Chapter 6 State-Space Design
Xmath Control Design Module 6-16 ni.com
Ruu is a scalar because you have only one input for this particular model.
[Kr,ev,P] = regulator(ipsys,Rxx,Ruu);
Kr
Kr (a row vector) =
-348.778 -32.1056 -100 -27.3036
Note You will use this regulator gain later in designing a compensator.
Linear Quadratic Estimator
The LQR approach discussed in the preceding section is based on the
assumption that the values of all the states are available. In the real world,
only the output values are generally available and they are frequently
corrupted with noise. You know from the Observability and Estimation
section that you can obtain an estimate of the states using an observer if the
system is reachable. The problem solved with the optimal estimator
function estimator( ) is that of finding the best estimate of the states,
given certain assumptions about the noise associated with the output.
As shown for the continuous case in Figure 6-5, the plant system is
augmented with an estimator—an observer used in conjunction with a
noisy system. The estimator supplies estimates of all the system states and
feeds back the difference between the estimated and the actual outputs
through the optimal estimator gain Ke. estimator( ) calculates the
constant, optimal state-estimator gain matrix Ke for a dynamic system. The
estimator gain is derived by minimizing the expected mean square of the
error between the measured output y and the output from the estimator,
This model takes into account that there may be some process noise within
the system model (plant) itself as well as some noise inherent in the device
used to measure the outputs.
y
ˆ
.