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Controller design

Design a continuous PI controller to achieve approximately 20% overshoot to a step input.
Set the integral action time to be in the range 0.8Tdom < Ti < 1.2Tdom ( but not equal to Tdom), where Tdom is the dominant process time constant.
A continuous PI controller is With a chosen value of Ti,
>> s=tf(‘s’);
>> g=tf([0 2.5],[30 11 1])

Transfer function:

>> gi=1+1/(7*s)
Transfer function:

>> g1=g*gi
Transfer function:

>> sisotool(g1) this part have been done

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3.2 A digital PI using backward difference discretisation, s = (z-1)/Tz, can be implemented in SIMULINK as shown in the following diagram. (Your diagram can be different from this).

Set the sampling time in each so that one returns the values
Every sample time and the other returns the values in between samples, e.g. T/4.
Initially use a sampling time Tdom/10 then use two further sampling times, one faster and one slower