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138 CHAPTER 4. DEMONSTRATION EXAMPLES
1 10 100 10000.1 10000
0.5
1
1.5
0
2
Singular value plot of the closed loop
4.1.5 µ AnalysisoftheH
∞
Controller
The H
∞
control law can be analyzed using µ-analysis. The closed-loop system, g1,has4
inputs and 4 outputs. The first two inputs and outputs correspond to the uncertainty
block, and the second two correspond to the disturbance rejection block, or performance
block. Therefore, we can define the uncertainty inputs and outputs as a full 2×2
uncertainty block and the disturbance rejection inputs and outputs as a full 2×2
performance block. If the µ value for this control design is 1, then we are able to achieve
robust performance for the set of defined weights and this control design.
The mu function analyzes the robust performance and stability of the closed loop system.
The syntax of the function is:
[bnds,D,Dinv,Delta,sens] = mu(M,blk)
The variable M is usually the frequency response of the closed loop system. blk defines
the structure of the perturbations. In this example the block structure is two 2×2