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I'm doing my homework, and encountered a problem.

The problem is the one as attached. It includes a part of solution that I don't understand.

I've known that when designing the PI controller, we start from D(s) = (Kp + Ki/S)

The condition of the PI controller is, firstly, unity DC gain.

So the way I started is setting D(0) = 1, but couldn't proceed anymore cuz there is 1/s

in D(s), also it is obviously different from the solution.

The second way was setting whole transfer function of the system Gcl(0) = 1,

but couldn't find the right solution.

According to solution, it approaches Kp and Ki separately.

And it uses (G(0)/(1+Kp*G(0))=1), but I can't understand this.

Could somebody help me out??

The problem is the one as attached. It includes a part of solution that I don't understand.

I've known that when designing the PI controller, we start from D(s) = (Kp + Ki/S)

The condition of the PI controller is, firstly, unity DC gain.

So the way I started is setting D(0) = 1, but couldn't proceed anymore cuz there is 1/s

in D(s), also it is obviously different from the solution.

The second way was setting whole transfer function of the system Gcl(0) = 1,

but couldn't find the right solution.

According to solution, it approaches Kp and Ki separately.

And it uses (G(0)/(1+Kp*G(0))=1), but I can't understand this.

Could somebody help me out??

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