PID

A simple PID library for use with Arduino or other C++ applications.

A PID Controller is a method of system control in which a correctional output is generated to guide the system toward a desired setpoint (aka target). The PIDController calculates the output based on the following factors:

Gains (proportional, integral, and derivative)
Target
Feedback

The gains act as multipliers for their corresponding components of PID.

The target is a user-specified value which the system strives to reach by manipulating the output.

The feedback is the system's actual position or status in regards to the physical world. This can be a position read by an encoder, an orientation from an accelerometer, etc. Something important to note is that the unit of the system matches the unit of the feedback, and the PIDController will try to maintain the value of the target in terms of the feedback. For example:

Assuming a feedback read from a robot's position on a number line, the target would represent the desired position and the PIDController would use the output to maneuver the robot to that position.
Assuming a feedback reading the angular rate of a gyroscope, the target would represent a desired angular rate and the PIDController would use the output to maintain a rotation matching that rate.

For each application of PID, the user must understand the desired behavior of the system and provide a method of feedback appropriate to achieve the goal (see PIDSource).

Another important term in PID is error, which refers to the difference between the target and the feedback.

Each of the three components of PID contributes a unique behavior to the system.

Proportional

The Proportional component introduces a linear relationship between the error (target minus feedback) and the output. This means that as the feedback grows further away from the target, the output grows proportionally stronger.

Proportional component = (P Gain) * (error)
                       = (P Gain) * (target - feedback)

Integral

The Integral component is designed to give a very precise approach of the feedback to the target. Depending on the scale of the physical system and the precision of feedback (e.g. sensors), the proportional component alone is likely not sufficient to provide adequate power (e.g. to motors) to guide the system in regards to small-scale correction. The Integral component integrates the error of the system (target - feedback) over time. If the system reaches a point where it is close to - but not exactly on top of - the target, the integration will slowly build until it is powerful enough to overcome static resistances and move the system precisely to the target.

Integral component = (I Gain) * Integral of error over time

In this implementation, Integral is calculated with a running summation of the system's error, updated at each tick().

Derivative

The Derivative component measures the rate of change of the feedback. It can reduce the strength of the output if 1) the feedback is approaching the target too quickly or 2) if the feedback is moving away from the target.

Derivative component = (D Gain) * ((change in error) / (change in time))
                     = (D Gain) * ((error - lastError) / (time - lastTime))

PID Equation

Now that we know what each component of PID contributes, the output of a PIDController can be nicely summed up with:

PID Output = Proportional component + Integral component + Derivative component

Library Features

Platform Independence

This library was built with versatility in mind. Though the project it was built for is Arduino, no Arduino-specific function calls are made. Instead, function pointers provide hooks for gathering necessary inputs, such as system time.

PID Source, Output, and other Hooks

Since one of the primary focuses in this library is platform independence, there are several instances where function pointers are used to provide hooks into the parent program. Three notable instances are:

PIDSource
PIDOutput
RegisterTimeFunction

The PIDSource and PIDOutput are used for retrieving feedback from the parent system and delivering the calculated output, respectively. At the construction of a PIDController, two function pointers are passed in which represent functions created by the user which perform these tasks. Below is an example of using PIDSource and PIDOutput functions:

int pidSource()
{
  return mySensor.getValue();
}

void pidOutput(int output)
{
  myRobot.driveAtSpeed(output);
}

// P, I, and D represent constants in the user's program
PIDController myPIDController(P, I, D, pidSource, pidOutput);

RegisterTimeFunction() is a method that gives the user a chance to tell the PIDController how to retrieve system time. This is useful because different platforms have different APIs but we can use handling functions to pass in references to time-getting functions (if the return type matches the PIDController's function pointer type) or to make conversions so that the types are made to match. Below are some examples:

On an Arduino system, the millis() function returns time in milliseconds as an unsigned long, which matches the function pointer type for the registerTimeFunction() method.

myPIDController.registerTimeFunction(millis);

On a system that has no matching time-getting function, we can create a wrapper method that will convert the value and allow us to pass it as a parameter.

// Let's assume this platform's time function is
// double getSeconds();

unsigned long timeFunction()
{
  // Multiply by 1000 to convert seconds to milliseconds
  return (unsigned long) (getSeconds() * 1000);
}

myPIDController.registerTimeFunction(timeFunction);

Feedback Wrap

Feedback wrap is an optional feature that can cause the number line of the input range to "wrap" around on itself. As an example, assume a PIDSource that set to retrieve a value from a magnetometer sensor that returns a value from 0 to 360. Under normal circumstances, a feedback of 15 and target of 345 would cause the system to generate an output to navigate it in the positive direction to compensate for the error of 330. However, in this scenario, it would be much more effective to generate a negative output to cover a distance of 30 rather than a distance of 330. Feedback Wrap allows us to cause the upper and lower bounds of the range to appear adjacent to one another for the purpose of calculating the error. This also fixes problems with overshoot: if the system's target was set to 0 and it overshot, a magnetometer or other rotation sensor would return a value near to 360, which would cause the error to spike quickly and make the system travel the entire distance in the negative direction again. Setting the feedback to be wrapped at 0 and 360 causes the error to accurately represent the physical state of the system.

To setup Feedback Wrap (this automatically enables it as well):

myPIDController.setFeedbackWrapBounds(0, 360);

To disable or re-enable Feedback Wrap:

myPIDController.setFeedbackWrapped(false);
myPIDController.setFeedbackWrapped(true);

Calculation Transparency

This library provides many getter functions that will allow insight into the system's state. Any function that sets an option or value has a corresponding getter which can be useful in recalling the settings that the PIDController is operating under. Additionally, methods are provided to display the contribution of each component of PID to the current output, which is very useful when tuning the system.

myPIDController.getProportionalComponent();
myPIDController.getIntegralComponent();
myPIDController.getDerivativeComponent();
myPIDController.getP(); // Returns P Gain
myPIDController.getI(); // Returns I Gain
myPIDController.getD(); // Returns D Gain
myPIDController.getTarget();
myPIDController.getFeedback();
myPIDController.getOutput();
myPIDController.getError();

These getter functions are updated at every run of tick().

Templates

In C++, using templates allows you to create classes that are prepared to handle different types of data. This PID library uses templates to allow you to perform calculations using different types of numeric values. For example:

PIDController<int> myIntPIDController(...);
PIDController<long> myLongPIDController(...);
PIDController<float> myFloatPIDController(...);
PIDController<double> myDoublePIDController(...);

The data type passed into the angle brackets <> determines what type of value the PIDController will handle. A PIDController will need PIDSource and PIDOutput function pointers that are compliant with an int, but a PIDController will need to comply with doubles. For example:

// For an int PIDController
int pidIntSource()
{
  return mySensor.getIntValue();
}
void pidIntOutput(int output)
{
  myRobot.setIntSpeed(output);
}
// P, I, and D represent constants in the user's program.
PIDController<int> myIntPIDController(P, I, D, pidIntSource, pidIntOutput);


// For a double PIDController
double pidDoubleSource()
{
  return mySensor.getDoubleValue();
}
void pidDoubleOutput(double output)
{
  myRobot.setDoubleSpeed(output);
}
// P, I, and D represent constants in the user's program.
PIDController<double> myDoublePIDController(P, I, D, pidDoubleSource, pidDoubleOutput);

Additionally, the getter methods covered in the "Calculation Transparency" section and their corresponding setter methods will also adapt to handle the data type specified for the PIDController at construction.

License

This project is licensed under MIT or Apache-2.0, at your option.

See LICENSE-MIT or LICENSE-APACHE for more details.

nicholastmosher/PID

PID