BasicPID

Math behind the controller

PID Controller in laplace domain:

$U(s) = K_p + K_i * \frac{1}{s} + K_d * s $

PID Controller in discrete domain:

$P_n = Kp*E_n $

$I_n = Ki * \frac{t}{2} * (E_n + E_{n-1}) + I_{n-1} $

$D_n = \frac{2Kd}{2T +t} * (E_n - E_{n-1} + \frac{2T-t}{2T+t} * D_{n-1} $

$U_{n} = P_{n} + I_{n} + D_{n} $

Practical Notes

• Derivative term amplifies high frequency noise, must apply low pass filter.

• Derivative spikes during change in setpoint, must take derivative on measurements not error.

• Integral can saturate output if held at one point for awhile: Use integral anti-windup. (clamping integral when control signal is at max for a long time)

• Real world actuators have limits, U term must be clamped.

Usage

• Create a pid object and call init().
• During each iteration of a control loop pass in measurement data and a desired output to update().
• Convert output signal to inputs to actuators