بسم الله الرحمن الرحيم Advanced Control Lecture four Mohammad Ali Fanaei Dept. of Chemical Engineering Ferdowsi University of Mashhad Reference: A. Visioli, Practical PID Control, Springer 2006

Computer Control 1.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. 2.The computer performs the control calculations on the sampled process signal(s) and computes the output(s) to the process. 3.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 : T s, Number of Sampling : k, Time : t = kT s

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 -n y(k) Tuning of Digital PID : Moore et al. (1969) Use the continuous tuning formula of PID controller with corrected dead time