5. Consider four second order systems denoted by the following transfer functions: (10 pts) 64 System 1: H (3)= (s? +64)

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5 Consider Four Second Order Systems Denoted By The Following Transfer Functions 10 Pts 64 System 1 H 3 S 64 1 (27.99 KiB) Viewed 103 times

5 Consider Four Second Order Systems Denoted By The Following Transfer Functions 10 Pts 64 System 1 H 3 S 64 2 (62.77 KiB) Viewed 103 times

5. Consider four second order systems denoted by the following transfer functions: (10 pts) 64 System 1: H (3)= (s? +64) 64 System 2: H,(s)= (s? +2s +64) 64 System 3: Hz()= (5* +165 +64) 64 System 4: H.(s)= (s? +32s +64) a. Give the values of on and for each case & fill in the blank whether the system is overdamped, underdamped, undamped and critically damped: System 1: System 2: System 3: System 4:

b. Using MATLAB, determine the poles & plot the real and imaginary part of the poles of the four systems on the x-y axis using the plot(real(p), imag(p), 'x') command where p represents the poles of the system. Plot all the poles in the same graph using four different colors, give appropriate legend and x-y labels. Discuss the differences in the locations of the poles for the four systems. Give the two Poles for System : Give the two Poles for System 2: Give the two Poles for System 3: Give the two Poles for System 4:_ c. Using MATLAB determine the impulse responses of all the four systems using the impulse command. Plot all the four impulse responses on the same graph using four different colors, give appropriate legend and x-y labels. Compare and discuss the differences in the four results. Use time [0:0.01:5). d. Using MATLAB determine the step responses of all the four systems using the step command. Plot all the four step responses on the same graph using four different colors, give appropriate legend and x-y labels. Compare and discuss the differences in the four results. Use time [0:0.01:5).