Variable structure control with sliding mode can provide good control performance and excellent robustness. Unfortunately, the chattering phenomenon investigated due to discontinuous switching gain restricting their applications. In this paper, a chattering free improved variable structure control (IVSC) for a class of mismatched uncertain interconnected systems with an unknown time-varying delay is proposed. A sliding function is first established to eliminate the reaching phase in traditional variable structure control (TVSC). Next, a new reduced-order sliding mode estimator (ROSME) without time-varying delay is constructed to estimate all unmeasurable state variables of plants. Then, based on the Moore-Penrose inverse approach, a decentralized single-phase robustness sliding mode controller (DSPRSMC) is synthesized, which is independent of time delays. A DSPRSMC solves a complex interconnection problem with an unknown time-varying delay term and drives the system’s trajectories onto a switching surface from the initial time instance. Particularly, by applying the well-known Barbalat’s lemma, the chattering phenomenon in control input is alleviated. Moreover, a sufficient condition is established by using an appropriate Lyapunov theory and linear matrix inequality (LMI) method such that a sliding mode dynamics is asymptotically stable from the beginning time. Finally, a developed method is validated by numerical example with computer simulations.

In this paper, a novel variable structure control (VSC) approach is investigated for a class of mismatched uncertain systems. The VSC approach, which includes output variables only, shows finite-time convergence of the sliding mode, complete invariance to the matched uncertainties, the asymptotic stability property, and is free of the chattering phenomenon. A suitable reduced-order observer (ROO) is constructed to estimate the unmeasured variables. Additionally, a novel finite-time sliding-mode controller (FTSMC), based on the constructed ROO and the output variables, is proposed to stabilize a class of mismatched uncertain systems. To ensure finite-time stability and chattering removal, a discontinuous FTSMC is replaced by a continuous FTSMC utilizing a tanh function. Moreover, a new linear matrix inequality (LMI) condition is derived so that the system in the sliding mode is not only completely invariant to matched uncertainties but also asymptotically stable. Finally, a numerical example is presented, which demonstrates the effectiveness and advantages of this method.

In this paper, an attenuated-chattering adaptive second order variable structure controller (ACASOVSC) is proposed for mismatched uncertain systems using a Moore-Penrose inverse method. The key achievements of this study include three tasks: 1) influence of the chattering in control input is diminished, 2) finite-time convergence of system states is guaranteed, and 3) external disturbance is generally assumed to be unknown in advance. Firstly, a switching manifold which comprises only output information is defined. Secondly, a reduced-order variable structure estimator (ROVSE) with lower dimension is designed to reduce the computation burden and enhance the robustness. Thirdly, an adaptive approach is used to guess the upper bound of the unknown exogenous disturbance. Next, an ACASOVSC is investigated for attenuating the chattering phenomenon and stabilizing the system. Then, a novel linear matrix inequality (LMI) constraint by the Lyapunov technique is given such that the plant is entirely invariant to matched uncertainties and asymptotically stable. Finally, a mathematical illustration is simulated, which exhibits the usefulness and the feasible application of the proposed method.

In multi-area interconnected power systems (MAIPS), all the plant state’s measurement is stiff due to the lack of a device or the cost of the sensor is expensive. To solve this restriction, a novel sliding mode control technique- based load frequency controller (LFC) is investigated for MAIPS where the estimation states of the system is utilized fully in the switching surface and controller. Initially, a single-phase switching function is suggested to dismiss the reaching phase in traditional sliding mode control (TSMC) approach. Secondly, the MAIPS’s unmeasurable variables is estimated by using the suggested observer tool. Next, a new single phase robustness load frequency sliding mode controller (SPRLFSMC) for the MAIPS is established based on the support of the observer instrument and output data only. The entire plant’s stability is ensured through the Lyapunov theory. Even though the plant’s variables are not measured, the obtained results in the simulation display that the frequency remains in the nominal domain under load instabilities on the MAIPS. The simulation results for a three-area interconnected electricity plant verify the preeminence of the anticipated SPRLFSMC over other current controllers with respect to settling time and overshoot.

This research studies the shipboard microgrid (MG) scheme's frequency fluctuations problem contrary to the impulsiveness of renewable resources, load instabilities, and the uncertainty of the parameters in the ship MG plant. A shipboard MG system consists of some of the renewable energy resource s (RESs) such as photovoltaic (PV), wind turbine generator (WTG), battery energy storage system (BESS), ship diesel generator (DG), fuel cell (FC), aqua electrolyzer (AE), and loads. A new fuzzy proportional integral derivative (FPID) controller is established to attain the desired frequency stability for the shipboard MG system. Additionally, various scenarios are executed in this research to validate the robustness of the anticipated controller to various load disturbances, parameter changes of plant, and fluctuations of solar irradiance and wind speed. The numerical simulation results obtained in three scenarios compared with those of the conventional PID controller and the existing time-varying derivative fractional order PID (TVD-FOPID) controller in literatures to validate the high usefulness and applicability of the planned control strategy. In brief, the established load frequency controller (LFC) based on FPID technique can improve frequency deviation in shipboard MG plant effectively.

Novel results on complex interconnected time-delay systems with single phase second order sliding mode control is investigated. First, a reaching phase in traditional sliding mode control (TSMC) is removed by using a novel single phase switching manifold function. Next, a novel reduced order sliding mode observer (ROSMO) with lower dimension is suggested to estimate the unmeasurable variables of the plant. Then, a new single phase second order sliding mode controller (SPSOSMC) is established based on ROSMO tool to drive the state variables into the specified switching manifold from beginning of the motion and reduce the chattering in control input. Then, a stability condition is suggested based on the well-known linear matrix inequality (LMI) method to ensure the asymptotical stability of the whole plant. Finally, an illustrated example is simulated to validate the feasible application of the suggested technique.