PID Controller for Rust

A proportional-integral-derivative (PID) controller.

Features

• 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.

Example

use pid::Pid;

// Create a new proportional-only PID controller with a setpoint of 15
let mut pid = Pid::new(15.0, 100.0);
pid.p(10.0, 100.0);

// Input a measurement with an error of 5.0 from our setpoint
let output = pid.next_control_output(10.0);

// Show that the error is correct by multiplying by our kp
assert_eq!(output.output, 50.0); // <--
assert_eq!(output.p, 50.0);

// It won't change on repeat; the controller is proportional-only
let output = pid.next_control_output(10.0);
assert_eq!(output.output, 50.0); // <--
assert_eq!(output.p, 50.0);

// Add a new integral term to the controller and input again
pid.i(1.0, 100.0);
let output = pid.next_control_output(10.0);

// Now that the integral makes the controller stateful, it will change
assert_eq!(output.output, 55.0); // <--
assert_eq!(output.p, 50.0);
assert_eq!(output.i, 5.0);

// Add our final derivative term and match our setpoint target
pid.d(2.0, 100.0);
let output = pid.next_control_output(15.0);

// The output will now say to go down due to the derivative
assert_eq!(output.output, -5.0); // <--
assert_eq!(output.p, 0.0);
assert_eq!(output.i, 5.0);
assert_eq!(output.d, -10.0);

Assumptions

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

Formulation

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

C(t) = K_p \cdot e(t) + K_i \cdot \int{e(t)dt} - K_d \cdot \frac{dP(t)}{dt}

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.

Todo

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

License

Licensed under either at your discretion:

• Apache License, Version 2.0 (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
• MIT license (LICENSE-MIT or http://opensource.org/licenses/MIT)