CSharp-PID

A Proportional Integral Derivative (PID) controller, written in C#. Use this project as a guide for implementing a PID controller.

Limitation

Implementing anti-windup in the final discrete form would prove quite the effort. Consider another form if you need an aggressive integrator and/or if windup will be an issue.

Constructor

public PID(double Kp, double Ki, double Kd, double N, double OutputUpperLimit, double OutputLowerLimit)

• Kp Proportional Gain
• Ki Integral Gain
• Kd Derivative Gain
• N Derivative FIlter Coefficient
• OutputUpperLimit Controller Upper Output Limit
• OutputLowerLimit Controller Lower Output Limit

Methods

public double PID_iterate(double setPoint, double processValue, TimeSpan ts)

The PID_iterate method is called once a sample period to run the controller.

• setPoint is the desired (target) setpoint for the system to reach.
• processValue is the current process value which is being controlled.
• ts is the TimeSpan since the last time PID_iterate was called.
• The returned value is the controller output (input to what is being controlled).

public void ResetController()

ResetController resets the controller history effectively resetting the controller.

• This should be called when the system is idle if gains have been drastically modified.

Properties

Property	Type	Access	Description
Kd	double	get/set	The proportional gain
Ki	double	get/set	The integral gain
Kd	double	get/set	The derivative gain
N	double	get/set	The derivative filter coefficient
TsMin	double	get/set	The minimum sample time allowed
OutputUpperLimit	double	get/set	The maximum value the controller return
OutputLowerLimit	double	get/set	The minimum value the controller return

Notes on Properties

• The N property is the filter coefficient on the derivative terms low pass filter. A higher value of N equates to less filtering and a lower value of N equates to more filtering. See the Controller Derivation section below for technical details.
• The TsMin property is by default 1 millisecond. TsMin should be left alone so long the intended sample period is greater than 1 millisecond. This property mostly exists to keep the controller from being passed a zero timespan and causing a division by zero.

Controller Derivation

This class implements a Proportional-Integral-Derivative (PID) controller with a fixed sample period. This readme assumes the reader has some understanding of a PID controller. Here I offer a bit of the logic used to derive the algorithms utilized.

We begin with the parallel form of a PID controller:

Hit this up with some Laplace transform magic:

While this form is great in the ideal realm, taking the derivative of an error will prove a hot mess and therefore it is much more common to modify the derivative portion with a low pass filter thusly:

Where N is the filter coefficient.

Now things get a bit interesting with some bilinear transformation. We begin by making the following substitution:

This is where things get ugly… Making the substitution and rearranging things we now have this:

Before proceeding, this hot mess has to be made causal by having the numerator and denominator divided by the highest order of z. Leaving us with the slightly modified:

For sanity's sake we make some substitutions:

Now we rearrange some terms:

Then we take the inverse z-transform:

Moving right along to solve for y[n]:

This equation now defines how we can calculate the current output, y[n], based on previous outputs, y[n-k], the current error, e[n], and previous errors, e[n-k].