Accurate and fast estimation of single phase grid voltage phase and frequency has the potential to improve the performances of various control and monitoring techniques used in electric power system. This letter applies an adaptive sliding mode observer for frequency and phase estimation. The observer is simple, easy to tune and suitable for real-time implementation. The proposed adaptive observer can be considered as an alternative to phase-locked loop (PLL) with better performance. dSPACE based experimental results are given to show the effectiveness and performance improvement of the proposed approach with respect to two other advanced PLL techniques namely pseudo linear - enhanced PLL (PL-EPLL) and Second order generalized integrator- frequency locked loop (SOGI-FLL).

The properties of robustness and finite‐time convergence provided by sliding mode (SM) theory have motivated several researches to deal with the problems of control and state estimation. In the SM theory, the super‐twisting algorithm (STA), a second‐order SM scheme, has demonstrated remarkable characteristics when it is implemented as a controller, observer or robust signal differentiator although the presence of noise and parametric uncertainties. However, the design of this algorithm was originally developed for continuous‐time systems. The growth of microcomputers technology has attracted the attention of researchers inside the SM discrete‐time domain. Recently, discretisations schemes for the STA were studied using majorant curves. In this study, the stability analysis in terms of Lyapunov theory is proposed to study a discrete‐time super twisting‐like algorithm (DSTA) for non‐linear discrete‐time systems. The objective is to preserve the STA characteristics of robustness in a quasi‐sliding mode regime that was proved in terms of practical Lyapunov stability. An adequate combination of gains obtained by the same Lyapunov analysis forces the convergence for the DSTA. The problem of state estimation is also analysed for second‐order mechanical systems of n degrees of freedom. Simulation results regarding the design of a second‐order observer using the DSTA for a simple pendulum and a biped model of seven degrees of freedom are presented.

This study presents the development of a hybrid active disturbance rejection control (H-ADRC) implementing a homogeneous extended state observer (ESO) to solve the trajectory tracking problem of an inchworm bioinspired flexible robotic device (IBFRD) with partially unknown dynamics. The proposed controller is implemented on a self-designed IBFRD instrumented with shape memory alloys (SMAs) operating as actuators in each joint of the robotic mobile device. The set of SMAs constitutes an agonist–antagonist mechanism together with regular springs that counteract the SMA displacement. The characteristic two-anchor crawling of an inchworm is modeled as a hybrid system and exerted by a bistable pneumatic circuit that switches suction cups at the terminal links of the IBFRD to exert the inchworm walking. The corresponding reference trajectories emulate an inchworm in a regular gait cycle. Experimental results compare the H-ADRC with a proportional derivative and a proportional–integral–derivative (PID) controller. The obtained results show that the proposed H-ADRC enforces a reduced tracking error than the other controllers used for validation.