Describing functions in non-linear systems with structured and unstructured uncertainties

Impram, Serkan T.; Munro, N.

doi:10.1080/00207170010023160

Cited by 11 publications

(10 citation statements)

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“…Ferreres and Promion [9] propose a m-based method for limit cycle analysis, but the method assumes uncertainties only in the LTI element. Impram and Munro [10] pose the describing function analysis problem in a generalized interval polynomial framework, addressing both structured and unstructured uncertainties in Reference [11]. The authors extend their method to systems with multiple nonlinearities in Reference [12].…”

Section: Introductionmentioning

confidence: 97%

Limit cycle computation for describing function approximable nonlinear systems with box-constrained parametric uncertainties

Nataraj

Barve

2005

Int. J. Robust Nonlinear Control

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SUMMARYWe propose an algorithm to compute the limit cycle set of uncertain non-rational nonlinear systems with nonlinear parametric dependencies. The proposed algorithm computes the limit cycles for a wide class of uncertain nonlinear systems, where the transfer function of the linear element and describing function of the nonlinear element need to be only continuous with respect to the parameters and continuously differentiable with respect to the amplitude and frequency of periodic input signal. The proposed algorithm guarantees that the limit cycles are reliably computed to a prescribed accuracy, and that none of the actual limit cycle point is missed out irrespective of the tightness of the prescribed accuracy. Moreover, for a prescribed accuracy, the proposed algorithm computes all the limit cycles in a finite number of iterations, and an upper bound for this number is also computable. The algorithm is demonstrated on a challenging non-rational example with nonlinear parametric dependencies.

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Section: Introductionmentioning

confidence: 97%

Limit cycle computation for describing function approximable nonlinear systems with box-constrained parametric uncertainties

Nataraj

Barve

2005

Int. J. Robust Nonlinear Control

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“…Usually, the overall picture turns out to be the proper tuning of the adjustable parameters to effectively suppress or to remove the limit cycle. To achieve this, the extensions of the describing function method-based limit cycle analysis to nonlinear systems with parametric uncertainties have recently been proposed [14][15][16][17][18][19][20]. In one of such works, Barmish and Khargonekar attempted to address the former point in [14].…”

Section: Introductionmentioning

confidence: 98%

“…It should be emphasized that a family of admissible controller gain sets, instead of just one, can be selected from the Kharitonov region, which provides a flexible choice of controller coefficients. Existing techniques provide just one controller gain set [16][17][18][19][20]. Further, since the choices are multiple, the controller gains can be properly scheduled to guarantee robustness even in the case of controller implementation uncertainty.…”

Section: Introductionmentioning

confidence: 98%

“…Ferreres and Fromion employed the structured singular value µ-based method to analyze limit cycles of control systems containing nonlinearity in [16], but the method assumes uncertainties only in the LTI element. Extensions of [16] to the generalized interval polynomial framework whereby some of the parameters are assumed to vary in prescribed ranges are recast in [17] and [18]. In addition, a new approach to the stability analysis and limit cycle occurrence of nonlinear systems with uncertainty in the linear part is proposed in [19].…”

Section: Introductionmentioning

confidence: 99%

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Robust prevention of limit cycle for nonlinear control systems with parametric uncertainties both in the linear plant and nonlinearity

Wang

2007

ISA Transactions

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“…Other papers focus on simplifications of the nonlinear system, e.g. using a describing function analysis (Impram et al, 2001) and linearization.…”

Section: Introductionmentioning

confidence: 99%

Estimation of the Output Deviation Norm for Uncertain, Discrete-Time Nonlinear Systems in a State Dependent Form

Orłowski¹

2007

International Journal of Applied Mathematics and Computer Science

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Numerical evaluation of the optimal nonlinear robust control requires estimating the impact of parameter uncertainties on the system output. The main goal of the paper is to propose a method for estimating the norm of an output trajectory deviation from the nominal trajectory for nonlinear uncertain, discrete-time systems. The measure of the deviation allows us to evaluate the robustness of any designed controller. The first part of the paper concerns uncertainty modelling for nonlinear systems given in the state space dependent form. The method for numerical estimation of the maximal norm of the output trajectory deviation with applications to robust control synthesis is proposed based on the introduced three-term additive uncertainty model. Theoretical deliberations are complemented with a numerical, water-tank system example.

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Describing functions in non-linear systems with structured and unstructured uncertainties

Cited by 11 publications

References 0 publications

Limit cycle computation for describing function approximable nonlinear systems with box-constrained parametric uncertainties

Limit cycle computation for describing function approximable nonlinear systems with box-constrained parametric uncertainties

Robust prevention of limit cycle for nonlinear control systems with parametric uncertainties both in the linear plant and nonlinearity

Estimation of the Output Deviation Norm for Uncertain, Discrete-Time Nonlinear Systems in a State Dependent Form

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