If we compare Figure 4 with Figure 2, it is evident that stable region of K is much larger for the compensated system than the uncompensated system. Next we need to calculate K from the magnitude criterion.

Thus the required controller is $G_D(z)=10.5\dfrac{z-0.82}{z-0.244}$ . The SIMULINK block to compute the output response is shown in Figure 5. All discrete blocks in the SIMULINK model should have same sampling period which is 0.2 sec in this example. The scope output is shown in Figure 6.

$\includegraphics[width=10cm]{simexmp.eps}$

Figure 5: Simulink diagram of the closed loop system

$\includegraphics[width=8cm]{output.eps}$

Figure 6: Output response of the closed loop system