Linear Controller Design: Limits of Performance by Stephen Boyd and Craig Barratt - HTML preview

CHAPTER 11 A PICTORIAL EXAMPLE

11.2

Regulation

11.2.1

Asymptotic Rejection of Constant Disturbances

We rst consider the e ect on p of a constant disturbance applied to proc. Fig-

y

n

ure 11.6 shows the subset of slice where such a disturbance asymptotically has no

H

e ect on p, , where the a ne function

y

i.e.

(a)

(b)

(c)

11 (0) +

11 (0) + (1

) 11 (0)

(11.4)

H

H

;

;

H

vanishes.

2

1:5

(0) 0

H

<

11

1

;

;

(0) = 0

H

11

0:5

(0) 0

H

>

11

0

;0:5

;1

;1

;0:5

0

0:5

1

1:5

2

Asymptotic rejection of constant actuator-referred distur-

Figure

11.6

bances on .

y

p

11.2.2

Rejection of a Particular Disturbance

Suppose now that an actuator-referred disturbance is the waveform part( ) shown

d

t

in gure 11.7. Figure 11.8 shows the level curves of the peak output p due to the

y

actuator-referred disturbance part, ,

d

i.e.

(a)

(b)

(c)

11 +

11 + (1

) 11 part

(11.5)

H

H

;

;

H

d

1

which is a convex function on 2.

R

11.2 REGULATION

255

0:5

0:4

0:3

0:2

() 0:1

t