Data-Driven $H_-/H_\infty$ Fault Detection and Control in Finite-Frequency Domain With Application to Steel Rolling Process

This study investigates the problem of data-driven fault detection and control (FDC) with the help of $H_-$ and $H_\infty$ performance indices for systems with unknown model parameters. To guarantee disturbance attenuation performance and fault sensitivity performance under data-driven framework, two data sets will be excited from disturbances and faults respectively. However, different data sets make it hard to solve a common control gain which satisfies the above two performance constraints simultaneously. Regarding this, a new data-driven parametrization method is developed by introducing a separation technology, which achieves the separation of excited data from the analytical solution of controller gain. Then, the joint design of controller and detector is realized by solving the $H_-/H_\infty$ optimization problem. Particularly, in terms of single-objective $H_-$ and $H_\infty$ optimization problems in finite frequency domain, sufficient and necessary controller design conditions are formulated. Finally, the proposed method is applied to the FDC problem of hot strip rolling and cold strip rolling whose model parameters are hard to obtain, and the effectiveness is verified by simulation experiments. Note to Practitioners —The determination of model parameters in both hot strip and cold strip rolling systems is restricted by the forward slip equation. However, it may be difficult to determine the forward slip equation accurately due to complex coupling effects, which makes the model-based control and detection problems challenging. In view of this, an improved data-driven method combining with $H_-$ and $H_\infty$ optimization technologies is proposed in this paper, which can be used to solve the FDC problem of industrial systems with unknown model parameters. The proposed data-driven method overcomes the difficulty of using two different data sets excited from disturbances and faults, respectively, to design a unique controller that satisfies both $H_-$ and $H_\infty$ performances. Particularly, faults and disturbances in practical industrial systems tend to occur in finite frequency ranges, which inspires us to further develop the finite frequency data-driven FDC technology. The effectiveness of the results in the simulation experiments is validated for both cold strip and hot strip steel systems using data generated based on the simulation model as well as field rolling data.