Robust control systems 2018b mk lecture notes

CONTROL SYSTEM DESIGN
Lecture Notes
Robust Control Systems
Page
r
6
- Sr  i : ri is the ith root.
i

 / 
n

- ST  
i 1

8

n

- ST  
i 1

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11
12
14

Sri
s  ri

: if zeros of T(s) are independent of the parameter α.

Sri
s  ri

: relationship of two sensitivities.

- This system is not very robust.
- This is a PD controller.
- This system is not very robust.
- Gm(s): a multiplicative perturbation.
- M ( j )  1 

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Notes

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Gc ( j )G ( j )

for all  :

assume that G & Gm have the same.

number of poles in the right-hand s-plane.
- If K = 1, the system is unstable.
- Gm (s)  G(s)[1  M (s)] : the process G becomes Gm.
- M ( j )  1 

1
Gc ( j )G ( j )

for all  :

condition for a stable system.

- sn  an1sn1  an2 sn2  ...  a0  0 : the characteristic equation.
q1 (s)  s3   2 s 2  1s  0

-

q2 (s)  s3  2 s 2  1s  0
q3 (s)  s3  2 s 2  1s  0

: 4 possible characteristic equations when coefficients

q4 (s)  s3   2 s 2  1s  0

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change.
- According to Routh – Hurwitz criterion, this system is stable.
- q(s)  s3  3s 2  2s  4.5  0 : the nominal characteristic equation.
- T (s) 

Y (s)

 1:
R( s )

one possible objective in the design of a control system is that

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the controlled system's output should exactly and instantaneously reproduce its
input. That is, the system transfer function should be unity.
- Gp (s) : the prefilter.

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- s3  1.75n s2  2.15n2 s  n3 : see page #46, Performance of FCS.
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Notes
32 - Percent overshoot is not very good, then a prefilter is required.
36 - This system is very stable.
39 - K = 0: no state variable feedback.
- s2  3.2n s  n2 : see page #47, Performance of FCS.
40 - Suppose that settling time is 1 second.
41 - This system is very stable.
42 - Poles can change by 50%.
43 - Table: see page #53, Design of FCS.
- Suppose that Ka = 10, Kb = 2.

44 - This system is very stable.

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