Three-Stage Gradient-Based Optimization Scheme in Design of Feedback Gains Within Eurofighter Primary Control Laws

Moritz, Nikolaus; Osterhuber, Robert

doi:10.2514/6.2006-6311

Cited by 7 publications

(3 citation statements)

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“…26 ) if the exponential convergence rates are a function of x, x d (t) and qc(t) since this allows to optimize the controller performance w.r.t. the changing plant and actuator effectiveness.…”

mentioning

confidence: 99%

Exact Decomposition and Contraction Analysis of Nonlinear Hamiltonian Systems

Lohmiller¹,

Slotine

2013

AIAA Guidance, Navigation, and Control (GNC) Conference

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This paper decomposes nonlinear 2 nd -order Hamiltonian dynamics into a hierarchy of two 1 st -order complex component dynamics. This allows the stability of the 2 nd -order dynamics to be assessed based on the two nonlinear 1 st -order complex dynamics, using the tools of contraction theory.This decomposition is a tensor result, independent of the chosen coordinate system. It extends well-known Lyapunov asymptotic stability results, based on energy dissipation, to the exact characterization of exponential convergence rates for damped non-autonomous Hamiltonian systems. Specifying the nonlinear damping and complex action φ is sufficient to tune the performance of an associated observer or controller design. Explicit exponential stability guarantees are then given based on the second covariant derivative of φ.The result allows state and time-dependent complex exponential convergence or contraction rates to be placed exactly in a controller or observer design. As such, it extends linear time-invariant eigen-value placement to time-varying or state-dependent eigen-values. Simple applications include state-dependent eigen-value placement for an aircraft or an inverted pendulum controller. The corresponding observer design is illustrated for the Mach-dependent vertical channel dynamics of the strap-down navigation system in polar regions.

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confidence: 99%

Exact Decomposition and Contraction Analysis of Nonlinear Hamiltonian Systems

Lohmiller¹,

Slotine

2013

AIAA Guidance, Navigation, and Control (GNC) Conference

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“…The required robustness margins are chosen according to [18] for this assessment is marked by the outermost diamond, whereas the two smaller diamonds are applied e.g. in case of failure.…”

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confidence: 99%

Comparison of L1 Adaptive Augmentation Strategies for a Differential PI Baseline Controller on a Longitudinal F16 Aircraft Model

Hellmundt

Wildschek

Maier

et al. 2015

Advances in Aerospace Guidance, Navigation and Control

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Abstract. In this paper two different approaches are presented to design an adaptive augmentation using L1 Adaptive Control. In terms of reference dynamics, the first one takes the closed-loop aircraft with baseline controller into account. The second approach tries to maintain nominal open-loop aircraft dynamics, with the baseline controller wrapped around the adaptive augmentation. They are compared by application to a model of the longitudinal dynamics of a F16 aircraft. The aircraft model is equipped with a Differential PI (DPI) baseline controller. The design of the combination of baseline controller and augmentation takes saturation as well as rate limitation of the control signal directly into account. Simulation results show the nominal closed-loop behavior is not harmed by the adaptive augmentation and that an increase of performance in case of uncertainty can be achieved. As an exemplary uncertainty case a rapid shift of the center of gravity (CG) is examined. The robustness of the controller structure is assessed by the use of both linear and nonlinear methods to obtain the Time Delay Margin (TDM) and the Gain Margin (GM) of the closed loop system. It can be observed, the adaptive augmentation leads to a significant decrease of robustness w.r.t. the plant input channel. This drop in TDM and GM can be fully restored by the application of a hedging strategy.

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“…Let us now consider real non-linear systems before we go to the complex nonlinear case: Example 4.2: Let us now schedule λ 1 (z 1 , M a, q c ) and λ 2 (z 2 , M a, q c ) in example Example 1.1 (see e.g. [28]) in the characteristic equation (11) in Theorem 3…”

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Shaping State-Dependent Convergence Rates in Nonlinear Control System Design

Lohmiller

Sltine

2008

AIAA Guidance, Navigation and Control Conference and Exhibit

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This paper derives for non-linear, time-varying and feedback linearizable systems simple controller designs to achieve specified state-and timedependent complex convergence rates. This approach can be regarded as a general gain-scheduling technique with global exponential stability guarantee. Typical applications include the transonic control of an aircraft with strongly Mach or time-dependent eigenvalues or the state-dependent complex eigenvalue placement of the inverted pendulum.As a generalization of the LTI Luenberger observer a dual observer design technique is derived for a broad set of non-linear and time-varying systems, where so far straightforward observer techniques were not known. The resulting observer design is illustrated for non-linear chemical plants, the Van-der-Pol oscillator, the discrete logarithmic map series prediction and the lighthouse navigation problem.These results [23] allow one to shape globally the state-and time-dependent convergence behaviour ideally suited to the non-linear or time-varying system. The technique can also be used to provide analytic robustness guarantees against modelling uncertainties.The derivations are based on non-linear contraction theory [18], a comparatively recent dynamic system analysis tool whose results will be reviewed and extended.

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Three-Stage Gradient-Based Optimization Scheme in Design of Feedback Gains Within Eurofighter Primary Control Laws

Cited by 7 publications

References 1 publication

Exact Decomposition and Contraction Analysis of Nonlinear Hamiltonian Systems

Exact Decomposition and Contraction Analysis of Nonlinear Hamiltonian Systems

Comparison of L1 Adaptive Augmentation Strategies for a Differential PI Baseline Controller on a Longitudinal F16 Aircraft Model

Shaping State-Dependent Convergence Rates in Nonlinear Control System Design

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