A bifurcation-based procedure for designing and analysing robustly stable non-linear hydraulic servo systems

Kremer, Gregory; Thompson, David F.

doi:10.1243/0959651981539550

Cited by 13 publications

(9 citation statements)

References 10 publications

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“…In light of these insights it may be possible to reduce the dimensionality of the parameter space to include the parameters which are most influential in the damage propagation. Several methodologies for reduction of parameter space are known and as an example interested reader may consult [10].…”

Section: Smart Damage Prediction: a Methodologymentioning

confidence: 99%

“…In a multi-parameter system, there is a bifurcation curve/plane in the parameter space along which the system has an equilibrium point exhibiting the same bifurcation [14]. (9) and for the Hopf bifurcation is (Equation 10): (10) where Θ denotes the bi-alternate product [7,11] of two matrices. If more than one parameter is varied simultaneously to track a bifurcation curve Γ , then the following events might occur to the monitored nonhyperbolic equilibrium at some parameter values: extra eigenvalues can approach the imaginary axis and thus change the dimension of the center manifold or some of the non-degeneracy conditions for the co-dimension one bifurcation can be violated.…”

Section: Damage Detection and Prognosis: Distance To Bifurcationmentioning

confidence: 99%

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Smart damage prediction: a distance-to-bifurcation-based approach

Shukla

Frederick

2004

SPIE Proceedings

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Damage detection and prediction is essential for structural health monitoring. Vibration based methods have been used in health monitoring. In this work damage is proposed to be a nonlinear dynamical phenomenon and can be analyzed by utilizing the bifurcation theory. A methodology for predicting failure is proposed which utilizes the concepts of distance to stability boundary as estimated by bifurcation analysis. The proposed methodology is illustrated by developing bifurcation boundary for a two degree of freedom nonlinear mass-spring-damper system. Two damage models are investigated to illustrate the utility the proposed methodology in capturing and estimating the evolution of damage phenomenon.

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Section: Smart Damage Prediction: a Methodologymentioning

confidence: 99%

Section: Damage Detection and Prognosis: Distance To Bifurcationmentioning

confidence: 99%

Smart damage prediction: a distance-to-bifurcation-based approach

Shukla

Frederick

2004

SPIE Proceedings

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“…The observation that normal vectors and critical manifolds are not invariant under scaling has been discussed in detail in the context of hydraulic servo-systems. 18 For simplicity, it is assumed in the sequel that the parameters have been scaled according to eq 13. Note that in the scaled parameters, the hyperellipsoid (eq 10) that bounds the robustness region becomes the hyperball…”

Section: Building Blocks Of the Algorithmmentioning

confidence: 99%

Steady-State Process Optimization with Guaranteed Robust Stability and Flexibility: Application to HDA Reaction Section

Mönnigmann

Marquardt

2005

Ind. Eng. Chem. Res.

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This paper extends a recently suggested approach for the steady-state process optimization with guaranteed robust stability and flexibility under parametric uncertainty. The approach is based on measuring the distance of a candidate point of operation to so-called critical manifolds. Critical manifolds locally separate regions of the space of the process and controller design parameters with desired process traits from those regions with undesired traits. Pairs of desired and undesired traits may, for example, be feasibility and infeasibility of operation, stability and instability, or more generally, desired dynamical behavior and undesired dynamical behavior. While in previous applications knowledge on the existence and location of critical manifolds were assumed to be available before the optimization was attempted, the present paper presents an algorithm in which critical manifolds are automatically detected as the optimization proceeds. This algorithm, which is the conceptual contribution of the paper, allows the application of the critical manifold-based approach to processes for which no a priori information on the existence and location of critical manifolds exists. As a proof of concept the algorithm is applied to the reaction section of the HDA process. An analysis of the critical manifolds of this process model is not available. Since 12 uncertain parameters exists, analyzing the critical manifolds would be tedious. While an analysis of the 12 uncertain parameters is not practical, the critical manifoldbased optimization approach can be applied to models with this number of parameters and beyond. IntroductionA new approach to taking constraints on the process dynamics into account in steady-state process optimization has recently been suggested. [1][2][3] The key features of this new approach are that (i) it can be applied to a broad class of dynamical features, among them stability and disturbance rejection; (ii) it guarantees the desired dynamical behavior despite parametric uncertainty in the process model; and (iii) it can be applied to ensuring the desired dynamics and process feasibility simultaneously. While the new approach is more general, a typical application is to guarantee stability and feasibility of the optimal point of operation despite parametric uncertainty of the process model when optimizing the process with respect to an economic objective function. 1 The two central concepts behind the new approach are the notion of a critical manifold and the normal space to that manifold. Readers not familiar with the notion of a manifold may think of the nonlinear generalization of a linear subspace of a vector space. Just as a plane defined by a single linear equation is a linear subspace of the linear vector space R 3 , nonlinear equations or sets of equations can define sets of points in R n . These so-called manifolds can locally be approximated by linear subspaces. Globally, however, nontrivial nonlinear manifolds may bend and fold to form nonlinear geometrical objects. The stability bound...

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“…These nonlinearities are inherent to the system and their interaction can lead to highly nonlinear dynamic behavior of the overall test-stand. The dynamics, control and stability of servo-hydraulic systems have been studied in detail by numerous investigators some of which include Alleyne and Liu (1999), Burton (1975) Blackburn, Reethof and Shearer (1960), Cox and French (1986), Foster and Kulkarni (1968) Hahn and Hecker (1997), Kremer and Thomson (1998), Lewis and Stern (1962), Maccari (2000), McCloy and Matrin (1980), Scheidl and Manhartsgruber (1998), Van Schothorst (1997), Viersma (1980), Watton (1988 and Yau, Bajaj, and Nwokah (1992). The primary aim of this work is to demonstrate a method for accurately characterizing the effect of linear feedback control structures on the bifurcation stability of a servohydraulic system via experimentation as well as numerical computation.…”

Section: Experimental Test Stand Developmentmentioning

confidence: 99%

An Investigation of the Effect of Feedback Control on the Bifurcation Stability of a Nonlinear Servohydraulic System

Shukla

Thompson

2005

International Journal of Fluid Power

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The Servo-hydraulic systems are commonly used for motion and force control and exhibit nonlinear dynamic phenomena. One such nonlinear phenomenon is the loss of stability via bifurcations. In this work, a computational and experimental investigation is performed to characterize with a higher degree of accuracy the effect of linear feedback control on the bifurcation stability of a nonlinear servo-hydraulic system. A low-order model of the experimental test stand is first developed, validated and analyzed. It is then shown that the use of an appropriate linear feedback control structure can improve the bifurcation stability of a nonlinear servo-hydraulic system. Parametric space investigation is conducted to study the bifurcation stability behavior of the system and stability boundaries are developed to demonstrate the effect of linear feedback on the nonlinear systems.

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A bifurcation-based procedure for designing and analysing robustly stable non-linear hydraulic servo systems

Cited by 13 publications

References 10 publications

Smart damage prediction: a distance-to-bifurcation-based approach

Smart damage prediction: a distance-to-bifurcation-based approach

Steady-State Process Optimization with Guaranteed Robust Stability and Flexibility: Application to HDA Reaction Section

An Investigation of the Effect of Feedback Control on the Bifurcation Stability of a Nonlinear Servohydraulic System

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