Title: Model for Application to Higher Harmonic Control and Flight Control System Interaction

This dissertation addresses a system, generally known as “**Higher Harmonic Control**” (HHC) because it consists of superimposing high frequency rotor inputs to the conventional low frequency ones used to control and maneuver the helicopter….

Contents

1 Introduction

1.1 Motivation

1.2 Literature review

1.2.1 *Higher harmonic control technology*

1.2.2 Linear models

1.3 Objectives of study

1.4 Principal contributions

1.5 Organization of the dissertation

2 Mathematical Model

2.1 History of helicopter simulation model

2.2 Helicopter model

2.3 HHC implementation

2.4 Solution methods: trim

2.4.1 Algebraic trim

2.4.2 Periodic trim

2.5 Solution methods: linearization of the equation of motion

2.6 Solution methods: time integration

2.7 Vibration calculation

2.7.1 Hub loads calculation

2.7.2 Cockpit vibration calculation with the rigid fuselage

2.7.3 Cockpit vibration calculation with the ﬂexible fuselage

2.8 Optimization formulation

3 Active Rotor Control System for Vibration Suppression

3.1 Harmonic analyzer

3.1.1 Analog bandpass ﬁlter method

3.1.2 Fourier analyzer method

3.1.3 Eﬀect of windowing

3.1.4 Equivalent lowpass ﬁlter

3.2 Higher **harmonic control algorithm**

3.2.1 T-matrix method

3.2.2 T-matrix validation

3.3 Discrete HHC update

4 Extraction of the Constant-Coeﬃcient Linearized Model

4.1 Extraction of a linearized model without higher harmonics

4.2 Extraction of a linearized model with higher harmonics

4.2.1 Deﬁnitions

4.2.2 Extraction of the control matrix B

4.2.3 Extraction of the state matrix A

4.2.4 Extraction of the feedforward matrix D

v4.2.5 Extraction of the output matrix C

4.3 Application to simple rotor equations

4.3.1 Prescribed solution form

4.3.2 Perturbation of the equations of motion

4.3.3 Extract four/rev harmonic components

4.3.4 …

5 HHC and AFCS Interaction Study

5.1 Eﬀect of a ﬁxed HHC input on rigid body dynamics

5.1.1 Open-loop frequency response validation

5.1.2 Eﬀect of an optimum three/rev input on rigid body dynamics

5.2 Interaction of HHC and AFCS

5.2.1 Broken control loop response validation

5.2.2 ……

6 Summary and Conclusions

Appendix

Bibliography

Author: Cheng, Rendy Po-Ren

Source: University of Maryland