Piecewise Polynomial Modeling for Control and Analysis of Aircraft Dynamics Beyond Stall

Cunis, Torbjørn; Burlion, Laurent; Condomines, Jean-Philippe

doi:10.2514/1.g003618

Cited by 14 publications

(23 citation statements)

References 30 publications

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“…2 shows the piecewise model and their polynomial segments. Defined as piecewise polynomials, we are able to account for full-envelope characteristics both of the lift and drag coefficients as well as the coefficients in body axes [20]. The resulting models are continuous over the entire domain but not necessarily differentiable in its joint.…”

Section: A Equations Of Motionmentioning

confidence: 99%

“…Where classical control synthesis relies upon linearized models, the region of attraction estimation provides knowledge about the limitations of the chosen control implementation. Unlike the safe set [see, e.g., 6, 7], which provides an exploratory study in order to estimate the abilities of the aircraft to be controlled, we study a region of attraction in the context of a given controller and the respective trim condition [20]. For the latter we choose a low-inclination gliding descent trim at η * glide = −5°(see Appendix A).…”

Section: Region Of Attraction At Trim Pointmentioning

confidence: 99%

“…Mere polynomials are often unsuitable to fit full-envelope aerodynamics accurately, whereas advanced modeling techniques, such as multivariate splines [19], are too computationally heavy to analyze using SOS. Simple piecewise-defined models, as proposed by the authors in [20], have the potential of bridging this gap; namely, these models accurately describe aircraft dynamics in the domains of low and high angles of attack while only slightly increasing the computational load for sum-of-squares programming.…”

mentioning

confidence: 99%

“…Continuing our work in [20], we present an extended V-s-iteration for piecewise-defined aircraft dynamics in order to obtain feedback control laws subject to state and inputs constraints. In particular, we focus on two aspects: Analysis of an aircraft model with separately modelled, high angle-of-attack dynamics; and the synthesis of a control feedback to specifically recover from a deep-stall trim condition.…”

mentioning

confidence: 99%

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Sum-of-Squares Flight Control Synthesis for Deep-Stall Recovery

Cunis

Condomines

Burlion

2020

Journal of Guidance, Control, and Dynamics

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Certification of inflight loss-of-control recovery is complicated by the highly nonlinear flight dynamics beyond stall. In lieu of extensive Monte-Carlo simulations for flight control certification, sum-of-squares programming techniques provide an algebraic approach to the problem of nonlinear control synthesis and analysis. However, reliance on polynomial models has hitherto limited applicability to aeronautical control problems. Taking advantage of recently proposed piecewise polynomial models, this paper revisits sum-of-squares techniques for recovery of an aircraft from deep-stall conditions using a realistic yet tractable aerodynamic model. Local stability analysis of classical controllers is presented as well as synthesis of polynomial feedback laws with the objective of enlarging their nonlinear region of attraction. A newly developed synthesis algorithm for infinite-horizon backwards-reachability facilitates the design of recovery control laws, ensuring stable recovery by design. The paper's results motivate future research in aeronautical sum-of-squares applications. Nomenclature α Angle of attack (rad); α 0 Low-angle of attack boundary (α 0 = 16.2949°); γ A Flight-path angle relative to air (rad); η Elevator deflection (rad), negative if leading to positive pitch moment;

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Section: A Equations Of Motionmentioning

confidence: 99%

Section: Region Of Attraction At Trim Pointmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Sum-of-Squares Flight Control Synthesis for Deep-Stall Recovery

Cunis

Condomines

Burlion

2020

Journal of Guidance, Control, and Dynamics

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“…10 After scaling the system tox = Dx with D ∈ R 2×2 , we compute the invariant set of the origin using Algorithm 1b. Such a problem has been discussed in [14] for a polynomial model and in [17] for a once-piecewise polynomial model. Algorithm 1b finds the optimal invariant set shown in Fig.…”

Section: Application Examplementioning

confidence: 99%

Local stability analysis for large polynomial spline systems

2020

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Polynomial switching systems such as multivariate splines provide accurate fitting while retaining an algebraic representation and offering arbitrary degrees of smoothness; yet, application of sum-of-squares techniques for local stability analysis is computationally demanding for a large number of subdomains. This communiqué presents an algorithm for region of attraction estimation that is confined to those subdomains actually covered by the estimate, thereby significantly reducing computation time. Correctness of the results is subsequently proven and the run time is approximated in terms of the number of total and covered subdomains. Application to longitudinal aircraft motion concludes the study.

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