Robust feedforward design in the presence of LTI/LTV uncertainties

SUMMARY A non‐smooth optimization technique to directly compute a lower bound on the skew structured singular value ν is developed. As corroborated by several real‐world challenging applications, the proposed technique can provide tighter lower bounds when compared with currently available techniques. Moreover, in many cases, the determined lower bound equals the true value of ν. Thanks to the efficiency of the non‐smooth technique, the algorithm can be applied to problems involving even a significant number of uncertain parameters. Another appealing feature of the proposed non‐smooth approach is that the dimension of repeated scalar uncertainties in the overall structured uncertainty matrix has little impact on the computational time. The technique can be used to compute a lower bound on the structured singular value μ as well. Copyright © 2012 John Wiley & Sons, Ltd.

Section: Theorem 5 ([28 Th2713])mentioning

confidence: 99%

“…Unfortunately, a well‐known limitation of such an approach is that sharp peaks of μ can be easily missed if the frequency grid is not dense enough. An interesting alternative to the gridding approach is given by the frequency sweeping technique in .…”

Section: Non‐smooth Lower Boundmentioning

confidence: 99%

A non‐smooth lower bound on ν

Lemos

Simões

Apkarian

2012

“…In Equation 22, Π −T is the transpose of the matrix inverse of Π evaluated pointwise across frequency. Since Π is assumed to be a strict PN multiplier, Definition 1 implies that Π 11 ( jω) > 0 and Π 22 ( jω) < 0 ∀ω ∈ R ∪ {∞}.…”

Section: Dual Iqcsmentioning

confidence: 99%

“…17 As a result, many of the previous results summarized above have parallel results for the robust feedforward synthesis problem. 8,[21][22][23][24][25] For example, robust feedforward synthesis results have been obtained for the LTI plants under structured LTI, LTV, or nonlinear uncertainties, 21 linear time-varying plants under mixed LTI and time-varying uncertainties, 22 and LTI plants under uncertainties described by dynamic IQCs. 8,23 In addition, feedforward synthesis results have been obtained for the LPV plants with polytopic parameter spaces 24 and the LPV plants with bounded parameter rates-of-variation using parameter-dependent Lyapunov functions.…”

Section: Introductionmentioning

confidence: 99%

Convex LPV synthesis of estimators and feedforwards using duality and integral quadratic constraints

Venkataraman

Seiler

2017

Summary A method is presented for synthesizing output estimators and disturbance feedforward controllers for continuous‐time, uncertain, gridded, linear parameter‐varying (LPV) systems. Integral quadratic constraints are used to describe the uncertainty. Since the gridded LPV systems do not have a valid frequency‐domain interpretation, the time domain, dissipation inequality approach is followed. There are 2 main contributions. The first contribution is that a notion of duality is developed for the worst‐case gain analysis of uncertain, gridded LPV systems. This includes notions of dual LPV systems and dual integral quadratic constraints. Furthermore, several technical results are developed to demonstrate that the sufficient conditions for bounding the worst‐case gain of the primal and dual uncertain LPV systems are equivalent. The second contribution is that the convex conditions are derived for the synthesis of robust output estimators for uncertain LPV systems. The estimator synthesis conditions, together with the duality results, enable the convex synthesis of robust disturbance feedforward controllers. The effectiveness of the proposed method is demonstrated using a numerical example.

“…This is a skew μ analysis problem for which efficient computational tools exist, and especially the routine mu_margin.m of the System Modeling, Analysis and Control (SMAC) Toolbox developed by ONERA in MATLAB‐Simulink (available at http://w3.onera.fr/smac). Conversely, when parameters θ i are supposed to be time varying, without bound on the rate of variation, real frequency‐independent scaling matrices D and G are handled, and inequality must be simultaneously solved on the frequency continuum using IQC tools, see, eg, the works of Ferreres and Roos and Kao and the SMAC Toolbox. Last note that a bound on the rate of variation of the parameters can be introduced, using a generalization of the D,G scalings, in the framework of IQC analysis …”

Section: Gain‐scheduling and Robustness Toolsmentioning

confidence: 99%

Adaptive LFT control of a civil aircraft with online frequency‐domain parameter estimation

Ferreres

Hardier²

2017

Summary This paper describes the application of an indirect linear fractional transformation (LFT)–based state‐space adaptive control scheme to a transport aircraft, within the context of the European project REconfiguration of CONtrol in Flight for Integral Global Upset REcovery. The principle of the scheme is to design and validate off‐line a gain‐scheduled controller, depending on the plant parameters to be estimated, and to combine it online with a model estimator, so as to minimize the onboard computational time and complexity. A modal approach, very classical for the design of a flight control law, is used to directly synthesize the static output feedback LFT controller, depending on the control and stability derivatives, ie, the parameters of the linearized aerodynamic state‐space model to be estimated. Since the gain‐scheduled LFT controller online depends on the parameter estimates instead of the true values, its robustness to transient and asymptotic estimation errors needs to be assessed using μ and integral quadratic constraint analysis techniques. A primary concern being an online implementation, a fully recursive frequency‐domain estimation technique is proposed, with a low online computational burden and the capability to track time‐varying parameters. Full nonlinear simulations along a trajectory validate the good performance properties of the combined estimator and gain‐scheduled flight controller. To some extent, minimal guaranteed stability and performance properties of the adaptive scheme can be ensured by switching to a robust controller when the parameter estimates are not reliable enough, thus bypassing the Certainty Equivalence Principle.