This simple example shows the application of P, I, D alone, and PI, PD, and PID controller to spring-mass-damper model.
Model Equation: mx'' + cx' + kx = F
where,
m = mass of block,
c = damping constant,
k = spring constant
and F is the applied force, x is the resulting displacement of the block
Transfer Function (Laplace Transform of model):
X(s)/F(s) = 1/(ms^2 + cs + k)