1. If the time delay term is replaced by 1/1 Pade approximation, determine the poles and zeros of G(s)=s+2e?2s? 2. Find the maximum Kc value for the close loop system of GOL?=(s+1)(s+2)(s+3)2Kc?? to be stable with i) Routh array method and ii) direct substitution method. 3. Find the first order plus time delay model for G=(2s+1)(3s+1)(4s+1)1? solutionspile.com

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1. If the time delay term is replaced by

1/1

Pade approximation, determine the poles and zeros of

G (s) = \frac{e ^{? 2 s}}{s + 2}

2. Find the maximum

Kc

value for the close loop system of

G_{O L} = \frac{2 K _{c}}{( s + 1 ) ( s + 2 ) ( s + 3 )}

to be stable with i) Routh array method and ii) direct substitution method. 3. Find the first order plus time delay model for

G = \frac{1}{( 2 s + 1 ) ( 3 s + 1 ) ( 4 s + 1 )}

4. Find the equation of the straight 1 ine which fits best for data

(0, 0), (1, 2), (2, 1)

5. For closed feedback control system of

G_{c} = 1, G_{v} = 1, G_{p} = \frac{1}{s ( s + 1 )}, G_{m} = 1

The set point is changed by unit step function. Find the of fset. ? 6. Draw Bode diagram and Hyquist diagram for

G (s) = 1/ s

and

G (s) = s

. 7. Find the time constant and damping coefficient of

C / R

for the closed feedback control system of

G_{c} = 1 + \frac{1}{s} + s, G_{v} = 1, G_{p} = \frac{1}{s + 1}, G_{m} = 1

8. Find the limit value of

(1 + \frac{2}{t})^{t}

as

t

goes to infinity. 9. The transfer function of a process and measurement element connected in series is given by

G (s) = \frac{e ^{? s}}{5 s + 1}

a. Sketch the open-1oop Bode diagram (gain and phase) for a control system involving this process and measurement lag. (Assume Gc=Kc, Gv=1) b. Specify the maximum (ultimate) gain of a proportional controller to be used in this control system. 10. Find the minimum amplitude ratio and its angular velocity for the PID controller of

G_{c} = 1 + \frac{1}{s} + s

11. Find the amplitude ratio at the critical frequency for

G = \frac{1}{( s + 1 ) ^{4}}

12. Draw the feasible region satisfying

\frac{2 x + y}{x + y} < 0

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