A Complex Variable Approach to the Analysis of Linear Multivariable Feedback Systems

1975 ◽  
Vol 8 (5) ◽  
pp. 179-187 ◽  
Author(s):  
A. G. J. MacFarlane

A comprehensive survey is given of recent work on the use of matrix-valued functions of a complex variable for the analysis and design of linear multivariable feedback systems. Several emerging design techniques are outlined and a simple illustrative design example given showing how such methods may be used in practice.


Author(s):  
Li Wang ◽  
Boris Diskin ◽  
Leonard V. Lopes ◽  
Eric J. Nielsen ◽  
Elizabeth Lee-Rausch ◽  
...  

A high-fidelity multidisciplinary analysis and gradient-based optimization tool for rotorcraft aero-acoustics is presented. Tightly coupled discipline models include physics-based computational fluid dynamics, rotorcraft comprehensive analysis, and noise prediction and propagation. A discretely consistent adjoint methodology accounts for sensitivities of unsteady flows and unstructured, dynamically deforming, overset grids. The sensitivities of structural responses to blade aerodynamic loads are computed using a complex-variable approach. Sensitivities of acoustic metrics are computed by chain-rule differentiation. Interfaces are developed for interactions between the discipline models for rotorcraft aeroacoustic analysis and the integrated sensitivity analysis. The multidisciplinary sensitivity analysis is verified through a complex-variable approach. To verify functionality of the multidisciplinary analysis and optimization tool, an optimization problem for a 40% Mach-scaled HART-II rotor-and-fuselage configuration is crafted with the objective of reducing thickness noise subject to aerodynamic and geometric constraints. The optimized configuration achieves a noticeable noise reduction, satisfies all required constraints, and produces thinner blades as expected. Computational cost of the optimization cycle is assessed in a high-performance computing environment and found to be acceptable for design of rotorcraft in general level-flight conditions.


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