Basics of PID Control

PID control components Proportional Integral PID_proportonal = Kp * ERRORPID_integral = Ki * integral(error) dt = Ki * ( summation of error from t n-i to t n ) Differential PID_differential = Kd * (dERROR/dt)Kd * (ERROR i - ERROR i-1 ) PID_CONTOL_FUNCTION = PID_proportional + PID_integral + PID_differential

Effect of Kp Kp == pGain Small pGain - response too slow Large pGain - too fast, overshoot, oscillation

Effect of Ki Control system using only a Ki term.. Again Ki == iGain in the figure, even forvery small Ki, the system is difficult to stabilize (why?)

Kp and Ki combined The combined Ki and Kp terms tend to improve the slower Kp responses frombefore but does less to improve the stability of the faster Kp responses

PID controller code typedef struct { double dState;double iState;double iMax, iMin;// Last position input // Integrator state // Maximum and minimum allowable integrator stat Example codefrom tim wescott website double iGain, // integral gain pGain, // proportional gain dGain; // derivative gain } SPid; double UpdatePID(SPid * pid, double error, double position) { double pTerm, dTerm, iTerm; pTerm = pid->pGain * error; // calculate the proportional term // calculate the integral state with appropriate limiting pid->iState += error; if (pid->iState > pid->iMax) pid->iState = pid->iMax; else if (pid->iState < pid->iMin) pid->iState = pid->iMin; iTerm = pid->iGain * iState; // calculate the integral term dTerm = pid->dGain * (pid->dState - position); pid->dState = position; return pTerm + dTerm + iTerm; }