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

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Advanced control

بسم الله الرحمن الرحيمAdvanced Control

Discrete forms of PID controllers

Reference: A. Visioli, Practical PID Control, Springer 2006

Computer control
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 control1
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
Discrete Form of PID Controllers

  • Position Form

Sampling Time : Ts , Number of Sampling : k , Time : t = kTs

Discrete form of pid controllers1
Discrete Form of PID Controllers

  • Position Form

  • Velocity Form

Discrete form of pid controllers2
Discrete Form of PID Controllers

  • Velocity Form

  • Where:

Discrete form of pid controllers3
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