PID_controller

PID —- proportional, integral, derivative

chapter 0:

0-1 ~ 0-3

chapter 1:

1-1 ~ 1-9

chapter 2:

2-1 ~ 2-4

proportional only

    u(t) = Kp * e(t)    error = setpoint - processValue;
                        output = K * error;

proportional + Integral

    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))

proportional + Derivative

    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

proportional + Integral + Derivative

    u(t) = Kp * e(t) + Kt*∫e(t)dt + Kd * de(t)/dt
    Output = Proportional + Integral + Derivative
    Output = error now + errors past + error future