Gain-scheduled missile autopilot design using linear parameter varying transformations

Shamma, Jeff S.; Cloutier, J.R.

doi:10.2514/3.20997

Cited by 343 publications

(166 citation statements)

References 7 publications

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“…In order to solve this problem an extension of the result from [16] is presented, that allows us to calculate a constant similarity transformation matrix representing a given interval of matrices to an interval of Metzler matrices. This result can be used to design interval observers for LPV systems with measurable vector of scheduling parameters [11], [18], [20] or LTV systems, that is the main novelty of the work. Two examples of such systems are considered in this work: LTV system and the Lorenz chaotic model (as a nonlinear system in the output canonical form).…”

Section: Introductionmentioning

confidence: 99%

Interval state observer for nonlinear time varying systems

et al. 2013

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This paper is devoted to design of interval observers for Linear Time Varying (LTV) systems and a class of nonlinear time-varying systems in the output canonical form. An interval observer design is feasible if it is possible to calculate the observer gains making the estimation error dynamics cooperative and stable. It is shown that under some mild conditions the cooperativity of an LTV system can be ensured by a static linear transformation of coordinates. The efficiency of the proposed approach is demonstrated through numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Interval state observer for nonlinear time varying systems

et al. 2013

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“…Any incorrect estimation of u eq (y) may jeopardize the robust property of the closed-loop system. To avoid this problem, an integrator at the plant input, which stores the trim input value u eq (y), can be added as suggested in [21]. As a consequence Equation (2) can be rewritten as follows:…”

Section: Quasi-lpv Transformationmentioning

confidence: 99%

“…In this development, a Quasi-Linear Parameter Varying (quasi-LPV) representation [21] is an appealing candidate owing to the following reasons: (i) plant's nonlinearity can be captured by selecting appropriate scheduling parameters; (ii) it is not a linearized version of the nonlinear plant, instead it is derived through a state transformation; (iii) a family of local linear models can be easily obtained by merely freezing the scheduling parameters. In summary, the focal point of this paper is to develop an indirect closed-loop nonlinearity measure by exploiting the ν-gap metric notion and the special structure of systems which admit a quasi-LPV transformation.…”

Section: Introductionmentioning

confidence: 99%

Vinnicombe metric as a closed-loop nonlinearity measure

Tan

Huzmezan

Kwok

2003

2003 European Control Conference (ECC)

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The focal point of this paper is to develop a measure of closedloop nonlinearity. In this work, the Vinnicombe metric and the quasi-linear parameter varying (quasi-LPV) representation of nonlinear systems are exploited for this purpose. The proposed measure can serve as a decision making tool for control engineers when deciding whether a linear or nonlinear control strategy should be employed to solve their control problems. A continuous stirred tank reactor (CSTR) simulation example is used to illustrate the proposed measure.

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“…In the LPV approach the gains are automatically scheduled with respect to the plant varying parameters. Another advantage is many nonlinear systems can be naturally approximated by LPV systems [13], [14]. Recent results on LPV based fault detection schemes appears in [15], [16], [17] from work in the EU-funded ADDSAFE project.…”

Section: Introduction Fault Detection and Isolation (Fdi)mentioning

confidence: 99%

Fault detection in uncertain LPV systems with imperfect scheduling parameter using sliding mode observers

Chandra¹,

Alwi

Edwards

2017

European Journal of Control

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This paper presents a sliding mode fault detection scheme for linear parameter varying (LPV) systems with uncertain or imperfectly measured scheduling parameters. In the majority of LPV systems, it is assumed that the scheduling parameters are exactly known. In reality due to noise or possibly faulty sensors, it is sometimes impossible to have accurate knowledge of the scheduling parameters and a design based on the assumption of perfect knowledge of the scheduling parameters cannot be guaranteed to work well in this situation. This paper proposes a sliding mode observer scheme to reconstruct actuator and sensor faults in a situation where the scheduling parameters are imperfectly known. The efficacy of the approach is demonstrated on simulation data taken from the nonlinear RECONFIGURE benchmark model . One approach to extending linear methods to make them work effectively across the whole plant operating range is to design (linear) observers at select operating points, and then schedule the gains with respect to certain parameters [4]. One of the main difficulties with gain scheduling is the selection of the operating points and how to choose the gains at intermediate points. Furthermore, formally, between the operating points the stability of the observer cannot be guaranteed.A more rigorous alternative approach is based on so-called linear parameter varying (LPV) system designs. In the LPV approach the gains are automatically scheduled with respect to the plant varying parameters. Another advantage is many nonlinear systems can be naturally approximated by LPV systems [13] [20]). However in all these papers the scheduling parameters are assumed to be perfectly known. However in reality this may not be the case: for example inaccurate sensors and/or faults can lead to imperfect knowledge of the parameters. The use of this corrupted information will affect the performance of the observer. The design of Luenberger-like observers in scenarios involving uncertain scheduling parameters has been investigated. In [21], using a Linear matrix inequality (LMI) framework an LPV observer was proposed. Later, a controller and a combined controllerobserver scheme for inexact continuous LPV polytopic systems was presented in [22], [23]. In [24], [25] H ∞ filters were employed to deal with uncertainty in the scheduling parameters; exploiting parameter dependent LMI methods. More recently, an H ∞ filter has been proposed to deal with both additive and multiplicative uncertainties in the LPV parameters in [26]. Recent applications of these ideas to aerospace systems have been explored in [27], [28]. A fault reconstruction scheme for LPV systems with perfect scheduling parameter knowledge, using H ∞ methods has been investigated in [29]. Very few papers have addressed specifically the fault reconstruction problem for LPV systems with uncertain scheduling parameters, notable exceptions are [30]. To the authors' knowledge,

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Gain-scheduled missile autopilot design using linear parameter varying transformations

Cited by 343 publications

References 7 publications

Interval state observer for nonlinear time varying systems

Interval state observer for nonlinear time varying systems

Vinnicombe metric as a closed-loop nonlinearity measure

Fault detection in uncertain LPV systems with imperfect scheduling parameter using sliding mode observers

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