This document discusses PID tuning to achieve exact gain and phase margin for a process. It provides the tuning procedure, calculates the PID gains for a given process, and includes MATLAB code to plot the bode diagrams and step responses of the uncompensated and compensated systems. The calculations result in a proportional gain of 1.94, integral gain of 1.47, and derivative gain of 1.36 to achieve a phase margin of 1.047 radians and crossover frequency of 1.04 radians/second.

1. PID TUNINIG WITH EXACT GAIN AND PHASE MARGIN (EXAMPLE #03) PRESENTED BY Muhammad Ahsen Al Muhammad Younas Muhammad Omer Khan Department of Electrical Engineering, PIEAS

4. BODE PLOT OF UNCOMPHENSATED SYSTEM

5. OUR CALCULATIONS: wp=wc=1.04rad/sec Am=3.0 PM=1.047 Kp=1.94 ,KI=1.47 and KD=1.36 OUR EXAMPLE AND CALCULATIONS:

9. BODE PLOT OF COMPHENSATED SYSTEM s=tf('s'); Gp=1/((s^2+s+5)*(s+1)) Gp.OutputDelay=2 Gc=(1.950+1.478/s+1.372*s) Gser=series(Gp,Gc ); bode(Gser)

10. Addition of step disturbance