Chattering-Free Single-Phase Robustness Sliding Mode Controller for Mismatched Uncertain Interconnected Systems with Unknown Time-Varying Delays

Abstract

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.

Adaptive terminal sliding mode controller design for cyber‐physical systems under external disturbance and actuator cyber‐attack

“…The global SMC method is presented to recommend a general structure to remove the reaching phase so that the sliding mode exists exactly from all initial conditions. 42 As a promising procedure, the integral-type SMC method usually consists of a continuous nominal section with goal of the sliding mode dynamics (SMD) stabilization and a discontinuous compensating section which is used to insure the sliding motion. The attractive property of integral-type SMC is the obliteration of reaching phase required in conventional SMC methods and keeping of the system original order.…”

“…Therefore, a suitable design approach is needed so that the SMC reaching phase is eliminated. The global SMC method is presented to recommend a general structure to remove the reaching phase so that the sliding mode exists exactly from all initial conditions 42 . As a promising procedure, the integral‐type SMC method usually consists of a continuous nominal section with goal of the sliding mode dynamics (SMD) stabilization and a discontinuous compensating section which is used to insure the sliding motion.…”

Adaptive non‐singular second‐order terminal sliding mode control for cyber‐physical systems subject to actuator cyber‐attacks and unwanted disturbances

“…Therefore, a suitable design approach is needed so that the SMC reaching phase is eliminated and the sliding phase to be existed exactly from all initial conditions. 43,44 Besides this in the conventional SMC with linear sliding surface, the convergence to origin is slow and in the form of asymptotically stable. 45 Also, the chattering phenomenon in the sliding mode control leads to high fluctuations in the system control input, which in turn causes oscillations in the physical system performance, heat and even instability.…”

“…Indeed, the system robustness behavior is gratified only when the system state trajectories reach the sliding surface. Therefore, a suitable design approach is needed so that the SMC reaching phase is eliminated and the sliding phase to be existed exactly from all initial conditions 43,44 . Besides this in the conventional SMC with linear sliding surface, the convergence to origin is slow and in the form of asymptotically stable 45 .…”

Analysis of Harmonic Resonance for Locomotive and Traction Network Interacted System Considering the Frequency-Domain Passivity Properties of the Digitally Controlled Converter

“…More importantly, the time delay and the zero-order-holder (ZOH) effect of the digital pulse width modulation (DPWM) should be taken into consideration for the modeling of the integrated model. Furthermore, the time delay is a common phenomenon in digital control systems (Nguyen et al, 2020). The dynamic performance of the digital controllers of the power electronics plays an important role in the harmonic resonance for the electronic device penetrated source-load system (Harnefors et al, 2008).…”