Please help me fill in the box Thank you PID Controller Desi

Please help me fill in the box

Thank you

PID Controller Design Introduction: This is a Satellite Tracking System. More precisely, it tracks is the Azimuth angle of the satellite. Azimuth is defined as \"a horizontal angle measured clock wise from any fixed reference plane. The reference is usually taken as true north, which is considered 0 azimuth. Potentiometer Antenna Desired Azimuth azimuth angle input output power amplifier Motor Potentiometer This system can be presented by the following schematic diagram, table of parameter values, and a block diagram

Solution

solution:

1)here transfer function for given system is given by

T.F.=G(s)/1+G(s)=5.088K/[(s^2+1.32s)(s+10)+5.088K]

2)here characteristic equation for RH method is denometer term and it is

[(s^2+1.32s)(s+10)+5.088K]=0

on simplifying we get

s^3+11.32s^2+13.2s+5.088K=0

on solving by forming matrix by RH method we get value of K as 0<K<29.4

so for stable result Kcr=29.4

3)where for tuning PID controller by ZN method we have to set Ki and Kd to zero and increase only Kp and it is maximum at Kcr,so auxillary equation is

s^2(13.2s-5.088K)=0

so roots are

s=0 and s=11.3323 so our frequency is

wa=11.3323 rad/s

and time period Pcr=2*pi/wa=.5544 sec and from that we can get value of Ti and Td and set value of gain Ki and Kd