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

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.

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

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

Discrete Form of PID Controllers Position Form Velocity Form

Discrete Form of PID Controllers Velocity Form Where:

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