In this contribution, the design of multiband transmission functions is considered. Independent and arbitrary number of bands can be designed. Moreover, the whole transmission function is synthesized by one wave digital lattice structure. The approximation process starts by extracting the scattering matrix properties of multiband reference lattice structures. Consequently, the approximation problem reduces to generating a polynomial Q of degree n, which is the degree of the filter. The degree n is depending on the number of the designed bands. Hence, if the number of bands is even, n will be odd, and if the number of bands is odd, n will be even. The polynomial Q will approximate the difference phase function of the two branch polynomials. It is composed of two subpolynomials, one of them is Hurwitz and the other is anti-Hurwitz. The degrees of these subpolynomials differ by odd number if the number of bands is even and differ by even number if the number of bands is odd. Q is generated according to iterative interpolation and using explicit recursive formulas. After obtaining Q, the two subpolynomials are calculated and the two branch all-pass functions are constructed. Consequently, the filter is synthesized in the digital frequency domain. The method is applied through an illustrative example. Copyright © 2011 John Wiley & Sons, Ltd.

A common problem in the context of linear parameter- varying (LPV) systems is how input-output (IO) models can be efficiently realized in terms of state-space (SS) representations. The problem originates from the fact that in the LPV literature discrete-time identification and modeling of LPV systems is often accomplished via IO model structures. However, to utilize these LPV-IO models for control synthesis, commonly it is required to transform them into an equivalent SS form. In general, such a transformation is complicated due to the phenomenon of dynamic dependence (dependence of the resulting representation on time-shifted versions of the scheduling signal). This conversion problem is revisited and practically applicable approaches are suggested which result in discrete-time SS representations that have only static dependence (dependence on the instantaneous value of the scheduling signal). To circumvent complexity, a criterion is also established to decide when an linear-time invariant (LTI)-type of realization approach can be used without introducing significant approximation error. To reduce the order of the resulting SS realization, an LPV Ho-Kalman-type of model reduction approach is introduced, which, besides its simplicity, is capable of reducing even non-stable plants. The proposed approaches are illustrated by application oriented examples.

In thispaper,apracticalprocedureforlinearparameter-varying(LPV)modelingandidentificationof a roboticmanipulatorispresented,whichleadstoasuccessfulexperimentalimplementationofan LPV gain-scheduledcontroller.Anonlineardynamicmodelofatwo-degrees-of-freedommanipulator containingallimportanttermsisobtainedandunknownparameterswhicharerequiredtoconstructan LPV modelareidentified.Animportanttoolforobtainingamodelofcomplexitylowenoughtobe suitableforcontrollersynthesisistheprinciple-component-analysis-basedtechniqueofparameterset mapping.Sincetheresultingquasi-LPVmodelhasalargenumberofaffineschedulingparametersanda large overbounding,parametersetmappingisusedtoreduceconservatismandcomplexityin controllerdesignbyfindingtighterparameterregionswithfewerschedulingparameters.Asufficient a posteriori condition isderivedtoassessthestabilityoftheresultingclosed-loopsystem.Toevaluate the applicabilityandefficiencyoftheapproximatedmodel,apolytopicLPVgain-scheduledcontrolleris synthesizedandimplementedexperimentallyonanindustrialrobotforatrajectorytrackingtask.The experimentalresultsillustratethatthedesignedLPVcontrolleroutperformsanindependentjointPD controllerintermsoftrackingperformanceandachievesaslightlybetteraccuracythanamodel-based inverse dynamicscontroller,whilehavingasimplerstructure.Moreover,itisshownthattheLPV controllerismorerobustagainstdynamicparameteruncertainty.