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

1. 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

2. 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.2007…continuing. • 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

3. 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

4. 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.

5. Command Tracking in High Performance Aircrafts: A New Dynamic Inversion Design

6. Airplane Dynamics(F-16): Six Degree-of-Freedom

7. 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*

8. Control Synthesis Procedure • Define new variables: • Key observation: • Known:

9. 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:

10. Control Synthesis Procedure • Combined Longitudinal and Lateral Maneuver Pilot commands: • Roll Rate (about velocity vector): • Normal Acceleration: • Lateral Acceleration: • Total Velocity:

11. Control Synthesis Procedure • Design a controller such that • After some algebra, Finally:

12. Results: Longitudinal Control Variables Tracked Variables

13. Results: Lateral Mode Control Variables Tracked Variables

14. Results: Combined Longitudinal and Lateral Tracked Variables Control Variables

15. 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

16. 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.

17. 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

18. Longitudinal Mode

19. Longitudinal Mode

20. Lateral Mode

21. Lateral Mode

22. Lateral Mode

23. Lateral Mode

24. Lateral Mode

25. Combined Mode

26. 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

27. Enhancement of Robustness Augment Dynamic inversion with Neuro -Adaptive Design

28. Adaptive Approach(Lateral case) • Nominal Outputs: • Actual Outputs: • Approximate Outputs:

29. Adaptive Approach • Goal: • Strategy: • Steps for assuring : Solve for adaptive controller

30. Adaptive Approach • Steps for assuring • Error • Error Dynamics

31. Adaptive Approach • Error Dynamics • NN Training Lyapunov Function Candidate

32. Adaptive Approach • Weight Update Rule: • Condition For stability:

33. A STRUCTURED Approach forAttitude Maneuver of Spacecrafts

34. Neuro-adaptive Control: Generic Theory Assumption • Actual plant • Total tracking error • Tracking error dynamics Unknown function

35. NN Approximation Neuro-adaptive Control: Generic Theory • Objective of adaptive controller: • Approximate System: • Model-following strategy:

36. Step I: Assuring • Universal approximation property: • Error : • Error dynamics for the individual i th error channel: Weight vector Basis function vector

37. Neural Network Training by Lyapunov Analysis Lyapunov function candidate:

38. Neural Network Training with Stability • Weight Update Rule: • Sufficient condition: where

39. SATELLITE Attitude Dynamics • Attitude kinematics • Angular rate dynamics Nominal Dynamics Actual Dynamics • Objective of Control Design: ,

40. Nominal Control : Problem Specific Formulation • Tracking error for nominal system: • Tracking error dynamics: • Solving for nominal control

41. Neuro-adaptive Control : Problem Specific Formulation • Tracking error for actual plant: • Expanding the following terms as: • Tracking error dynamics: • Basis function selection:

42. Simulation Results:Nominal vs. Adaptive Control for actual system (I) Constant disturbances & parameter uncertainties MRPs Angular rates

43. Simulation Results:Nominal vs. Adaptive Control for actual system (II) Constant disturbances & parameter uncertainties Unknown function capture Control

44. 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 - adaptiveControl Designfor 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.

45. 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.

46. Questions And comments