Consider the following system Reference T=0.1 sec Controller D(z) ZOH 1-e S Plant 10 (s+1)(s+2) System...

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Consider the following system Reference T=0.1 sec Controller D(z) ZOH 1-e S Plant 10 (s+1)(s+2) System Y(z) Output Figure 2 a) Obtain the discrete time equivalent closed loop transfer function and determine the system type (use MATLAB for the discretization) b) Design a digital controller in order to preserve a zero steady-state error, for a step input signal and for a minimum velocity error constant equal to 5. Consider the following system Reference T=0.1 sec Controller D(z) ZOH 1-e S Plant 10 (s+1)(s+2) System Y(z) Output Figure 2 a) Obtain the discrete time equivalent closed loop transfer function and determine the system type (use MATLAB for the discretization) b) Design a digital controller in order to preserve a zero steady-state error, for a step input signal and for a minimum velocity error constant equal to 5.