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Explore geometric nonlinear controllability approach for novel rolling mechanism near stall in airplanes presented by experts in mechanical and aerospace engineering at a prestigious conference.
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Geometric Nonlinear Controllability Approach to a Novel Rolling Mechanism for Airplanes Near Stall HaithemTaha and Ahmed Hassan Mechanical and Aerospace Engineering University of California, Irvine AMS Spring Central and Western Joint Sectional Meeting, 22-24 Mar 2019, Honolulu, HI HaithemTaha
Make Geometric Control Great Again! Geometric Approaches to Mechanics and Control “Mechanics is the paradise of mathematical sciences, because by means of it one comes to the fruits of mathematics.” Leonardo da Vinci HaithemTaha
Make Geometric Control Great Again! Geometric Approaches to Mechanics and Control Linear Control Geometric Nonlinear Control Early 1960’s Taught in all engineering schools! Early 1960’s Rarely taught in Engineering Schools! HaithemTaha
Why Geometric Control? • Engineering Control Payoffs from the Geometric Control Theory • Global Intrinsic Assessment of the System Behavior No global asymptotic stability for a continuous system with rotational degrees of freedom (Bhat & Bernstein Systems & Control Letters 2000) • Nonlinear Controllability and Motion Generation in Un-actuated Directions Periodic Excitation and Locomotion • Time-Varying Vector Fields and Vibrational Stabilization Chronological calculus and averaging ( Bullo 2002; Burdick, Vela, Morgansen2002) • Periodic Excitation and Locomotion HaithemTaha
Linear and Nonlinear Controllability Controllability:The ability to steer(drive) a system from point A to point B in finite time. (1) (2) ??? Orbit Theorem (Rashevsky-Chow 1938-1939) Sussmannand Jurdjevic (1972): The analytic system (2) is accessible from if and only if the accessibility distribution : has rank n. The system (1) is controllable if and only if the controllability matrix has rank n. Reachable Set HaithemTaha
Linear and Nonlinear Controllability y Kinematic Car Example Linearization: x + + Linearly Uncontrollable! HaithemTaha
Nonlinear Controllability Motion Generation in Unactuated Directions + y Kinematic Car Example Lie Bracket x Nonlinearly Controllable! Motion Generation in Unactuated Directions! HaithemTaha
Nonlinear Controllability Motion Generation in Unactuated Directions Spacecraft Attitude Control • Three pairs of gas jets • Two pairs of gas jets • One pair of gas jets • Geometric Nonlinear Analysis: Crouch, IEEE Transactions on Automatic Control, 1984. The system is still controllable with only one pair of gas jets. What about Airplane Controllability in case of “loss-of-control”? Linearly Controllable. Spacecraft Attitude Control: Linearly Uncontrollable. Linearly Uncontrollable. Hassan and Taha, Nonlinear Dynam. 2017. HaithemTaha
Nonlinear Controllability Thrust-Only Flight Control Loss of Hydraulics Turkish Airlines 1974 United Airlines 1989 DHL 2003 Hassan and Taha, Nonlinear Dynam. 2017. HaithemTaha
Airplane Nonlinear Controllability ++ HaithemTaha Hassan and Taha, Nonlinear Dynam. 2017.
Airplane Nonlinear Controllability New Rolling/Yawing mechanism Rolling moment or acceleration Yawing moment or acceleration HaithemTaha Hassan and Taha, Nonlinear Dynam. 2017.
Airplane Nonlinear Controllability Novel Roll Mechanism Using Lie Brackets (LIBRA) NovelConventional Versus • Loss of Control: #1 factor in fatal accidents worldwide, last 10 years: • stall45.8% • sideslip-induced rolls25.0% • rollsfrom other causes 12.5% • Pilot induced oscillation 12.5%, & • yaw 4.2% HaithemTaha Hassan and Taha, Nonlinear Dynam. 2017.
Nonlinear Controllability A Fundamental Problem: Degree of Nonlinear Controllability NovelConventional Versus Direct Control Lie Bracket Linear in time Quadratic in time Sensitivity Vs Growth Rate Develop Computableanalytic definitions for the Degree of Controllability of Nonlinear Systems. Need Simulation! How to realize motion along a Lie Bracket Direction?! Nonlinear Controllability is NOT constructive! Motion Planning (Nonholonomic Motion Planning) Laerriere &Sussmann(1991), Gurvits(1992), Murray & Sastry(1993), Liu (1997), … HaithemTaha Hassan and Taha, SciTech 2019.
Nonlinear Controllability Nonholonomic Motion Planning Liu (1997): (1) Tracking the trajectory (*) Theorem (Liu 1997): Our practical Modification (*) Lemma (Hassan & Taha 2019): HaithemTaha Hassan and Taha, SciTech 2019.
Airplane Nonlinear Controllability Novel Roll Mechanism Using Lie Brackets (LIBRA) LIBRA Conventional Versus 400 % Enhancement in roll response over the first second HaithemTaha Hassan and Taha, SciTech 2019.
Conclusions New Rolling Mechanism Near Stall Theory Application Degree of Nonlinear Controllability! HaithemTaha
Acknowledgment Ahmed Hassan
Acknowledgment Ahmed Hassan wake
Geometric Nonlinear Controllability Approach to a Novel Rolling Mechanism for Airplanes Near Stall Thank You! HaithemTaha and Ahmed Hassan Mechanical and Aerospace Engineering University of California, Irvine AMS Spring Central and Western Joint Sectional Meeting, 22-24 Mar 2019, Honolulu, HI HaithemTaha