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

1979 ◽  
Keyword(s):  
Complex Variable ◽  
Feedback Systems ◽  
Variable Approach ◽  
Multivariable Feedback

Relationships between Recent Developments in Linear Control Theory and Classical Design Techniques (Part 1)

1975 ◽  
Vol 8 (5) ◽  
pp. 179-187 ◽  
Author(s):  
A. G. J. MacFarlane
Keyword(s):  
Complex Variable ◽  
Linear Control ◽  
Feedback Systems ◽  
Analysis And Design ◽  
Linear Control Theory ◽  
Classical Design ◽  
Recent Developments ◽  
Comprehensive Survey ◽  
Multivariable Feedback ◽  
Design Techniques

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.

High-Fidelity AeroAcoustic Optimization Tool for Flexible Rotors

2020 ◽  
Author(s):  
Li Wang ◽  
Boris Diskin ◽  
Leonard V. Lopes ◽  
Eric J. Nielsen ◽  
Elizabeth Lee-Rausch ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Complex Variable ◽  
High Performance ◽  
Computational Cost ◽  
Geometric Constraints ◽  
General Level ◽  
High Fidelity ◽  
Variable Approach ◽  
Multidisciplinary Analysis ◽  
Tightly Coupled

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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