National Instruments 370753C-01 Manual De Usuario

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

You will use this regulator gain later in designing a compensator.

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 

 

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 K

. 

estimator( )

 calculates the 

constant, optimal state-estimator gain matrix K

 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.

yˆ

.