A PID (proportional/integral/derivative) controller in Elixir. “PID” in this context is not to be confused with process ID.

controller =
  PidController.new(kp: 0.2, ki: 0.1)
  |> PidController.set_setpoint(5.0)

# in a loop
{:ok, output, controller} = PidController.output(input, controller)

PidController implements a control loop-style feedback controller similar to what is commonly found in industrial control systems. It takes a measured value from the system under control (the process value or process variable), compares it to a setpoint value to produce an error term, then generates a control value based on proportional, integral, and derivative functions of the error term. The control value is then fed back into the system under control.

For a full description of PID controllers and how they work, see https://en.wikipedia.org/wiki/PID_controller.

While the proportional term is a function of the error value only, the integral and derivative terms are also functions of time. The first iteration of PidController acts as if the output/2 function is being called at regular and consistent intervals, even though in practice this is unlikely. A future version will take into account the elapsed time between calls to output/2.

Simply put, control theory is the math used to control a system whose state is a function of time. More precisely, we’re interested in controlling the system such that it is stable (none of the values which compose the state grow to infinity) and that when disturbed returns to a steady state without excessive oscillation or damping.

Control theory covers a broad range of possible systems, so we’ll limit ourselves to closed-loop (or feedback) control of a single state variable of a linear system.

Okay. Every closed-loop controller is made up of several parts.

• The system being controlled
• An input to the system, to change its state
• An output from the system, to be measured
• A reference value (the set point) against which the output is compared
• The error signal (the difference between the measured output and the set point)
• The controller, which converts the error signal to the output fed back into the system

For the system, think of your residence—your house, apartment, parents’ basement, yurt, whatever. There are lots of state variables which describe the time-dependent state of the system (temperature, humidity, air pressure, to name just three). The controller will control only one state variable; We’ll call this one of interest the process variable.

We want to hold the temperature constant, so temperature is our process variable. For the sake of the metaphor, assume that it’s winter where you are, so outside of your residence is colder than the inside, so the temperature will drop over time.

Some sensor, somewhere in your residence, measures the current temperature. It is compared to the desired temperature (the set point); the difference between the two is the error value.

Add pid_controller to your list of dependencies in mix.exs:

def deps do
  [
    {:pid_controller, "~> 0.1.3"}
  ]
end

Don’t forget to run mix deps.get afterwards.

Documentation can be found at https://hexdocs.pm/pid_controller.

1. Clone the repository.
2. Install dependencies with mix deps.get.

Pull requests are welcome. Pull requests with specs covering the changes are especially welcome. Pull requests with specs, which have been run through mix format, and pass mix credo are extra-especially welcome. 😄

Unit tests were written with ESpec.

See the open issues on Github.

Copyright (c) 2019-2020 Craig S. Cottingham, except where stated otherwise.

Licensed under the Apache License, Version 2.0 (the “License”); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an “AS IS” BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.