Adaptive, Optimal and Reconfigurable Nonlinear Control Design for Futuristic Flight Vehicles

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Adaptive, Optimal and Reconfigurable Nonlinear
Control Design for Futuristic Flight Vehicles

• Radhakant Padhi
• Assistant Professor

Abha Tripathi Project Assistant
Dept. of Aerospace Engineering Indian Institute
of Science, Bangalore, India
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Project Plan

• Date of Commence 1st October 2006
• Project duration 2.5 Years
• Staff members
• Shree Krishnamoorthy, Project Assistant, Oct-Dec
  2006.
• Kaushik Das, Ph.D. student, January-July, 2007.
• Abha Tripathi, Project Assistant,
  Aug.2007continuing.
• Apurva chunodhkar, a B. Tech. student from
  IIT-Bombay and Siddharth Goyal, a B.E. student
  from Punjab Engineering College have worked in
  sporadic engagements
• Jagannath Rajshekharan, Project Assistant, has
  also worked in sporadic engagements

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Summary

• Two parallel directions have been explored in
  this project.
• Firstly, a new dynamic inversion approach
  has been developed and is experimented on a
  low-fidelity model of a high performance aircraft
  (F-16). Comparatively, it leads to some potential
  benefits
• Elimination of non-minimum phase behavior of the
  closed loop response
• Less oscillatory behavior
• Lesser magnitude of control
• Robustness study was carried out for the above
  approach with uncertainties in aerodynamic force
  and moment coefficients and inertia parameters

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Summary

• Secondly, a structured neuro adaptive control
  design idea has been developed which treats the
  kinematics and dynamics of the problem
  separately.
• Modeling and parameter inaccuracies are
  considered by using neural network which
  dynamically capture the unknown functions that
  are used to design a model-following adaptive
  controller.
• Sigma correction was done in the weight update
  rule.
• This idea is found to be successful on a
  satellite attitude problem.

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Command Tracking in High Performance Aircrafts A
New Dynamic Inversion Design
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Airplane Dynamics(F-16) Six Degree-of-Freedom
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Definitions and Goal

• Total Velocity
• Roll Rate (about x-axis)
• Roll Rate (about velocity vector)
• Normal Acceleration
• Lateral Acceleration
• Goal

where are pilot commands
P, Pw, nz, ny, VT
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Control Synthesis Procedure

• Define new variables
• Key observation
• Known

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Control Synthesis Procedure

• Longitudinal Maneuver
• Pilot commands
• Roll Rate (bank angle rate)
• Normal Acceleration
• Lateral Acceleration
• Total Velocity
• Lateral Maneuver
• Pilot commands
• Roll Rate (bank angle rate)
• Normal Acceleration
• Lateral Acceleration
• Total Velocity

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Control Synthesis Procedure

• Combined Longitudinal and Lateral Maneuver
• Pilot commands
• Roll Rate (about velocity vector)
• Normal Acceleration
• Lateral Acceleration
• Total Velocity

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Control Synthesis Procedure

• Design a controller such that
• After some algebra, Finally

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Results Longitudinal
Control Variables
Tracked Variables
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Results Lateral Mode
Tracked Variables
Control Variables
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Results Combined Longitudinal and Lateral
Tracked Variables
Control Variables
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Summary

• Existing Method
• Assumption
• Need of integral control
• More number of design parameters (10-12)
• Works

• New Method
• Assumption
• No such need (No wind-up)
• Less number of design parameters (5-7)
• Works better...!
• Lesser control magnitude
• Smoother transient response
• Better turn co-ordination

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Robustness Study

• Nominal Controller given to the actual system
  having uncertainties
• Perturbation assumed in the inertia parameters
  and aerodynamic force and moment coefficients
• Normal distribution used for introducing
  randomness in the parameters with mean value as
  the nominal value of the parameters and standard
  deviation as 1/3 of maximum allowed perturbation
  in that parameter.

