Basic Weighting Functions

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This page introduces some basic first-order weighting functions used in Examples 1 and 2.

Often, the following mixed sensitivity problem is solved in H∞ control:
 
Thus W1-1 can be interpreted as the desired sensitivity, and W3-1 as the desired complementary sensitivity.

Explanation about the use of values in dB: The numbers you would have to insert for the parameters are expected to be in dB, such that you can easily read them of from the diagrams' axes labeling.

The following structure is considered for the weight of sensitivity S:
 
In the example on the right, the values are:

S0 = -30 [dB]
S∞ = 40 [dB]
ωD1 = 30 [rad/s]

Singular value diagram of W1-1:
 

The weight on the control variable (respectively transfer function KS) is a constant value for simplicity:
 

 

 

 

 

 

The following structure is considered for the weight of complementary sensitivity T:
 
The values in the example on the right are:

T0 = 10 [dB]
T∞ = -20 [dB]
ωD2 = 100 [rad/s]

Singular value diagram of W3-1: