Modeling and Identification of Linear Parameter-Varying by Roland Toth

By Roland Toth

Through the previous two decades, the framework of Linear Parameter-Varying (LPV) platforms has develop into a promising process theoretical method of h- dle the controlof mildly nonlinear and particularly place established structures that are universal in mechatronic purposes and within the approach ind- try out. The beginning of the program type used to be initiated by way of the necessity of engineers to accomplish higher functionality for nonlinear and time-varying dynamics, c- mon in lots of business purposes, than what the classical framework of Linear Time-Invariant (LTI) keep an eye on supplies. despite the fact that, it used to be additionally a p- mary objective to maintain simplicity and “re-use” the robust LTI effects via extending them to the LPV case. The growth persevered in line with this philosophy and LPV keep an eye on has turn into a good proven ?eld with many promising purposes. regrettably, modeling of LPV structures, particularly in accordance with measured information (which is termed procedure identi?cation) has obvious a constrained improvement sincethebirthoftheframework. Currentlythisbottleneck oftheLPVfra- paintings is halting the move of the LPV conception into business use. with no reliable versions that ful?ll the expectancies of the clients and with out the und- status how those types correspond to the dynamics of the appliance, it truly is di?cult to layout excessive functionality LPV regulate options. This ebook goals to bridge the distance among modeling and keep watch over through investigating the elemental questions of LPV modeling and identi?cation. It explores the lacking information of the LPV process conception that experience hindered the formu- tion of a good validated identi?cation framework.

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20) ⎦ . . φlnY 1 (z) . . φlnY nU (z) nY ×nY where each {φli j }∞ (E) l=1 corresponds to a basis of H2− (E). 21) i=0 where Wi ∈ CnY ×nU and denotes the element-by-element matrix product. Similar to the SISO case, with different basis sequences {φli j }∞ l=1 , different convergence rates of the series-expansion can be achieved. However, the degree of freedom in the basis selection is much higher in the MIMO case. 20), which gives the possibility of several structural classifications of this type of MIMO bases (see [205]).

Denote the transfer function of F as F(z) : C → CnY ×nU . Let (u, y) be valid signal trajectories of F with left compact support and denote the Z-transform of u and y by Y (z) = Z {y} and U(z) = Z {u} defined on their appropriate region of convergence1 (ROC) with z ∈ C called the Z-variable. 1) for any z in the intersection of the ROC of Y (z) and U(z). Substitution of z in F(z) by eiω gives the frequency response of the discrete-time system for ω ∈ (−π , π ). Assume that F is stable, so the domain of F(z) is the exterior of the unit circle.

In other approaches, interpolation is accomplished via pole locations [136]. e. by the applied LTI identification, these approaches focus on the question: how to accomplish interpolation in a more efficient sense. These approaches closely relate to the local-linear-modeling framework [121]. 4 Set-Membership Approaches Set-membership based identification of LPV-SS models has been first considered in [184] using a LFR form with a linear dependence: Δ (p) = Diag(I p1 , . . , I pnP ) and D11 = 0. 12) i=0 where Ei ∈ RnY ×nY and e is a ∞ sequence.

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