Consider a Linear Time-Invariant real physical dynamical discrete-time (in short LTI) system that is described by the fo

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Consider A Linear Time Invariant Real Physical Dynamical Discrete Time In Short Lti System That Is Described By The Fo 1 (142.59 KiB) Viewed 43 times

Consider a Linear Time-Invariant real physical dynamical discrete-time (in short LTI) system that is described by the following 3rd order Ordinary Differential Equation (ODE), y" (t)+ay"(t)+ay (t)+ay (t)=u" (t)+bu'(t)+b^ (t). 1. Use the Routh-Hurwitz Stability Test to select a set of coefficients other than zeros so that the system is stable and have unity gain. 2. Let a, = 2= 6, , = 11,6, = 2 and bo = 3. If y (0-)= 1, y'(0-)=-1, and y" (0-) =1, and i. ii. u(t)=8(t). u(t)=u, (t). u(t)=e*u, (t). iii. Find analytically the output response using both the time and the frequency domains. 3. Use Matlab to verify your answers of problem 2. 4. Use Simulink to verify your answers of problem 2. 5. Consider a unity-feedback Standard Block Diagram (SBD) where the plant’s transfer function is given in problem 2. Draw the root locus by hand and then use Matlab to verify.