Robust fractional‐order fast terminal sliding mode control with fixed‐time reaching law for high‐performance nanopositioning

Abstract

For high-performance trajectory tracking at the nanometer scales, this paper presents a new fast terminal sliding mode controller, which combines a recursive integer-order non-singular high-order sliding manifold and a fractional-order fast fixed-time reaching law to ensure globally fast convergence, and adopts a time-delay-estimation (TDE) based disturbance estimator deeming the designed controller robust to parameter uncertainty. Stability of the designed controller is verified through the Lyapunov framework, where the full analyses of convergence region and settling time are also presented. The tracking performance is experimentally verified on a piezo-stack driven nano-positioning platform. To showcase the performance improvements, measured closed-loop performance of the proposed controller is contrasted with those obtained using three benchmark control approaches namely the basic Proportional-Integral-Derivative (PID), the popular Positive Position Feedback with Integral action (PPF+I), and the traditional linear sliding mode controller (LSMC).

Fixed-time synchronization of fractional-order chameleon hyperchaotic systems based on hyperbolic sliding mode

“…Later, there has been increasing researches on chaotic synchronization, and many methods have emerged, such as fuzzy [6], sliding mode [7] [8], adaptive [9] and projection methods [10].In fact, chaotic systems often contain parameter uncertainties and external disturbances, and researchers have become very interested in how to get the state trajectories of two chaotic systems to synchronize in finite or fixed time [11]. The terminal sliding mode control is not only simple to operate, but also has finite-time convergence and robustness to external disturbances, and is widely used to study finite and fixed time synchronization [12][13][14][15]. In [16], researchers use the fractional order sliding mode control in which hyperbolic tangent and inverse sinusoidal hyperbolic functions are incorporated into the proposed controller, and numerical simulations achieved convergence to zero in finite time for three different sets of fractional order state error systems.…”