PhD Shaping the performance of nonlinear systems through control design

Eindhoven University of Technology
November 20, 2023
Offerd Salary:€2,770
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Contract Type:Other
Working Time:Full time
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PhD Shaping the performance of nonlinear systems through control design



Irène Curie Fellowship



Electrical Engineering



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Job description

For decades, loop shaping has been the main workhorse of controller design in industries, achieving optimal performance and robustness. If we take the high- tech industry as an example, at the core of every high-precision mechatronic system, there is a weighting filter shaping the mixed sensitivity of the system and pushing the limit of its achievable performance. In practice, Linearity and Time-Invariance (LTI) are two crucial assumptions that seriously limit the applicability of loop shaping. When it comes to nonlinear systems, there are multiple limitations of loop shaping. First, quantification and shaping of system performance rely on frequency-domain tools such as Bode plots and Nyquist diagrams. However, Laplace and Fourier transform are not defined for nonlinear operators. Second, unlike in the LTI case, nonlinear systems can exhibit bifurcation, multiple equilibria with distinct stability properties at each of them, and oscillatory behavior with dynamically changing periodicity. Currently, no generic method exists that can quantitatively assess system performance under such phenomena, let alone optimize it.

This research aims is to develop a unified framework for loop shaping to analyze, compute and optimize the performance of nonlinear systems. By developing a computational tool for efficient loop-shaping, this project will push beyond the limitations of the current state-of-the-art and enable the design of high-performance control systems for the next generation of engineering applications. Implications of such a framework will be multi-fold:

  • Oscillatory patterns, multiple equilibria behavior and bifurcation are critical for neuromorphic computing, control of electromechincal systems, managing power grids, and treating neurological diseases. This framework will provide the very first control-theoretic tool to quantify and shape the performance and enable safe and reliable operation of such nonlinear systems.
  • In the LTI case, the Bode sensitivity integral limits the achievable bandwidth due to the waterbed effect it invokes on the sensitivity functions. To break that cycle, researchers have played with the idea of designing nonlinear controllers for linear plants, but the current methods are limited to a few building blocks and the easiness of the overall framework is lost due to the lack of good understanding of nonlinear systems and control performance in the frequency domain. This framework will circumvent this limitation and enable novel approaches for unprecedented performance in motion-control.
  • In more and more applications, nonlinear aspects of the dynamics become dominant and even if efficient tools such as Linear Parameter Varying (LPV) control design have been established it is largely not understood how to apply performance shaping in terms of weighting filters to get the desired control performance with the nonlinear system in the closed loop.
  • Tasks:

  • Study the literature of nonlinear control theory, monotone operators, and theory of optimization.
  • Develop analytical tools to characterize the input-output behavior of nonlinear feedback systems. Specifically, analogous to linear control systems, the theories of Nyquist stability, gain margin, phase margin and input-output stability will be developed for classes of nonlinear feedback systems.
  • Build algorithmic tools to design nonlinear controllers that shape the feedback loop and achieve specific performance and robustness margins.
  • Demonstrate the effectiveness of the developed methods with the help of use cases related to high-tech systems and/or neuro-engineering. In the case of high-tech systems, there is a possibility to collaborate with mechatronic companies in Eindhoven. Collaborations with the Center for Care and Cure Technology Eindhoven (C3Te) and Cyber-Physical Systems Center (CPSe) are also a possibility for specific applications in neuro- engineering.
  • Dissemination of the results of your research in top international peer- reviewed journals and conferences.
  • Writing a successful dissertation based on the developed research and defending it.
  • Assume educational tasks like the supervision of Master students and internships.
  • Job requirements

    We are looking for a candidate who meets the following requirements:

  • You are a talented and enthusiastic young researcher.
  • You have experience with or a strong background in systems and control, mathematics, and signal processing. Preferably you finished a master's in Systems and Control, (Applied) Physics, (Applied) Mathematics, Information Technologies, Electrical Engineering or Mechanical Engineering.
  • You have good programming skills and experience (Matlab and/or Julia is an asset).
  • You have good communicative skills, and the attitude to partake successfully in the work of a research team.
  • You are creative and ambitious, hard-working, and persistent.
  • You have a good command of the English language (knowledge of Dutch is not required).
  • Conditions of employment

    A meaningful job in a dynamic and ambitious university, in an interdisciplinary setting and within an international network. You will work on a beautiful, green campus within walking distance of the central train station. In addition, we offer you:

  • Full-time employment for four years, with an intermediate evaluation (go/no-go) after nine months. You will spend 10% of your employment on teaching tasks.
  • Salary and benefits (such as a pension scheme, paid pregnancy and maternity leave, partially paid parental leave) in accordance with the Collective Labour Agreement for Dutch Universities, scale P (min. €2,770 max. €3,539).
  • A year-end bonus of 8.3% and annual vacation pay of 8%.
  • High-quality training programs and other support to grow into a self- aware, autonomous scientific researcher. At TU/e we challenge you to take charge of your own learning process.
  • An excellent technical infrastructure, on-campus children's day care and sports facilities.
  • An allowance for commuting, working from home and internet costs.
  • A Staff Immigration Team and a tax compensation scheme (the 30% facility) for international candidates.
  • Information and application

    About us

    Eindhoven University of Technology is an internationally top-ranking university in the Netherlands that combines scientific curiosity with a hands- on attitude. Our spirit of collaboration translates into an open culture and a top-five position in collaborating with advanced industries. Fundamental knowledge enables us to design solutions for the highly complex problems of today and tomorrow.

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    Do you recognize yourself in this profile and would you like to know more? Please contact dr. ir. Amritam Das,

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    We invite you to submit a complete application by using the apply button. The application should include a:

  • Cover letter in which you describe your motivation and qualifications for the position.
  • Curriculum vitae, including a list of your publications and the contact information of three references.
  • We look forward to receiving your application and will screen it as soon as possible. The vacancy will remain open until the position is filled.

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