Periodic Reporting for period 1 - NL2LPV (Nonlinear system modelling for linear parameter-varying control design)
Periodo di rendicontazione: 2018-03-01 al 2020-02-29
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
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
The project developed and realized a wide range of new engineering tools for the data-driven modelling, control and representation of nonlinear dynamical engineering systems.
In a first step, the equivalences between a wide range of nonlinear model structures and linear parameter-varying (LPV) models has been analyzed. This resulted in an automated transformation algorithm that can generate LPV representations starting from a very broad nonlinear model class. Sufficient requirements have been derived to obtain continuous scheduling signal mappings within this LPV representation.
Secondly, the frequency-domain representation of LPV models has been studied. To obtain such a representation, inspiration was drawn from the vast linear time-varying systems literature. Furthermore, advances have been made towards obtaining a 'best LPV approximation' framework for nonlinear systems, i.e. what is the best LPV approximation one can obtain of a nonlinear system, given some constraints on the LPV model structure and the scheduling signals. This framework would not only given an upper bound on the modelling capabilities of the LPV framework for the system under study, it immediately offers robust uncertainty bounds on the obtained model as well.
Finally, innovative nonlinear system identification tools for robust LPV control have been developed. The nonlinear LFR (linear fractional representation) model has been considered in this work due to its close link to robust control theory, the generality of the nonlinear model structure, and its link to both nonlinear state-space and block-oriented identification. The followed approach merged the optimization techniques and best practices obtained in the (deep) neural network setting with state-of-the-art system identification approaches. This resulted in the representation of the nonlinear LFR and state-space models as a special class of recurrent neural networks. The initialization of the weights and biases of this neural network class has been studied, and a novel BLA-based initialization approach has been proposed.
In a first step, the equivalences between a wide range of nonlinear model structures and linear parameter-varying (LPV) models has been analyzed. This resulted in an automated transformation algorithm that can generate LPV representations starting from a very broad nonlinear model class. Sufficient requirements have been derived to obtain continuous scheduling signal mappings within this LPV representation.
Secondly, the frequency-domain representation of LPV models has been studied. To obtain such a representation, inspiration was drawn from the vast linear time-varying systems literature. Furthermore, advances have been made towards obtaining a 'best LPV approximation' framework for nonlinear systems, i.e. what is the best LPV approximation one can obtain of a nonlinear system, given some constraints on the LPV model structure and the scheduling signals. This framework would not only given an upper bound on the modelling capabilities of the LPV framework for the system under study, it immediately offers robust uncertainty bounds on the obtained model as well.
Finally, innovative nonlinear system identification tools for robust LPV control have been developed. The nonlinear LFR (linear fractional representation) model has been considered in this work due to its close link to robust control theory, the generality of the nonlinear model structure, and its link to both nonlinear state-space and block-oriented identification. The followed approach merged the optimization techniques and best practices obtained in the (deep) neural network setting with state-of-the-art system identification approaches. This resulted in the representation of the nonlinear LFR and state-space models as a special class of recurrent neural networks. The initialization of the weights and biases of this neural network class has been studied, and a novel BLA-based initialization approach has been proposed.
The nonlinear viewpoint of this project offers a novel approach to the LPV framework on one hand, and it opens new perspective on providing reliable models in a data-driven way for the control of a wide class of nonlinear systems on the other hand. The frequency-domain uncertainty analysis and representation of LPV systems opens new perspectives on robust LPV control design. The developed nonlinear system identification tools build upon the available state-of-the-art in both the control engineering and the machine learning field, resulting in innovative and performant ssytem identification approaches. Combining these results in a complete framework offers a systematic nonlinear/LPV modeling tool chain that has not been presented before.
The results of this research project impact on a wide range of engineering fields ranging from process control, over mechanical engineering, to energy applications and the automotive sector.
The results of this research project impact on a wide range of engineering fields ranging from process control, over mechanical engineering, to energy applications and the automotive sector.