Nonlinear Adaptive Flight Control of a Hypersonic Vehicle

PhD - ProposalSanchito Banerjee

1

Table of Contents

1 Brief Overview of Study..................................................................................3

2 Introduction....................................................................................................4

2.1 Rationale...................................................................................................4

2.2 Purpose.....................................................................................................5

3 Literature Review...........................................................................................6

4 Methodology...................................................................................................9

5 Approach to Analysis....................................................................................10

6 Timeframe and Resources Required.............................................................11

References..........................................................................................................12

List of Figures

Figure 1. Longitudinal Control Loop [2]...............................................................4Figure 2. Hypersonic Glider - complete flight dynamics model [2]......................5Figure 3. Flow Diagram - Adaptive Control Setup................................................8Figure 4. Project Work Flow...............................................................................10Figure 5. Gantt chart..........................................................................................11

1 Brief Overview of Study

Hypersonic flight presents major challenges to airframe and control systems

engineers. High velocity can cause a hypersonic vehicle to be highly sensitive to

changes in flight conditions that can result in instability or weakly damped

transient oscillations of the airframe [5]. The design problem is further

compounded by the fact that hypersonic aerodynamic parameters, as predicted

from ground tests and/or theoretical computational methods, may not reflect

the actual flight parameters; there are significant uncertainties in the

parameter values required for airframe and control system design.

This proposal outlines the area of work and highlights the gaps in knowledge in

the area of control for Hypersonic Vehicles (HSV). Thereafter, it presents the

methodology and the approach of this research project which will be carried out

at the Centre for Hypersonics at University of Queensland.

2 Introduction

In order to appropriately design control laws for hypersonic vehicles, it is

paramount to understand how the flight dynamics are impacted by the

interactions between the aerothermodynamics, propulsion system, structural

dynamics, and control system. To this end, there has been a significant

investment into the modelling of these sub-systems and their integration into a

comprehensive model that can be used to characterise the flight dynamics of

scramjet-powered hypersonic aircraft and still remain amenable to control law

design and analysis [1].

2.1 Rationale

Creagh in [2] has presented a preliminary design and simulation results of an

adaptive longitudinal control system for a Mach 8 hypersonic glider. The system

that has been implemented is placed in the figure below. The block on the left,

acceleration ramp up/down is just a testing tool for the algorithm. The figure

below depicts just one loop of the figure placed in Figure 2.

Figure 1. Longitudinal Control Loop [2]

The above figure only depicts the longitudinal control loop of the hypersonic

glider. This simplified model is used in [2] to carry out the simulations. In the

figure above, the control loop with respect to the lateral dynamics have not

been considered. However in order to have a full nonlinear adaptive controller

for this system, it is important to incorporate the lateral dynamics in the model.

2.2 Purpose

The purpose of this research is to carry out the following tasks:

An adaptive flight control system for a nonlinear Hypersonic Vehicle.

Carry out simulations of the adaptive flight control system.

Determine the lateral dynamic behavior of the vehicle. And of particular

interest is to determine the coupling of the lateral and longitudinal

dynamics and its effect on the adaptive controller design.

Establish the maximum aerodynamic error that can be tolerated for such

a controller. This is of much usefulness to the aerodynamicists.

The full model, lateral and longitudinal, of the hypersonic glider is placed in the

figure below. An example of a full system has two control loops and the basic

form of the guidance and model parameter estimations. The two main

components of the system are: a longitudinal acceleration controller and a

lateral heading hold controller [2].

Figure 2. Hypersonic Glider - complete flight dynamics model [2]

3 Literature Review

Hypersonic flight presents major challenges to airframe and control

system designers. High velocity can cause a hypersonic vehicle to be

highly sensitive to changes in flight conditions (Mach Number M#, and

angle of attack α) that can result in instability or weakly damped

transient oscillations of the airframe. The design problem is further

compounded by the fact that hypersonic aerodynamic parameters, as

predicted from ground tests or theoretical computational methods, do not

reflect the actual flight parameters; there are significant uncertainties in

the parameter values required for airframe and control system design

[5]. Examples of these uncertainties include the effects of travelling at

such Mach numbers on the structural integrity and also the effects of

shocks. The formation of strong shocks around aerodynamic bodies

means that the free stream Reynolds number is less useful as an estimate

of the behaviour of the boundary layer over a body. Consequently,

conventional techniques do not always lead to a design that is stable and

at the same time robust to parameter uncertainties.

In literature there are several papers that discuss the challenges

pertaining to the dynamics and control of a hypersonic vehicle [3].

Bolender in [1] outlines the different concepts that have developed over

time to deal with the issue of control of hypersonic vehicles (HSVs).

These include a comprehensive longitudinal model of the HSV with the

help of Newtonian Impact Theory. Thereafter Boelender himself in [1]

provides a model with the combination of the structural,

aerothermodynamic, and propulsion system coupling inherent in

scramjet powered vehicles. The final product of this article captures

many of the effects of the diverse physical phenomena that present

challenges to flight control law designers.

Apart from the disturbances that cause oscillations of the HSV, the flow

characteristics also have a significant impact on the stability and control

of the HSV. This is covered in [5] and the main characteristics of flow are

that:

The shock waves originating at the leading edge of the body lie

close to the body so that the interaction with the body is strong.

High temperatures exist in the regions between the shock waves

and the body and it may be necessary to consider real gas effects

(molecular vibration, dissociation, and ionisation) when analysing

the flow fields.

At very high Mach numbers, the shock waves may be assumed to

be almost identical to the body, at least at the front portion of the

body, and the molecules crossing the shock waves conserve the

tangential component of the velocity but lose most of the normal

component.

