Abstract
In the two-degree of freedom control, the performance of good command following and disturbance rejection are considered separately. Qualitatively, good performance is equivalent to minimizing the energy of the error for any inputs. In this work, usingH ∞-formulation in the frequency domain, robust stability and robust performance specifications have been analyzed for the two-degree of freedom control structure with a dynamic controller. When the two-degree of freedom system having a feed-forward loop is controlled by a dynamic controller, two different performance weight functions are imposed and the robust performance specification is proposed in terms of the return ratio and feed-forward loop. The design algorithm in the frequency domain is illustrated for the simplified retail model of Industrial Dynamics to compare three kinds of control laws, which are the output feedback control scheme and two additional dynamic control ones. Numerical simulation results show that the dynamic control laws provide a larger robust stability margin than the output feeback control one and has good performance robustness for disturbance rejection at low frequencies.
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Abbreviations
- IESF:
-
Integrated-Error with State-Feedback controller
- ISFF:
-
Integrated-Error with State-Feedback and Filtering controller
- H ∞ :
-
Hardy space
- ε j (s):
-
Sensitivity transfer function in the s-domain forj = 1, 2, 3
- η j (s):
-
Complementary sensitivity transfer function in the s-domain forj = 1, 2, 3
- μ j (s):
-
Pseudo-sensitivity transfer function in the s-domain forj = 1, 2, 3
- subscript 1, 2, 3:
-
1 stands for output feedback, 2 for IESF, and 3 for ISFF
- w(s) :
-
Performance weighting function
- l m :
-
Multiplicative uncertainty
- Δ:
-
Uncertainty
- DUD:
-
Delay due to unfilled orders at distributor
- UOD:
-
Unfilled orders at distributor
- IAR:
-
Actual inventory at retailer
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Jeong, S. Analysis of robust stability and performance for two-degree of freedom control structure with dynamic controller. KSME Journal 10, 128–137 (1996). https://doi.org/10.1007/BF02953652
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DOI: https://doi.org/10.1007/BF02953652