2. The simulink model for a closed-loop sampled-data system is given in Fig. 3. a) Before the experiment, calculate G(z) for the system and use the Routh-Hurwitz criterion to determine the range of K for stability. Also, calculate the frequency at which the system will oscillate when marginally stable. b) Plot the root locus of the system. Determine the range of K for stability. Compare the results with a. Is there any difference or similarities between them? If any, explain the reason. c) Plot the bode diagram of the system. Determine the range of K for stability. Compare the results with a, and b. Is there any difference or similarities between them? If any, explain the reason. d) Start simulink and construct the model that is given in Fig.3. Additionally, in order to plot the Y(t) by using workspace use a clock and a workspace blocks which are named as t, ytSampled. Set the sampling time -1 for all workspace blocks. Run it by clicking on the start button. Also, assume that zero-order hold reconstruction method is used and the sampling time will be 0.1 second (T = 0.1 sec). e) Observe the output signal Y(t) on the scope for different K value and check the validity the range of K. Plot the Y(t) by using t and ytSampled for marginally stable. f) Repeat from a to e for the system that is given in Fig. 4. E(t)=u(t) Zero-Order Hold -K- $2²+45 Gain Transfer Fcn1 Y(t) Fig. 3 A closed-loop sampled-data system 10 -K- $2 E(t)=u(t) Zero-Order Hold Gain Transfer Fcn1 Y(t) 0.02 Fig. 4 A closed-loop sampled-data system