Modelling and Control of Linear Parameter-Varying (LPV) Systems

Modelling and Control of Linear Parameter-Varying (LPV) Systems

The gain-scheduling techniques and LPV control theory are among of the most popular non-linear control design approaches which commonly used in practice. The LPV framework have been proved the ability to meet design specification over wide operating ranges. Control problems are formulated as Linear Matrix Inequalities (LMIs) optimization problems which can be computed via convex optimization. While many researchers have studied the design of gain-scheduled controllers for systems represented by LPV models, the question of how to obtain a suitable LPV model for a given nonlinear or time-varying plant has received much less attention. A physical model with completely nonlinear differential equations can be construct an LPV model with the suitable variable transformations. However, most of practical system is not well-enough understood and system identification techniques have to be used for this case.

This research aims to develop identification techniques to construct the LPV systems and combine them with LMI based gain-scheduling controller design techniques. The task is separated in three parts. Firstly, design the suitable input signals for a nonlinear system identification which is one of the most important on nonlinear system identification steps. Then the collected input-output data will be used to identify a input-output discrete-time nonlinear system in polynomial nonlinear auto regressive with external input (NARX) model. Since the models are obtained, they will be transform to a LPV form. Finally the LMI based gain-scheduling controller design will be adapted to work with the model described above. Results obtained in this work will be tested by simulations and real experiments. The simulation tests will be carried out by using SIMULINK and MATLAB while the real experiments will be tested on a titration and neutralization plant (TINA) and a six-degree-of-freedom articulated robot.