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CONTROL SYSTEMS EEE F242 ECE F242 INSTR F242

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Consider the root locus for a unity-gain negative

feedback system having the characteristic equation 

, where k denotes the compensator

gain of

the forward path transfer function. 

Let thetadep

(in degrees) be the

value of the angle of departure of the root locus branch starting from the pole at 

s = - 12.6 + j 12.6.

The value of thetadep (in degrees) = 

Note: Write your answer such that 0 <= thetadep<= 360 (degrees).

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Consider the root locus for a unity-gain negative

feedback system having the characteristic equation 

, where k denotes the compensator

gain of

the forward path transfer function. 

Let k = kBA > 0

be the

value of the gain at the break-away point.

Let s = sBA be the break-away point on the real axis axis at k = kBA > 0.

The value of sBA =  

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Consider a unity-gain negative

feedback system with

G1(s) as the (second-order) plant and Gc1(s) as the series compensator. 

We have magnitude of G1(s)=12.6 at s=0.

Design a lag compensator Gc1(s) = (s+zc1)/(s+pc1) so as reduce the steady-state error by a factor of 10, as compared to the steady-state error of the uncompensated closed-loop system.

Calculate the ratio zc1/pc1 =  

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Consider the root locus for a unity-gain negative

feedback system having the characteristic equation 

, where k denotes the compensator

gain of

the forward path transfer function. 

Let thetaarriv

(in degrees) be the

value of the angle of arrival of the root locus branch arriving at the zero at 

s =  j 12.6.

State the value of thetaarriv (in degrees) = 

Note: Write your answer such that 0 <= thetaarriv<= 360 (degrees).

View this question

Consider a unity-gain negative

feedback system with

G(s) as the (second-order) plant and Gc(s) as the series compensator. 

Design a PD compensator Gc(s) = kc (s+zc) so as to place one of the closed-loop poles at s=s* = -12.6 +j12.6 .

We have, the magnitude of G(s)=0.01 at s=s*.

Also, the angle of degrees at s=s*.

The value of zc =  

View this question

Consider a unity-gain negative

feedback system with

G(s) as the (second-order) plant and Gc(s) as the series compensator. 

Design a PD compensator Gc(s) = kc (s+zc) so as to place one of the closed-loop poles at s=s* = -12.6 +j12.6 .

We have, the magnitude of G(s)=0.01 at s=s*.

Also, the angle of degrees at s=s*.

The value of kc =  

View this question

Consider the root locus for a unity-gain negative

feedback system having the characteristic equation 

, where k denotes the compensator

gain of

the forward path transfer function. 

Let k = kmarginal > 0

be the

value of the gain at which the branches of the root locus intersect the imaginary axis. 

Let s = j wmarginal be the point on the imaginary axis at which one of the branches of the root locus intersects the positive half of the imaginary axis.

The value of kmarginal =  

View this question

Consider the root locus for a unity-gain negative

feedback system having the characteristic equation 

, where k denotes the compensator

gain of

the forward path transfer function. 

Let k = kBA > 0

be the

value of the gain at the break-away point.

Let s = sBA be the break-away point on the real axis axis at k = kBA > 0.

The value of kBA =  

View this question

Consider the unit step response of a negative feedback

closed-loop system with the forward path transfer function

and feedback path transfer function

. Here, the compensator

gain in the forward path is denoted by

k

Determine the steady-state error (ess1

)

corresponding to the unit step response of the

uncompensated

(that is,

with

k=1) closed-loop system.

The value of the settling time ess1 =  

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A unity-gain feedback system has

as the forward path transfer function. Obtain the unit step response

for the closed-loop system. Calculate the peak time (t

p

) for the

unit step response.

The value of the peak time (tp) =  

View this question

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