Figure 1) explains four Argand diagrams. In each diagram, there are two roots belonging to 2nd order process. Figure (II) includes four unit step responses. Mach diagrams in Figure () with the corresponding in Figure (II) and give the reason. 2 X Imaginary Axis seconds) Imaginary Axis (seconds) -1 Real Aals seconds) 3 Real Axls (seconds 2 X Imaginary Als seconds) Imaginary Axis seconds) 0 아 0 X 2 0 RealAxis seconds) Real Axis (seconds Figure (1) Roots Step response А Step response 1.5 Amplitude Amplitude 05 0.5 10 10 Time (seconds) Stop response C Time seconds Step response praphus Amplitude 05 10 10 Time (seconds) Time seconds) Figure (II) unit step response

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Figure 1) explains four Argand diagrams. In each diagram, there are two roots belonging to 2nd order process. Figure (II) inc
Step response А Step response 1.5 Amplitude Amplitude 05 0.5 10 10 Time (seconds) Stop response C Time seconds Step response

EXPERT ANSWER

Inginary anis а a (5) Roots are: -bi . S = -b I a а a heal anis (5)
Consider the two points marked. These are the roots of second order system A second order system with unit step input is give
< 1 since the roots are all imaginary As the above figure, the roots are: 5 = -la tai Comparing both the equations and b = es
2 al a 1 - 88 Eg 2 2 es 뿜 (4-2-re the [1+421 =) 2 ² = as 2 eus 1 + a2 1 b2 2 z 2 b ano 2 at 62 Z = es b V a2+62 2
het the response the above diagram be of 1,5 1 0.51 B В † 5 10 overshoot eap explanas 1-6² - A B
Diagram 1 1 a = 1 b = 0.3 2 Es 1) = 0.3 12+0.32 0.289 て= es = 0.284 -0.957 0.3 b es, = 0.287 zi 0.957
Лхб, 281 0.20 overshoot ер 1-о: 28-12- 0:39
Diagram 2 2 a = 0.8 b= 0.6 2 es 0.6 0.8+0.64 = 0.6 res 2 2 = 0.6 =) 2 0.6 C-Tx 0.6 overshoot = expl 1 -0.62 = 0.0947 Diagram
Diagram 4 a = 7 b= 1, 2, *, 1.2 2 11°+1.2- 2. А. е о. 51 Z= 0. 51 = 0:48 |-2 44 = 0. 51 C4 = 0. 48 overshoot - сухо. 51 ер уі
Diagrams @ and @ have almost equal values of overshoot Oil SS Juu o Diagrams 0 - and . Ⓡ have almost equal values of overshoo
Consider curves A and C C Curve 1 Thus A has a faster response compared to C A has a lower value of z: 1 24 = 0.48 Zz > Za <Z
Final Answer Figure II 1 Curve D Figure I Diagram Diagram 2 Diagram 3 Diagram 4 Curve Curve B 2 Curve A