Complicated nonlinear behavior is encountered in many physical dynamical systems in engineering. Such behavior is difficult to be described by means of mathematical models or to regulate during operation. Examples of such systems are present in high-tech and automotive applications to high-precision lithography machines, but also production-critical chemical operations in the process industry or in energy applications such as solar cells.
For a long time, it was considered adequate to operate these systems around steady-state conditions or specific regimes using digital controllers, designed via Linear Time-Invariant (LTI) control synthesis. Growing challenges in terms of system complexity, performance requirements, importance of operational constraints and energy efficiency have begun to push the limitations of the LTI framework, e.g. in the high-tech mechatronic field.
Advanced nonlinear modelling tools have been developed over the last years, including the block-oriented nonlinear framework. To address the demand for high-performance systems, advanced model-based nonlinear control tools need to be developed. However, these nonlinear models lack the intuitive and simple interpretation that are the trademark of LTI models. Therefore, these models do not allow for an intuitive and systematic control design framework.
The Linear-Parameter-Varying (LPV) framework has been developed as an extension of the LTI framework, preserving most of its intuitive features, with the possibility to use a systematic control design flow. LPV systems are dynamical models capable of describing a NL behavior in terms of a linear structure which is dependent on a measurable, so called scheduling-variable p in the system. The LPV framework is viewed as a high priority technological innovation by many high-tech industrial players.
Since the LPV framework is rather conceived as the extension of the LTI framework, a significant gap continues to exist between nonlinear systems and the LPV framework. Bridging this gap allows the community to obtain a unified framework from nonlinear modelling and identification to robust and systematic control design for nonlinear systems using the LPV framework.
How to bridge the gap between the LPV and nonlinear frameworks, and how to exploit the already available tools of nonlinear system identification for the estimation of LPV models for robust LPV control design is the topic of this research project by approaching the LPV framework starting from a nonlinear system point of view. Such a viewpoint allows one to include strongly nonlinear systems in the considered LPV system class, and to develop LPV-based control strategies for nonlinear systems.
A nonlinear systems viewpoint is obtained in this project by addressing three core research objectives:
1. Convert nonlinear models in LPV representations in a systematic way
2. Develop a frequency-domain linearization analysis framework of nonlinear systems for LPV modelling
3. Nonlinear identification for robust LPV control
