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3. Modify the I-controller to obtain a phase margin around 45 degree. Plot the step response of

the closed loop system. Is it possible to alter the dynamic characteristics with the chosen phase

margin?

4. Now, let us design a PI-controller. Let us chooseTI = 1/50, and implement a preliminaryPI-controller in Matlab.

5. To find the final continuous PI-controller, modify the PI-controller to obtain a phase margin

around 45 degree. Plot the step response of the closed loop system. Is it possible to alter the

dynamic characteristics with the chosen phase margin?

6. Make a bode plot of the closed loop system and find the bandwidth wb at the 3 dB bandwidth.Now, we want to make a digital design, and thus, we need a sample time. Calculate two different

sample times. One atws = 30wband one atws = 10wb.

7.Obtain four digital controllersD1(z),D2(z),D3(z), andD4(z).

D1(z) Use zero order hold (Matlab zoh), andws = 30wb.

D2(z) Use zero order hold (Matlab zoh), andws = 10wb.

D3(z) Use triangle hold (Matlab foh), andws = 30wb.

D4(z) Use triangle hold (Matlab foh), andws = 10wb.

8. Evaluate each discrete controller by plotting the closed loop step responses. Notice, you need

to transformG(s)into a discrete equivalent. Which technique should be used?

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