Question

Q3 (20 pts, 5pts/subpart) -- Constant zeta between systems (a) Create three 2nd-order systems (sys7, sys8, sys9) that have no zeros, each with zeta=0.150, and the real part of the poles (sigma) = -0.2, -0.4, and -0.6, respectively for each system. Echo out each system so the transfer function can be observed (that is, just remove the semi-colon at the end of the zpk() function). Ensure the system gain is normalized to one. (b) Create the pzmap for the above three systems using subplot(1,2,1). Add a grid, legend, title, and scale the x-axis from (-1 to 0) and the y-axis from (-4 to 4). (c) Show the step response for the above three system using subplot(1,2,2). Add a grid, legend, title, and scale the y-axis from (O to 2). Note, if modeled correctly, the steady-state value for each system's step response will be one. (d) What conclusions/tends can you make between these systems when the poles move, keeping zeta constant?

Answer 1

CODE:

clc close all § a) sys7 = zpk([],-0.2,0.2) sys 8 = zpk ([],-0.4,0.4) sys9 = zpk([],-0.6,0.6) % b) subplot (1,2,1) pzmap (sys7, sys8, sys9) grid on legend('sys7', 'sys8', 'sys9') xlim ([-1 0]) ylim ([-4 4]) % c) subplot(1,2,2) step (sys7, sys8, sys9) grid on legend ('sys7', 'sys8', 'sys9') ylim ( [0 2])

RESULT:

- 0 Figures - Figure 1 File Edit View Insert Tools Debug Desktop Window 2803 m ... @ 09 Figure 1 x Help 0 O BOO Step Response Pole-Zero Map 0.15 0.105 0.07 m 0.21 2 + 40: sys7 sys 7 3 0.32 sys9 sys8 sys9 NO 0:55 Imaginary Axis (seconds 1) Amplitude 0:55 N 1 -3 0:32 0.21 -0.8 1 0.15 0.105 0.070.0440.6825 -0.6 -0.4 -0.2 40 Real Axis (seconds-1) 0 10 40 20 30 Time (seconds)

as we move away from the origin (0,0) , corresponding to the pole location, the time constant will decrease and the system will settle quickly

Step Response sys 7 sys8 sys9 System: sys9 Settling time (seconds): 6.52 System: sys8 Settling time (seconds): 9.78 Ampl 0.5 System: sys7 Settling time (seconds): 19.6 - .- 1.5 -- .-.-.- 2 2.5 .- .- 3 -.-.- 1.0325 R 10 20 30 Time (seconds)