Application of the Polytope Model to Functional Programs

The polytope-based tolerance analysis in design process uses a finite set of constraints to represent specifications and propagates these constraints to any objective point in the Euclidean space. The operations of Minkowski sum and intersection on polytopes are well suited to serial and parallel assemblies. The polytope model has been applied to complex assemblies which contain a large number of joints and geometrical tolerances. However, the previous studies on this model consider toleranced features as surfaces of perfect form. The ignorance of form defects in tolerance analysis would result in a significant loss in accuracy and reliability. In this paper, an extension of the polytope model for tolerance analysis considering form defects is described in which the skin model shape representing the physical shape of the product is adopted to simulate the actual toleranced feature in place of the substitute one used conventionally. The combination of polytope model and skin model shape is expected to inherit many of the advantages of each model, combining easy-to-use tolerance propagation and form defects representation with accuracy guarantees. To demonstrate the method and its respective application, a case study of an assembly is illustrated in detail. The proposed method further enhances the capability of the polytope model in handling form defects and provides more realistic assembly results that approximate the actual assembly conditions for design evaluation.

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MRAC Control with Prior Model Knowledge for Asymmetric Damaged Aircraft

The Scientific World JOURNAL ◽

10.1155/2015/247301 ◽

2015 ◽

Vol 2015 ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

Xieyu Xu ◽

Lingyu Yang ◽

Jing Zhang

Keyword(s):

Prior Knowledge ◽

Structural Damage ◽

Transport Model ◽

Computational Cost ◽

Multivariable Model ◽

Linear Parameter Varying ◽

Asymptotic Error ◽

The Stability ◽

Model Reference Adaptive ◽

Polytope Model

This paper develops a novel state-tracking multivariable model reference adaptive control (MRAC) technique utilizing prior knowledge of plant models to recover control performance of an asymmetric structural damaged aircraft. A modification of linear model representation is given. With prior knowledge on structural damage, a polytope linear parameter varying (LPV) model is derived to cover all concerned damage conditions. An MRAC method is developed for the polytope model, of which the stability and asymptotic error convergence are theoretically proved. The proposed technique reduces the number of parameters to be adapted and thus decreases computational cost and requires less input information. The method is validated by simulations on NASA generic transport model (GTM) with damage.

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Representing dextrous manipulators with the spherically extended polytope model

10.1117/12.56757 ◽

1992 ◽

Author(s):

Gregory J. Hamlin ◽

Josep Tornero ◽

Robert B. Kelley

Keyword(s):

Polytope Model

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