Poulain in [3] outlines some of the methods used to control the longitudinal

motion of a HSV. These include the use of linear control theory, dynamic

inversion and sliding mode control. Each method has its shortfalls. Linear

control offers a simple and efficient way to locally stabilize most of (stabilisable)

dynamics process, with large possibilities of perfect tuning. However, aerospace

systems are often supposed to operate in a wide range of multidimensional state

excursions. This supposed to investigate controller interpolation. This may leads

to local instability and makes the global behaviour study complex. Dynamic

inversion based control laws allow to handle these difficulties. Nevertheless,

they lead to complex control structures, embedding huge amount of information

in the controller, usually not available in practice. From this point of view,

sliding mode control provide a way to control the vehicle addressed here which

override these difficulties. However this method is prone to introduce

chattering —unhealthy high frequency actuators excitation— which strongly

diminishes its efficiency.

Craegh in [2] takes the previous work further to present an adaptive controller

for the longitudinal dynamics of a Mach 8 Hypersonic Glider. The system

architecture in a three tier system to obtain the estimates of model

aerodynamics parameters. The process is outlined in the flow diagram overleaf.

Figure 3. Flow Diagram - Adaptive Control Setup

However as Craegh points out in [2] that due to the inherent lag of the system

outlined above, this system is not suitable in its current form for an up-and-over

trajectory profile. It may be suitable for vehicles that visit the same flight

conditions multiple times (i.e. const altitude & Mach). There are also

improvements that could be made.

From the literature covered so far, the following gaps were found in the

knowledge:

There is limited literature discussing the aerodynamic limits within which

the baseline controllers function.

Linear Least Squar

es

used to obtain the state transition methods and control matrix parameter estimates from a second order plant model.

Fusion

Algorithm

weights preloaded lookup table parameters and the least squares estimated parameters to obtain a fused estimate.The least-squares estimates are favoured when system excitation is present, while lookup table parameters are favoured when system excitation is negligible. The selection of measurement variances, lookup table parameter variances and sampling data provides the system tuning input.

Update

Lookup

Tables

The third tier of the adaptive control strategy is to update the lookup tables with a multiplying factor, which is calculated with a first-order filter. This enables the parameter estimates to retain trends learnt from earlier in the mission. Thus, for slow and consistent parameter changes, the closed-loop vehicle response is seen to improve slightly

4 Methodology

The research will follow on from the work outlined by Dr Michael Creagh in [2].

The main areas of work where this particular project (outlined in full in [2]):

1. A nonlinear adaptive control model to enhance the understanding of the

flight dynamics of the hypersonic vehicle. This model will include the

aerodynamic effects of travelling at Mach 8 and the changes will be

incorporated into the control model. Results for this part of the research

will be as a result of running simulations of the control systems on the in-

house code developed by the Centre for Hypersonics.

2. Experimental validation of the nonlinear adaptive control system. This

section of the research will concentrate on building a physical model of

the control system and carrying out tests to verify the simulation results.

3. An understanding of hypersonic aerodynamics such that aerodynamic

errors may be characterised and its impact on the baseline controller

understood and depicted in the model.

5 Approach to Analysis

The main approach methodology that will be used during the course of this

research project is split into two main sections. The first section of the project

looks at the theoretical development of the control system. The second part of

the research will look at experimental validation of the simulation results

obtained from part 1.

The stages of this project are outlined in the following flow diagram.

Figure 4. Project Work Flow.

In order to answer these research questions a rigorous approach to the control

system modelling and testing and subsequent applications of the results is

taken.  These include:

Building up the knowledge in the field of nonlinear control, adaptive

control and high speed gas dynamics.

Determination of the aerodynamic limits of the baseline controller.

Formulation and implementation of a nonlinear and adaptive control

system model of the hypersonic vehicle.

Investigation of the coupling effects of the lateral and longitudinal

dynamics and its implications on the control system design.

Simulation of the control system.

Development of a final report, publications and recommendations.

Phase A: Literature Review

and Initial Research

Phase B: Becoming familiar with inhouse tools

of analysis

Phase C: Initial implementation of

Models

Phase D: Simulations and Experimentatl

Validation

Phase E: Validation and

Data PresentationPublications

6 Timeframe and Resources Required

Initial Research

Simulation Tool Introduction

Initial Simulation Exercises

Literature Review

Standard 6DOF controller implementationAerodynamic limits of baseline controller

Adaptive controller design

Adaptive Controller implementation

Design of Testing for model

Testing of Model and validation

Thesis

Presentation

DATE (TIME) Year 1 Year 2 Year 3

A Gantt chart is placed below as a proposed breakdown of the time to be used

on each section of the research project.

Figure 5. Gantt chart

References

1. Bolender, M. 2009. “An Overview on Dynamics and Control Modelling of Hypersonic Vehicles.” American Control Conference.

2. Creagh, M and Beasley, P. 2011. “Adaptive Control for a Hypersonic Glider using Parameter Feedback from System Identification.” America Institute of Aeronautics and Astronautics.

3. Poulain, F. 2010. “Nonlinear Control of a Airbreathing Hypersonic Vehicle.” Journees des Theses, 25(27).

4. Wilcox, Z. 2010. “Nonlinear Control of Linear Parameter Varying Systems with Applications to Hypersonis Vehicles.” http://ncr.mae.ufl.edu/dissertations/wilcox_z.pdf (Accessed October 14, 2011)

5. Coleman, C. 2009. “On Stability and Control of Hypersonic Vehicles”. http://dspace.dsto.defence.gov.au/dspace/bitstream/1947/10037/1/DSTO-TR-2358%20PR.pdf (Accessed October 14, 2011).