1. Discrete forms of PID controllers
بسم الله الرحمن الرحيم
Discrete forms of PID controllers
Reference: A. Visioli, Practical PID Control, Springer 2006

2. Computer Control
The computer requests a value from the A/D converter. The A/D converter samples the process signal, converts it to a number, and stores it in the computer memory or a register.
The computer performs the control calculations on the sampled process signal(s) and computes the output(s) to the process.
The computer output is sent to the D/A converter, which converts it to an electronic signal, updates the output, and holds it constant until the next update.

3. Computer Control
A good rule of thumb is that the sample time should be about one-tenth of the effective process time constant

4. Discrete Form of PID Controllers
Position Form
Sampling Time : Ts , Number of Sampling : k , Time : t = kTs

5. Discrete Form of PID Controllers
Position Form
Velocity Form

6. Discrete Form of PID Controllers
Velocity Form
Where:

7. Discrete Form of PID Controllers
Backward Shift Operator (q -1) : y(k-n)=q-ny(k)
Tuning of Digital PID : Moore et al. (1969)
Use the continuous tuning formula of PID controller with corrected dead time