Process Control: Modeling, Design, and Simulation

M16.2. PID Controllers

Consider the continuous (analog) form of an ideal PID controller,

Equation M16.1

We use a constant sample time, Δt, and the index k to represent the value of the continuous time signal at discrete step k. For example, the error at discrete sample time k is equal to the continuous system value at time t = t_k.

Equation M16.2

We approximate the integral term

Equation M16.3

and the derivative term is approximated using backward ...