PID --- proportional, integral, derivative
0-1 ~ 0-3
1-1 ~ 1-9
2-1 ~ 2-4
u(t) = Kp * e(t) error = setpoint - processValue;
output = K * error;
u(t) = Kp * e(t) + Kt*∫e(t)dt error: = setpoint - processValue;
u(t) = Kp * e(t) + Ki*∑e(t) Reset: = Reset + K/tau_i + Reset;
u(t) = Kp * e(t) + Kt*∑{(K/†i)*e(t)} output: = K * Error + Reset;
units of tuning constants
K - Gain --------------> Dimensionless -> K*e(t) Proportional Band -> % of Span ------> e(t)/K
Tau_i - Seconds per Repeat ---> K/tau * sum(e(t)) Repeats per Minute ---> K * tau * sum(e(t))
u(t) = Kp * e(t) + Kd * de(t)/dt
u(t) = K * [e(t) + 1/†d * de(t)/dt]
u(t) = K * e(t) + K / †i * ∆e(t) Error : = setpoint - processValue;
output: = K * Error + K/tau_i * (Error - LatError);
LastError := Error; // save for next scan
units of tuning constants
Tau_d - seconds per repeat ---> K/tau repeat per minute ---> k * tau
u(t) = Kp * e(t) + Kt*∫e(t)dt + Kd * de(t)/dt
Output = Proportional + Integral + Derivative
Output = error now + errors past + error future