Magnetorheological Fluid Technology

27Control Strategies

where ω stands for random noise disturbance and ν represents random mea-

surement (sensor) noise. Both ω and ν are white Gaussian zero-mean station-

ary processes. It is noted that because the states and control are both random,

the performance index will be random. Thus, the problem is to nd the opti-

mal control that will minimize the average cost. Using the same procedure

as for the LQR problem, the solution is achieved as:

i. Controller:

0

1

1

u Kx

K R B P

A P PA PBR B P Q

T

T T



= −

=

+ − + =

−

−

(2.19)

ii. Estimator:

( )

0

1 1

1

1 1 1 1

1

1 1

x Ax Bu K y Cx

K P C R

AP P A P C R CP Q

e

e

T

T T T





 

= + + −

=

+ − + Γ Γ =

−

−

(2.20)

In the previo ...