\u0632 \u0627\u0633\u062a\u0641\u0627\u062f\u0647\u060c MPU-6050 \u0631\u0627 \u0631\u0648\u06cc \u0633\u0637\u062d \u0635\u0627\u0641 \u0628\u06af\u0630\u0627\u0631 \u0648 \u0627\u06cc\u0646 \u0631\u0627 \u0627\u062c\u0631\u0627 \u06a9\u0646:\n#include <MPU6050_6Axis_MotionApps20.h>\nMPU6050 mpu;\nvoid setup(){\n  Wire.begin(); Serial.begin(115200);\n  mpu.initialize();\n  mpu.CalibrateAccel(6);  \/\/ \u06f6 \u0628\u0627\u0631 \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646\n  mpu.CalibrateGyro(6);\n  mpu.PrintActiveOffsets();  \/\/ \u0622\u0641\u0633\u062a\u200c\u0647\u0627 \u0631\u0627 \u06cc\u0627\u062f\u062f\u0627\u0634\u062a \u06a9\u0646\n}\n\/\/ \u0633\u067e\u0633 \u062f\u0631 \u06a9\u062f \u0627\u0635\u0644\u06cc:\n\/\/ mpu.setXAccelOffset(\u0622\u0641\u0633\u062a\u200c\u062e\u0648\u062f\u062a);\n\/\/ mpu.setYAccelOffset(\u0622\u0641\u0633\u062a\u200c\u062e\u0648\u062f\u062a);\n\/\/ \u0645\u0642\u0627\u062f\u06cc\u0631 \u0631\u0627 \u0627\u0632 PrintActiveOffsets \u0628\u062e\u0648\u0627\u0646<\/code><\/pre>\n
\u062c\u062f\u0648\u0644 \u0639\u06cc\u0628\u200c\u06cc\u0627\u0628\u06cc PID<\/h2>\n\n\n\n\n\n\n\n\n\n
\u0639\u0644\u0627\u0645\u062a<\/th>\n\u0639\u0644\u062a<\/th>\n\u062f\u0631\u0645\u0627\u0646<\/th>\n<\/tr>\n<\/thead>\n
\u0646\u0648\u0633\u0627\u0646 \u0633\u0631\u06cc\u0639<\/td>\nKp \u06cc\u0627 Kd \u062e\u06cc\u0644\u06cc \u0632\u06cc\u0627\u062f<\/td>\n\u0647\u0631 \u062f\u0648 \u0631\u0627 \u06f2\u06f0\u066a \u06a9\u0645 \u06a9\u0646<\/td>\n<\/tr>\n
\u06a9\u0646\u062f \u0648 \u0628\u06cc\u200c\u062a\u0641\u0627\u0648\u062a<\/td>\nKp \u06a9\u0645<\/td>\nKp \u0631\u0627 \u062f\u0648 \u0628\u0631\u0627\u0628\u0631 \u06a9\u0646<\/td>\n<\/tr>\n
drift \u0645\u062f\u0627\u0648\u0645 \u0628\u0647 \u06cc\u06a9 \u0633\u0645\u062a<\/td>\n\u0622\u0641\u0633\u062a IMU \u06cc\u0627 setpoint \u0627\u0634\u062a\u0628\u0627\u0647<\/td>\nsetpoint \u0631\u0627 \u062a\u0646\u0638\u06cc\u0645 \u06a9\u0646\u060c IMU \u06a9\u0627\u0644\u06cc\u0628\u0631 \u06a9\u0646<\/td>\n<\/tr>\n
\u0644\u0631\u0632\u0634 \u0645\u0648\u062a\u0648\u0631 (buzz)<\/td>\ndt \u062e\u06cc\u0644\u06cc \u06a9\u0648\u0686\u06a9 \u06cc\u0627 Kd \u062e\u06cc\u0644\u06cc \u0628\u0632\u0631\u06af<\/td>\nKd \u06a9\u0645 \u06a9\u0646\u060c \u06cc\u0627 \u0627\u0632 \u0641\u06cc\u0644\u062a\u0631 \u0645\u0634\u062a\u0642 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646<\/td>\n<\/tr>\n
Integral Windup<\/td>\nKi \u00d7 \u0632\u0645\u0627\u0646 \u062c\u0645\u0639 \u062e\u0637\u0627<\/td>\nerrSum = constrain(errSum,-N,N)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n