7/24/2019 Assignment 5 EI304 - Principles of Automathic Control (A)

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Assignment for Chapter 5: Root Locus

5-1 Given the open-loop transfer function)(

)1()(

2ass

sK sG

  r 

+

+

=   for a

unity feedback system, please sketch the root locus for

+∞→= 0r 

K    with different 10,9,5   ===   α aa .

Please determine the breakaway (or break-in) points on the real

axis，the angles of asymptotes, and the real-axis intercept of the

asymptotes.

5-2 Sketch the root locus of the closed-loop system with the following

open-loop transfer function.

)22)(2()(

2+++

=

ssss

K sG

  r 

 

⑵ )3)(2)(1()(

+++

=

sss

K sG  r 

 

⑷

)6)(5)(2)(1(

)4)(3()(

++++

++

=

sssss

ssK sG

  r 

 

⑸

)11.0)(125.0(

)15.0()(

2++

+

=

sss

sK sG

 

5-3 Sketch the root-locus of the closed-loop system with the following

open-loop transfer function

3

)3)(1()()(

s

ssK s H sG  r 

  ++

=  

What is the range of r K    to ensure the stability of the

closed-loop system? Calculate the steady-state error sse   of the

system with unite ramp input.