Stability Metrics for Simulation and Flight-Software Assessment and Monitoring of Adaptive Control Assist Compensators

Hodel, A.S.; Whorton, Mark; Zhu, J. Jim

doi:10.2514/6.2008-7005

Cited by 20 publications

(10 citation statements)

References 23 publications

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“…The model uncertainties considered in this section are classified into the regular perturbations, which are defined in the nonlinear system perturbation theory as the perturbations that do not change the order of the nominal system, such as negligible nonlinearities, parametric dispersions and variations. [5,19].…”

Section: Robustness To Model Uncertaintiesmentioning

confidence: 99%

“…There are other sources of perturbations that increase the order of the system, such as actuator dynamics and higher-order elastic dynamics. These perturbations are classified into Singular perturbations [5,19]. Consider the singularly perturbed system model as [2] x = f (t, x, z p , ),…”

Section: Sensing and Singular Perturbationsmentioning

confidence: 99%

“…One popular approach is combining NDI control with linear robust control techniques such as structural singular value (µ) analysis [3,4] and H ∞ synthesis. Although these techniques have brought significant benefits to regular NDI, not all the uncertainties are taken into account or some known nonlinear, time-varying (NLTV) dynamics are treated as uncertainties, thus the closed-loop systems can be either marginally or overly conservative in performance and stability robustness [5].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stability Analysis for Incremental Nonlinear Dynamic Inversion Control

Wang

Kampen

Chu

et al. 2018

2018 AIAA Guidance, Navigation, and Control Conference

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As a sensor-based control approach, the Incremental Nonlinear Dynamic Inversion (INDI) method has been successfully applied on various aerospace systems and shown desirable robust performance to aerodynamic model uncertainties. However, its previous derivations based on the so-called time scale separation principle is not mathematically rigorous. There also lack of stability and robustness analysis for INDI. Therefore, this paper reformulated the INDI control law without using the time scale separation principle and generalized it to not necessarily relative-degree-one problems, with consideration of the internal dynamics. Besides, the stability of the closed-loop system in the presence of external disturbances is analyzed using Lyapunov methods and nonlinear system perturbation theory. Moreover, the robustness of the closed-loop system against regular and singular perturbations is analyzed. Finally, the reformulated INDI control law and main conclusions are verified by a rigid aircraft gust load alleviation problem.Regarding its applications on aerospace systems, the INDI method is generally used for the inner loop angular velocity control [9][10][11][12], which leads to a relative-degree-one problem for each control channel. The internal dynamics are then avoided by using cascaded control structure, which is a common practice in rigid aircraft flight control designs [10,11,14]. However, the stability of the cascaded control structure is not easy to prove because of its dependency on the time scale separations between different control loops. Also, this cascaded control structure is not suitable for some problems. e.g. It is neither physically meaningful nor practical to separate the higher-order elastic dynamics into cascaded loops. In view of these reasons, the INDI control will be broadened into not necessarily relative-degree-one problems in this paper with consideration of the internal dynamics.The existing derivations of the INDI control law are based on the so-called time scale separation principle, which claims that when the sampling frequency is high, the controls can change significantly faster than the states [9][10][11][12][13][14][15][16][17]. The nonlinear plants are then simplified into linear incremental dynamic equations by omitting state variation related nonlinear terms and higher-order terms in their Taylor series expansion, based on which the incremental control inputs are designed. This approach is not mathematically rigorous since the plant simplification is made before introducing the INDI control inputs and thus becomes deficient for unstable plants. Moreover, although the state related nonlinear terms and higher-order terms are not used in the INDI controller design, they should be kept in the closed-loop dynamic equations and remain influencing the closed-loop system stability and performance, which is also not the case in the existing derivations. Therefore, in this paper, the INDI control law will be reformulated without using the time scale separation principle, and the influences o...

