A continuous nonsingular fast terminal sliding mode (CNFTSM) control strategy with an automated double power reaching law is proposed to improve the performance of speed dynamic response and accuracy tracking for the permanent magnet synchronous motor (PMSM) servo system. In pursuit of robustness against system uncertainties, a finite-time convergent extended state observer (ESO) is designed to estimate external disturbances, parameter variation, and unmodeled dynamics as a feedforward compensation to the output feedback control system. The developed controller, based on Lyapunov stability theory analysis, can guarantee finite time stability from any initial state in the presence of internal and external disturbances. The modified sliding mode reaching law can achieve enough convergence rate compared with the exponential reaching law, and the inherent chattering of sliding mode is reduced when system states approach the equilibrium point. Theoretical analysis and simulation results demonstrate that the proposed composite controller can achieve higher performance than the conventional sliding mode method.

In this article, the intrinsic propagation mechanisms and dispersion properties of the dominant modes supported by different 2-D graphene-based transmission lines (GTLs) at terahertz (THz) are studied in detail. By employing a complete elliptic integral of the first kind, analytical expressions for the wavenumber of plasmons in different GTLs are obtained from the strongly coupled TM mode surface plasmons that propagate on each individual graphene stripline. Besides, per unit length equivalent circuits of different graphene coplanar transmission lines (GCTLs) are introduced. Again, analytical relations between their effective TM mode equivalent circuit lumped elements and graphene surface conductivity are investigated. Moreover, the effects of different GCTLs versus different parameters of the GCTL models for the wavenumber and circuit lumped elements are analyzed. The proposed analytical expressions could reveal the important mechanisms involved in spatially dispersive plasmon propagation connecting with the intrinsic properties of graphene. The features of GCTLs are detailed, showing their great potential for THz applications in future graphene-based nanoelectromagnetic and nanophotonic devices.