Jan De Caigny

Interpolation-Based Modeling of MIMO LPV Systems

This paper presents State-space Model Interpolation of Local Estimates (SMILE), a technique to estimate linear parameter-varying (LPV) state-space models for multiple-input multiple-output (MIMO) systems whose dynamics depends on multiple time-varying parameters, called scheduling parameters. The SMILE technique is based on the interpolation of linear time-invariant models estimated for constant values of the scheduling parameters. As the linear time-invariant models can be either continuous- or discrete-time, both continuous- and discrete-time LPV models can be obtained. The underlying interpolation technique is formulated as a linear least-squares problem that can be efficiently solved. The proposed technique yields homogeneous polynomial LPV models in the multi-simplex that are numerically well-conditioned and therefore suitable for LPV control synthesis. The potential of the SMILE technique is demonstrated by computing a continuous-time interpolating LPV model for an analytic mass-spring-damper system and a discrete-time interpolating LPV model for a mechatronic -motion system based on experimental data.

Interpolated Modeling of LPV Systems

This paper presents a new state-space model interpolation of local estimates technique to compute linear parameter-varying (LPV) models for parameter-dependent systems using a set of linear time-invariant models obtained for fixed operating conditions. The technique is based on observability and controllability properties and has three strong appeals, compared with the state of the art in the literature. First, it works for continuous-time as well as discrete-time multiple-input multiple-output systems depending on multiple scheduling parameters. Second, the technique is automatic to some extent, in the sense that, after the model selection, no user interaction is required at the different steps of the method. Third, the resulting interpolating LPV model is numerically well-conditioned such that it can be used for modern LPV control design. Moreover, the proposed technique guarantees that the local models have a coherent state-space representation encompassing existing results as a particular case. The benefits of the approach are demonstrated on a simulation example and on an experimental data set obtained from a vibroacoustic setup.

Interpolated Modeling of LPV Systems Based on Observability and Controllability

Abstract This paper presents a State-space Model Interpolation of Local Estimates (SMILE) technique to compute linear parameter-varying (LPV) models for parameter-dependent systems through the interpolation of a set of linear time-invariant (LTI) state-space models obtained for fixed operating conditions. Since the state-space representation of LTI models is not unique, a suitable coherent representation needs to be computed for the local LTI models such that they can be interpolated. In this work, this coherent representation is computed based on observability and controllability properties. It is shown that compared with the state of the art in the literature, this new method has three strong appeals: it is general, fully automatic and results in numerically well-conditioned LPV models. An example demonstrates the potential of the new SMILE technique.

A vibroacoustic application of modeling and control of linear parameter-varying systems

This paper applies recent advances in both modeling and control of Linear Parameter-Varying (LPV) systems to a vibroacoustic setup whose dynamics is highly sensitive to variations in the temperature. Based on experimental data, an LPV model is derived for this system using the State-space Model Interpolation of Local Estimates (SMILE) technique. This modeling technique interpolates linear time-invariant models estimated at distinct operating conditions of the system (in this case, different temperatures). Using the obtained LPV model, gain-scheduled and robust multiobjective H2/H∞ state feedback controllers are designed such that can consider a priori known bounds on the rate of parameter variation. Numerical simulations using the closed-loop systems are performed to validate the controllers and to show the advantages and versatility of the proposed techniques.

Gain-Scheduled H∞-Control for Discrete-Time Polytopic LPV Systems Using Homogeneous Polynomially Parameter-Dependent Lyapunov Functions

Abstract This paper presents H∞ performance analysis and control synthesis for discrete-time linear systems with time-varying parameters. The parameters are assumed to vary inside a polytope and have known bounds on their rate of variation. The geometric properties of the polytopic domain are exploited to derive parameter-dependent linear matrix inequality conditions that consider the bounds on the rate of variation of the parameters. A systematic procedure is proposed to construct a family of finite-dimensional relaxations based on Polyas Theorem and a homogeneous polynomially parameter-dependent parameterization of arbitrary degree for the Lyapunov matrix. A numerical example illustrates the proposed approach.

Modeling and control of LPV systems : A vibroacoustic application

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.