User`s guide

1 Quick Start
1-20
Control Design Tools
The Control System Toolbox supports three mainstream control design
methodologies: gain selection from root locus, pole placement, and
linear-quadratic-Gaussian (LQG) regulation. The first two techniques are
covered by the
rlocus and place commands. The LQG design tools include
commands to compute the LQ-optimal state-feedback gain (
lqr, dlqr,and
lqry), to design the Kalman filter (kalman), and to form the resulting LQG
regulator (
lqgreg). See “LQG Design” on page 7-8 for more information.
As an example of LQG design, consider the regulation problem illustrated by
Figure 1-1. The goal is to regulate the plant output around zero. The system
is driven by the white noise disturbance , there is some measurement noise
, and the noise intensities are given by
The cost function
is used to specify the trade-off between regulation performance and cost of
control. Note that an open-loop state-space model is
where is a state-space realization of .
y
d
n
Ed
2
() 1,= En
2
() 0.01=
Ju() 10y
2
u
2
+()td
0
∞
∫
=
x
·
Ax Bu Bd++= (state equations)
y
n
Cx n+= (measurements)
ABC
,,() 100 s
2
s 100++()⁄