A simulator of the PID controller for a system moving vertically with a free fall acceleration of 9.81. A force is applied to the system, this force is regulated by the PID controller. In the described example:
Kp = 0.1 - initial coefficient
Kd = 0.2 - initial coefficient
Ki = 0.0001 - initial coefficient
dt = 0.05 - sampling time of the system
timelapse = 120 - system simulation time
setpoint = 100 - setting value
startpoint = 0 - start value
mass = 0.8 - mass of the body
These values can be changed
The physical model of the system is described here, the controlling effect is force, the other parameters can be replaced.
Force = force - 9.81*mass
acc = Force / mass
currentspeed += acc * dt
currentpoint += currentspeed * dt + acc * pow(dt, 2) / 2
The algorithm calculates the reaction of the system for the timelapse time with a frequency of 1/dt and outputs data to the graph. Blue is the reaction of the system, Orange is the control action.
For example, replace gravity with the force of friction against the air. The expression for calculating air resistance is very approximate and unsuitable for real calculations
Force = force - 0.01 * pow(currentspeed,2)