how do i make a integral control with a setting time 6% of 1 sec

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Zain Ahmed 2020-5-14

I wanted to make an integral control and i have a state space model.

I have to ensure that my controller have setting time of 6% of 1 sec.

i needed to use pole placement design my controller.

This is my MIMO space state model

A = [0 1 0 0;0 -1 0 0.5;0 0 0 1;0 0 0 -0.2];
B = [0 -1 0 0.2;0 1 0 0.2];
C = [1 0 0 0;0 0 1 0];
D = [0 0;0 0];
sys = tf(A,B,C,D);

Then i determined its controllability and observability,

Co = ctrb(sys); % gives 4x8 matrix
Ob = obsv(sys); % gives 8x4 matrix

The system is observable and controllable

Then i extended my state space so i can perform integral control:

Ae = [A [0 0;0 0;0 0;0 0];C [0 0;0 0]];
Be = [B;[0 0;0 0]];
Ce = [C [0 0;0 0]];

I know that i can use place to finde state feedback matrix F.

But how do i find it by using pole placement?

Should i use control canonical form?

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R2019b

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