State Feedback Fault Tolerant Control for Flexible Bevel-Tip Needle Based on Proportional Multiple-Integral Observer

Abstract

A state feedback fault tolerant (SFFT) controller based on the proportional multiple-integral (PMI) observer is designed to guide the flexible bevel-tip needle (FBTN) into a desired plane safely under actuator faults. Firstly, the nonlinear model of the FBTN system is linearized by using the Jacobian method at the equilibrium point. Then, the PMI observer is designed based on the robust <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{H}_{\infty}$</tex> method, which can estimate unmeasurable states and faults simultaneously. Finally, the SFFT controller is proposed to guarantee the safety and accuracy of the FBTN control based on the state and fault estimations. The convergence and asymptotically stability of the proposed closed-loop system is proved through Lyapunov theory. simulations are obtained to demonstrate effectiveness of the proposed controller in the face of measurement noise and actuator faults.