Discrete PID Controller

Here is an implementation of a discrete PID in MATLAB

Continuous time: $$u(t) = K_pe(t)+K_i\int_{0}^{t} e(\tau)d\tau+K_d\frac{de(t)}{dt}$$

For the integral term, 2 methods are being used for numerical integration (Trapezoidal rule and Composite Simpson's 1/3 rule). We have an advanced integral term handling based on whether k is even or odd.

The derivative term is implemented using backward Euler.