Robust Controller Design For Linear Systems With Nonlinear Distortions: A Data-Driven Approach

The extensive use of frequency-domain tools for analyzing and controlling linear systems have become indispensable for the control systems engineer. However, due to the increased performance demands on today's industrial systems, the effects of certain nonlinearities can no longer be neglected in control applications, and the use of these tools becomes problematic. In the current literature, however, frequency-domain methods exist where the underlying linear dynamics of a nonlinear system can be captured in an identification experiment; in this manner, the nonlinear system is replaced by a linear model with a noise source where a best linear approximation of the nonlinear system is obtained with an associated frequency-dependent uncertainty. This allows the use of robust control algorithms to ensure performance for the underlying linear system. In this paper, a data-driven H-infinity robust control strategy is presented which implements a convex optimization algorithm to ensure the performance and closed-loop stability of a linear system that is subject to nonlinear distortions. A case study is presented to illustrate how the proposed method can be used to design controllers for this class of systems.

Robust Controller Design For Linear Systems With Nonlinear Distortions. A Data-Driven Approach

Alireza Karimi, Achille Nicoletti

The extensive use of frequency-domain tools for analyzing and controlling linear systems have become indispensable for the control systems engineer. However, due to the increased performance demands on today's industrial systems, the effects of certain nonlinearities can no longer be neglected in control applications, and the use of these tools becomes problematic. In the current literature, however, frequency-domain methods exist where the underlying linear dynamics of a nonlinear system can be captured in an identification experiment; in this manner, the nonlinear system is replaced by a linear model with a noise source where a best linear approximation of the nonlinear system is obtained with an associated frequency-dependent uncertainty. This allows the use of robust control algorithms to ensure performance for the underlying linear system. In this paper, a data-driven H ∞ robust control strategy is presented which implements a convex optimization algorithm to ensure the performance and closed-loop stability of a linear system that is subject to nonlinear distortions. A case study is presented to illustrate how the proposed method can be used to design controllers for this class of systems.

2018

A Data-Driven Frequency-Domain Approach for Robust Controller Design via Convex Optimization

Achille Nicoletti

The objective of this dissertation is to develop data-driven frequency-domain methods for designing robust controllers through the use of convex optimization algorithms. Many of today's industrial processes are becoming more complex, and modeling accurate physical models for these plants using first principles may be impossible. With the increased developments in the computing world, large amounts of measured data can be easily collected and stored for processing purposes. Data can also be collected and used in an on-line fashion. Thus it would be very sensible to make full use of this data for controller design, performance evaluation, and stability analysis. The design methods imposed in this work ensure that the dynamics of a system are captured in an experiment and avoids the problem of unmodeled dynamics associated with parametric models. The devised methods consider robust designs for both linear-time-invariant (LTI) single-input-single-output (SISO) systems and certain classes of nonlinear systems. In this dissertation, a data-driven approach using the frequency response function of a system is proposed for designing robust controllers with H∞ performance. Necessary and sufficient conditions are derived for obtaining H∞ performance while guaranteeing the closed-loop stability of a system. A convex optimization algorithm is implemented to obtain the controller parameters which ensure system robustness; the controller is robust with respect to the frequency-dependent uncertainties of the frequency response function. For a certain class of nonlinearities, the proposed method can be used to obtain a best-linear-approximation with an associated frequency dependent uncertainty to guarantee the stability and performance for the underlying linear system that is subject to nonlinear distortions. The concepts behind these design methods are then used to devise necessary and sufficient conditions for ensuring the closed-loop stability of systems with sector-bounded nonlinearities. The conditions are simple convex feasibility constraints which can be used to stabilize systems with multi-model uncertainty. Additionally, a method is proposed for obtaining H∞ performance for an approximate model (i.e., describing function) of a sector-bounded nonlinearity. This work also proposes several data-driven methods for designing robust fixed-structure controllers with H∞ performance. One method considers the solution to a non-convex problem, while another method convexifies the problem and implements an iterative algorithm to obtain the local solution (which can also consider H2 performance). The effectiveness of the proposed method(s) is illustrated by considering several case studies that require robust controllers for achieving the desired performance. The main applicative work in this dissertation is with respect to a power converter control system at the European Organization for Nuclear Research (CERN) (which is used to control the current in a magnet to produce the desired field in controlling particle trajectories in accelerators). The proposed design methods are implemented in order to satisfy the challenging performance specifications set by the application while guaranteeing the system stability and robustness using data-driven design strategies.

EPFL2018

A Data-Driven Frequency-Domain Approach for Robust Controller Design via Convex Optimization

Achille Nicoletti

EPFL2018