nonlinear adaptive flight control of a hyper sonic vehicle_2
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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).