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Robustness Study

• Inertia parameters varied from 5 to 10
• Aerodynamic coefficients varied from 1 to 10.
• Simulation were carried out for 50 cases in each
  mode.
• In each simulation study, the aim was to declare
  it as a success or failure

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Longitudinal Mode
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Longitudinal Mode
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Lateral Mode
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Lateral Mode
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Lateral Mode
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Lateral Mode
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Lateral Mode
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Combined Mode
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Conclusion

• When aerodynamic coefficients are perturbed by 5
  and the inertia parameters by 10, the controller
  is robust
• Increase in inertia parameters does not affect
  the percentage success
• Aerodynamic coefficients are more sensitive than
  inertia parameters

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Enhancement of Robustness

• Augment Dynamic inversion with Neuro -Adaptive
  Design

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Adaptive Approach(Lateral case)

• Nominal Outputs
• Actual Outputs
• Approximate Outputs

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Adaptive Approach

• Goal
• Strategy
• Steps for assuring
• Solve for adaptive controller

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Adaptive Approach

• Steps for assuring
• Error
• Error Dynamics

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Adaptive Approach

• Error Dynamics
• NN Training
• Lyapunov Function Candidate

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Adaptive Approach

• Weight Update Rule
• Condition For stability

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A STRUCTURED Approach forAttitude Maneuver of
Spacecrafts
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Neuro-adaptive Control Generic Theory

• Actual plant
• Total tracking error
• Tracking error dynamics

Assumption
Unknown function
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Neuro-adaptive Control Generic Theory

• Objective of adaptive controller
• Approximate System
• Model-following strategy

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Step I Assuring

• Universal approximation property
• Error
• Error dynamics for the individual i th error
  channel

Weight vector
Basis function vector
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Neural Network Training by Lyapunov Analysis
Lyapunov function candidate
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Neural Network Training with Stability

• Weight Update Rule
• Sufficient condition
• where

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SATELLITE Attitude Dynamics

• Attitude kinematics

• Angular rate dynamics

Nominal Dynamics
Actual Dynamics

• Objective of Control Design

,
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Nominal Control Problem Specific Formulation

• Tracking error for nominal system
• Tracking error dynamics
• Solving for nominal control

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Neuro-adaptive Control Problem Specific
Formulation

• Tracking error for actual plant
• Expanding the following terms as
• Tracking error dynamics
• Basis
• function
• selection

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Simulation ResultsNominal vs. Adaptive Control
for actual system
(I) Constant disturbances parameter
uncertainties
MRPs
Angular rates
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Simulation ResultsNominal vs. Adaptive Control
for actual system
(II) Constant disturbances parameter
uncertainties
Unknown function capture
Control
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Publications

• Conference Publications
• Radhakant Padhi, Narayan P. Rao, Siddharth Goyal
  and S.N. Balakrishnan, Command Tracking in High
  Performance Aircrafts A new Dynamic Inversion
  Design, 17th IFAC Symposium on Automatic control
  in Aerospace, Touolose, France.
• Apurva Chunodkar and Radhakant Padhi, Precision
  attitude Manoeuvers of Spacecrafts in Presence of
  Parameter Uncertainities and disturbances A
  SMART Approach, 17th IFAC Symposium on Automatic
  Control in Aerospace, Touolose, France.
• Radhakant Padhi and Apurva Chunodkar,
  Model-Following Neuro - adaptive Control Design
  for attitude maneuvers for rigid bodies in
  Presence of Parametric Uncertainties and
  disturbances", International Conference on
  advances in Control and Optimization of Dynamical
  Systems, Bangalore, India, 2007.
• Abha Tripathi and Radhakant Padhi ,Robustness
  Study of A Dynamic Inversion Control Law For A
  High Performance Aircraft, International
  Conference on Aerospace Science And Technology,
  to be held on 26 28 June 2008, Bangalore,
  India.

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Publications

• Journal Publications
• Radhakant Padhi, Siddharth Goyal, Narayan P. Rao
  and S.N. Balakrishnan, A Direct Approach for
  Nonlinear Flight Control Design of High
  Performance Aircrafts, Submitted to Control
  Engineering Practice.
• Jagannath Rajsekaran, Apurva Chunodkar and
  Radhakant Padhi, Precision Attitude Maneuver of
  Spacecrafts Using Structured Model-Following
  Neuro -Adaptive Control, Submitted to Control
  Engineering Practice.
• Radhakant Padhi and Apurva Chunodkar, Precision
  Attitude Maneuver of Spacecrafts Using Model -
  Following Neuro Adaptive Control, To appear in
  Journal of Systems Science Engineering.

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Questions And comments