A proportional-integral-derivative (PID) controller.

• Visibility into individual contribution of P, I, and D terms which often need to be logged for later analysis and parameter tuning.
• Output limits on a per term basis.
• Three-term control output limit.
• Mitigation of integral windup using integral term limit.
• Mitigation of derivative kick by using the derivative of the measurement rather than the derivative of the error.
• On-the-fly changes to setpoint/kp/ki/kd.
  • Mitigation of output jumps when changing ki by storing the integration of e(t) * ki(t) rather than only e(t).
• Generic float type parameter to support f32 or f64.
• Support for no_std environments, such as embedded systems.
• Optional support for Serde. Enable the serde Cargo feature, if you need Pid to implement Serialize/Deserialize.

extern crate pid;
use pid::Pid;

fn main() {
    // Set only kp (proportional) to 10. The setpoint is 15.
    // Set limits for P, I, and D to 100 each.
    let mut pid = Pid::new(10.0, 0.0, 0.0, 100.0, 100.0, 100.0, 100.0, 15.0);
    // Fake a measurement of 10.0, which is an error of 5.0.
    let output = pid.next_control_output(10.0);
    // Verify that kp * error = 10.0 * 5.0 = 50.0
    assert_eq!(output.output, 50.0);
    // Verify that all output was from the proportional term
    assert_eq!(output.p, 50.0);
    assert_eq!(output.i, 0.0);
    assert_eq!(output.d, 0.0);
    
    // Verify that the same measurement produces the same output since we
    // aren't using the stateful derivative & integral terms.
    let output = pid.next_control_output(10.0);
    assert_eq!(output.p, 50.0);
    
    // Add an integral term
    pid.ki = 1.0;
    let output = pid.next_control_output(10.0);
    assert_eq!(output.p, 50.0);
    // Verify that the integral term is adding to the output signal.
    assert_eq!(output.i, 5.0);
    assert_eq!(output.output, 55.0);

    // Add a derivative term
    pid.kd = 2.0;
    let output = pid.next_control_output(15.0);  // Match the desired target
    // No proportional term since no error
    assert_eq!(output.p, 0.0);
    // Integral term stays the same
    assert_eq!(output.i, 5.0);
    // Derivative on measurement produces opposing signal
    assert_eq!(output.d, -10.0);
    assert_eq!(output.output, -5.0);
}

• Measurements occur at equal spacing. (t(i) = t(i-1) + C)
• Output limits per term are symmetric around 0 (-limit <= term <= limit).

There are several different formulations of PID controllers. This library uses the independent form:

where:

• C(t) = control output, the output to the actuator.
• P(t) = process variable, the measured value.
• e(t) = error = S(t) - P(t)
• S(t) = set point, the desired target for the process variable.

kp/ki/kd can be changed during operation and can therefore be a function of time.

If you're interested in the dependent form, add your own logic that computes kp/ki/kd using dead time, time constant, kc, or whatever else.

• Helper for (auto-)tuning by detecting frequency & amplitude of oscillations.