Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Earthquake Control: An Emerging Application for Robust Control. Theory and Experimental Tests

Diego Gutiérrez-Oribio, Georgios Tzortzopoulos, Ioannis Stefanou, Franck Plestan

TL;DR

This paper investigates slowing earthquake energy dissipation through robust nonlinear control applied to a reduced-order fault model with fluid-pressure input $p$. It introduces two controllers—sliding-mode based CHOSMA variants producing local finite-time convergence and an extended LQR with integral action yielding global exponential stability—both delivering continuous control signals to mitigate chattering. Through numerical simulations and laboratory experiments on a spring-slider fault apparatus, the authors demonstrate successful tracking of a slow reference $r(t)$ and aseismic slip, with performance trade-offs: sliding-mode excels in displacement accuracy while e-LQR offers smoother velocity profiles. The work also outlines gain-scaling laws to upscale laboratory results to real faults, highlighting potential applications for safer energy production and earthquake mitigation, and identifies avenues for incorporating more detailed multi-physics fault models in future work.

Abstract

This paper addresses the possibility of using robust control theory for preventing earthquakes through fluid injections in the earth's crust. The designed robust controllers drive aseismically a fault system to a new equilibrium point of lower energy by tracking a slow reference signal. The control design is based on a reduced-order nonlinear model able to reproduce earthquake-like instabilities. Uncertainties related to the frictional and mechanical properties of the underlying physical process and external perturbations are considered. Two types of controllers are derived. The first one is based on sliding-mode theory and leads to local finite-time convergence of the tracking error and rejection of Lipschitz w.r.t. time perturbations. The second controller is based on LQR control and presents global exponential stability of the tracking error and rejection of Lipschitz w.r.t. states perturbations. Both controllers generate a continuous control signal, attenuating the chattering effect in the case of the sliding-mode algorithms. The developed controllers are tested extensively and compared on the basis of numerical simulations and experiments in the laboratory. The present work opens new perspectives for the application of robust nonlinear control theory to complex geosystems, earthquakes and sustainable energy production.

Earthquake Control: An Emerging Application for Robust Control. Theory and Experimental Tests

TL;DR

This paper investigates slowing earthquake energy dissipation through robust nonlinear control applied to a reduced-order fault model with fluid-pressure input . It introduces two controllers—sliding-mode based CHOSMA variants producing local finite-time convergence and an extended LQR with integral action yielding global exponential stability—both delivering continuous control signals to mitigate chattering. Through numerical simulations and laboratory experiments on a spring-slider fault apparatus, the authors demonstrate successful tracking of a slow reference and aseismic slip, with performance trade-offs: sliding-mode excels in displacement accuracy while e-LQR offers smoother velocity profiles. The work also outlines gain-scaling laws to upscale laboratory results to real faults, highlighting potential applications for safer energy production and earthquake mitigation, and identifies avenues for incorporating more detailed multi-physics fault models in future work.

Abstract

This paper addresses the possibility of using robust control theory for preventing earthquakes through fluid injections in the earth's crust. The designed robust controllers drive aseismically a fault system to a new equilibrium point of lower energy by tracking a slow reference signal. The control design is based on a reduced-order nonlinear model able to reproduce earthquake-like instabilities. Uncertainties related to the frictional and mechanical properties of the underlying physical process and external perturbations are considered. Two types of controllers are derived. The first one is based on sliding-mode theory and leads to local finite-time convergence of the tracking error and rejection of Lipschitz w.r.t. time perturbations. The second controller is based on LQR control and presents global exponential stability of the tracking error and rejection of Lipschitz w.r.t. states perturbations. Both controllers generate a continuous control signal, attenuating the chattering effect in the case of the sliding-mode algorithms. The developed controllers are tested extensively and compared on the basis of numerical simulations and experiments in the laboratory. The present work opens new perspectives for the application of robust nonlinear control theory to complex geosystems, earthquakes and sustainable energy production.
Paper Structure (16 sections, 4 theorems, 60 equations, 12 figures, 1 table)

This paper contains 16 sections, 4 theorems, 60 equations, 12 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Statement
  4. Reduced Model for Earthquakes
  5. Shifted System and Instability Condition
  6. Experimental setup
  7. Control Objective
  8. Control Design
  9. Sliding Mode based Control
  10. LQR-based Control
  11. Control Strategies Comparison
  12. Numerical Simulations and Experimental Confirmation
  13. Numerical Simulations
  14. Experimental Confirmation
  15. Conclusions
  16. ...and 1 more sections

Key Result

Lemma 1

Let $\eta: \mathbb{R}^n \rightarrow \mathbb{R}$ and $\gamma: \mathbb{R}^n \rightarrow \mathbb{R}$ be two $r$-homogeneous and upper semi-continuous single-valued functions, with the same weights $r = (r_1, ..., r_n)$ and homogeneity degree $m>0$. Suppose that $\gamma(x) \leq 0$ in $\mathbb{R}^n$. If then there exists a real number $\lambda^*$ and a constant $c > 0$ so that, for all $\lambda \geq

Figures (12)

  • Figure 1: Reduced mechanical model for reproducing earthquake-like instabilities.
  • Figure 2: Experimental apparatus for reproducing and controlling earthquake-like instabilities: (a)Schematic figure, (b)Real configuration
  • Figure 3: Slip and slip-rate in terms of time for two different scenarios. Blue curve: Natural earthquake. Red Dashed Curve: Induced earthquake.
  • Figure 4: Slip-weakening friction law used in the simulations.
  • Figure 5: Earthquake phenomenon in the real-fault simulation.
  • ...and 7 more figures

Theorems & Definitions (13)

  • Definition 1
  • Definition 2
  • Lemma 1
  • Lemma 2
  • Remark 1
  • Remark 2
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • ...and 3 more