Abstract
This chapter presents recent advances in both modeling and control of linear parameter-varying (LPV) systems. The proposed modeling technique follows the state-space model interpolation of local estimates (SMILE) approach which is based on the interpolation of a set of linear time invariant (LTI) models that are estimated for different fixed operating conditions and yields a state-space LPV model with a polytopic dependency on the scheduling parameter. The proposed control design technique considers a priori known bounds on the rate of parameter variation and can be used to compute stabilizing gain-scheduled state feedback as well as dynamic output feedback controllers for discrete-time LPV systems through linear matrix inequalities (LMIs). As extensions, H ∞ , \({\mathcal{H}}_{2}\), and suboptimal multiobjective control design problems can be conveniently solved. The presented techniques are applied to a vibroacoustic setup whose dynamics is highly sensitive to variations of the temperature. The numerical results show the advantages and versatility of the proposed approaches on a realistic engineering problem.
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Notes
- 1.
In the modeling of the uncertainty domain, \(\alpha\in{\mathbb{R}}^{N}\) and \(\Delta \alpha\in{\mathbb{R}}^{N}\) represent column vectors, that is, \(\alpha\in\mathbb{R}N\times 1\) and \(\Delta \alpha\in\mathbb{R}N\times 1\). Likewise, \((\alpha,\Delta \alpha )\) is a column vector \((\alpha,\Delta \alpha ) \in\mathbb{R}2N\times 1\). For reasons of compactness, this is not explicitly mentioned throughout the remainder of the text.
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Acknowledgements
The authors J.F. Camino, R.C.L.F. Oliveira and P.L.D. Peres are partially supported by the Brazilian agencies CAPES, CNPq and FAPESP. The authors J. De Caigny and J. Swevers are supported by the following funding: project G.0002.11 of the Research Foundation-Flanders (FWO-Vlaanderen), K.U.Leuven-BOF PFV/10/002 Center-of-Excellence Optimization in Engineering (OPTEC) and the Belgian Programme on Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office. The scientific responsibility rests with its author(s).
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De Caigny, J., Camino, J.F., Oliveira, R.C.L.F., Peres, P.L.D., Swevers, J. (2012). Modeling and Control of LPV Systems: A Vibroacoustic Application. In: Mohammadpour, J., Scherer, C. (eds) Control of Linear Parameter Varying Systems with Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1833-7_14
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