National Instruments 370757C-01 用户手册

The H

2

 Linear-Quadratic-Gaussian (LQG) control design methods are 

based on minimizing a quadratic function of state variables and control 
inputs. Conventionally, the problem is specified in the time domain. 
By converting the LQG performance index into the frequency domain, 
it becomes obvious that the conventional LQG places equal penalty on 
states and control inputs at all frequencies. It is possible to realize 
significant improvement in robustness and performance by making the 
penalty weighting matrices functions of frequency.

Bryson’s rule [BH69] can be extended to initially select a frequency 
shaping for a particular problem. For the control design problem, the 
frequency-shaped weighting matrices should be large at frequencies where 
control inputs are less desirable. For example, a large weighting on control 
signals at high frequency would produce less control activity at those 
frequencies, leading to a closed-loop system with lower bandwidth. Similar 
ideas apply to selection of state weighting in control design and the 
development of robust state estimators. 

Three functions are available to solve the problem of frequency-shaped cost 
functionals: 

•

fsregu( )

—frequency-shaped regulator

•

fsesti( )

—frequency-shaped estimator

•

fslqgcomp( )

—frequency-shaped linear-quadratic-gaussian 

compensator

[SysC, SysCC, vEV] = fsregu(SysA, ns, RXXA, RUUA, {RXUA})

The 

fsregu( )

 function computes a frequency-shaped control law. 

It assumes you start with:

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