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Section: Robustness To Model Uncertaintiesmentioning

confidence: 99%

Section: Sensing and Singular Perturbationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stability Analysis for Incremental Nonlinear Dynamic Inversion Control

Wang

Kampen

Chu

et al. 2018

2018 AIAA Guidance, Navigation, and Control Conference

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“…Most of the works looking at this important issue rely on simulation-based nonlinear stability techniques. [10][11][12] This article aims first to explore adaptive control features for the VEGA control system to augment a robust-control structured H ∞ controller and second, to compare the performance and robustness of this robust-based adaptive controller with a full-order LPV design.…”

Section: Introductionmentioning

confidence: 99%

Robust-Control-Based Design and Comparison of an Adaptive Controller for the VEGA Launcher

Navarro-Tapia

Marcos

Bennani³

et al. 2019

AIAA Scitech 2019 Forum

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This article presents the design and evaluation of an adaptive controller for the atmospheric phase VEGA launcher. This design uses an Adaptive Augmenting Control (AAC) architecture to further extend the performance and capabilities of a robust-control structured H∞ controller, which was designed based on the current VEGA control architecture. The main goal of this paper is first, to explore adaptive features for the VEGA control system and second, to evaluate its performance and robustness properties. To that end, the adaptive controller is compared with the structured H∞ baseline controller and a linear parameter varying (LPV) design (both without adaptive augmentation). The three controllers are analysed for several extreme off-nominal condition tests using a high-fidelity, nonlinear simulator of the VEGA launcher. And the main performance indicators for the atmospheric phase are evaluated through a Monte-Carlo campaign. The results show that the adaptive and LPV controllers successfully provide stability under extreme adverse flight conditions over the non-adaptive robust controller. It is also shown that the LPV approach provides a more formal and methodological way to achieve these improvements.

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“…However, there does not appear to have been reported for NLTV systems any stability margin metrics that are: (i) theoretically based, (ii) practically measurable, (iii) backward compatible in the sense that when applied to LTI systems, these metrics have a bijective correspondence with the GM and PM [7]. The lack of such effective stability metrics has inevitably hampered the acceptance of advanced LTV and NL control techniques in control engineering practices.…”

Section: Introductionmentioning

confidence: 99%

A singular perturbation approach for time-domain assessment of Phase Margin

Zhu

Yang

Hodel

2010

Proceedings of the 2010 American Control Conference

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Abstract-This paper considers the problem of time-domain assessment of the Phase Margin (PM) of a Single Input Single Output (SISO) Linear Time-Invariant (LTI) system using a singular perturbation approach, where a SISO LTI fast loop system, whose phase lag increases monotonically with frequency, is introduced into the loop as a singular perturbation with a singular perturbation (time-scale separation) parameter ε. First, a bijective relationship between the Singular Perturbation Margin (SPM) ε max and the PM of the nominal (slow) system is established with an approximation error on the order of ε 2 . In proving this result, relationships between the singular perturbation parameter ε, PM of the perturbed system, PM and SPM of the nominal system, and the (monotonically increasing) phase of the fast system are also revealed. These results make it possible to assess the PM of the nominal system in the time-domain for SISO LTI systems using the SPM with a standardized testing system called "PM-gauge," as demonstrated by examples. PM is a widely used stability margin for LTI control system design and certification. Unfortunately, it is not applicable to Linear Time-Varying (LTV) and Nonlinear Time-Varying (NLTV) systems. The approach developed here can be used to establish a theoretical as well as practical metric of stability margin for LTV and NLTV systems using a standardized SPM that is backward compatible with PM.

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Stability Metrics for Simulation and Flight-Software Assessment and Monitoring of Adaptive Control Assist Compensators

Cited by 20 publications

References 23 publications

Stability Analysis for Incremental Nonlinear Dynamic Inversion Control

Stability Analysis for Incremental Nonlinear Dynamic Inversion Control

Robust-Control-Based Design and Comparison of an Adaptive Controller for the VEGA Launcher

A singular perturbation approach for time-domain assessment of Phase Margin

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