Linear fractional representations of uncertain systems

In this paper a general approach for modelling structured real-valued parametric perturbations is presented. It is based on a decomposition of perturbations into linear fractional transformations (LFTs), and is applicable to rational multi-dimensional (ND) polynomial perturbations of entries in state-space models. Model reduction is used to reduce the size of the uncertainty structure. The procedure will be applied for the uncertainty modelling of an aircraft model depending on altitude and velocity (flight envelope).

Parametric Uncertainty Modeling using LFTs

Prediction error learning algorithms for neural state space models are developed, both for the deterministic case and the stochastic case with measurement and process noise. For the stochastic case, a predictor with direct parametrization of the Kalman gain by a neural net architecture is proposed. Expressions for the gradients are derived by applying Narendra's sensitivity model approach. Finally a linear fractional transformation representation is given for neural state space models, which makes it possible to use these models, obtained from input/output measurements on a plant, in a standard robust performance control scheme.

Nonlinear system identification using neural state space models, applicable to robust control design

The objective of this paper is to show how experimentally based modelling can be used for designing Linear Parametrically Varying (LPV) controllers. As a test system we use an industrial pick and place unit with one linear X-drive and two independent linear Ydrives. The dynamics of the Y-axes depend on the Xposition. An LPV model is derived by using measured Frequency Response Functions at different positions, fitting a parametric model on each measurement and combining these models by linking parameters via a fit as a function of operating point. Rewriting the LPV model into a LFT structure and applying model reduction in the space of the scheduling variable finalizes the modelling phase. With this model an LPV controller is calculated and shows robust performance for the whole operating range, in contrast to local H∞ controllers.

http://www.mate.tue.nl/mate/pdfs/2704.pdf

Experimental modelling and LPV control of a motion system

We realize a novel photonic microwave phase shifter/modulator based on a nonlinear optical loop mirror incorporating a Mach-Zehnder interferometer. A near-linear phase shifter exceeding 180° and a phase modulation with 2.5 Gbit/s baseband signal are obtained for a 10 GHz microwave signal by this proposed device.

/pdf/photonic-microwave-phase-shifter-modulator-based-on-a-9yzyv6q9q5.pdf

Photonic microwave phase shifter/modulator based on a nonlinear optical loop mirror incorporating a Mach-Zehnder interferometer.

The investigation of closed-loop systems subject to model perturbations is an important issue to assure stability robustness of a control design. A large variety of model perturbations can be described by norm-bounded uncertainty models. A general approach for modelling structured complex and real-valued parametric perturbations is presented. The resulting robustness analysis problem is solved nonconservatively using real and complex-structured singular-value calculations. The uncertainty modelling and robustness analysis are shown for a high-accuracy 5D electromechanical positioning device to be used in optical (Compact Disc) recording.

/pdf/uncertainty-modelling-and-structured-singular-value-5517cvr99p.pdf

SG Smit

Papers

Uncertainty modelling and structured singular-value computation applied to an electromechanical system