Integral Sliding Mode Controller Design Research Articles

Integral sliding mode control design for uncertain impulsive systems with delayed impulses

This paper addresses the integral sliding mode control (ISMC) problem of uncertain impulsive systems with delayed impulses. Firstly, an integral sliding surface with embedded impulse information is constructed, which is able to counteract the intermittent impact of delayed impulses. Then an ISMC law is designed to guarantee the finite-time reachability of the predefined sliding surface without special restriction on system dynamics. Secondly, two different types of linear control laws with switching gains are proposed to robustly stabilize the sliding mode dynamics. The first type is independent of the size of impulse delays, and is used to tackle the impulses with unknown bounded delays. The second type aims at providing impulse-delay-dependent stabilization algorithms under the assumption that the delays are smaller than the impulse intervals. In the situation where the upper bounds of the uncertainties are characterized by two unknown constants, an adaptive ISMC law is proposed to ensure the existence of sliding mode. Switching Lyapunov functions and the state augmentation technique are introduced to exploit the positive/negative effects of delayed impulses. Several tractable conditions for designing the switching gains and the sliding surfaces are derived in terms of linear matrix inequalities. Finally, three numerical examples are presented to show the effectiveness of the proposed control algorithms and highlight their merits.

Decentralized observer‐based integral sliding mode control design of large‐scale interconnected systems and its application to doubly fed induction generator‐based wind farm model

SummaryThis paper presents the design of a decentralized observer‐based control scheme for large‐scale interconnected systems based on the integral sliding mode control (ISMC) approach. To do this, a novel decentralized observer is designed via the ISMC approach that helps to estimate the unmeasured states. Then, by constructing a suitable Lyapunov function, sufficient conditions are derived in terms of matrix inequality, which guarantees the asymptotic stability of the interconnected system and the ultimate boundedness of estimation errors under external disturbances. An interconnected power system (IPS) integrated with a doubly fed induction generator (DFIG)‐based wind farm model is provided as a direct application. Theoretical conditions are validated through numerical simulations, in this regard, a well‐structured model of IPS with a DFIG‐based wind farm is introduced. From the simulation results, it is proven that the proposed decentralized observer‐based ISMC can provide a better estimation of the internal states in two area IPS with DFIG‐based wind farm.

Disturbance observer-based fuzzy event-triggered ISMC design: Tracking performance

This article presents a disturbance observer (DO)-based event-triggered integral sliding mode tracking control (ISMTC) for continuous-time Takagi–Sugeno (T–S) fuzzy model (TSFM) subject to external disturbances. Merging the event-triggered control (ETC) with integral sliding mode control (ISMC) approach is led to reach the better accommodate the features of ISMC. To do this, two forms of fuzzy integral sliding surfaces (FISSs) are proposed. The first is the periodic-time-based FISS that is presented to provide the robustness of the tracking performance from the initial moment. The second is the event-triggered-based FISS which is proposed to obtain the fuzzy event-triggered ISMTC law. To more decrease the chattering effects and compensate the tracking performance against the disturbances, a fuzzy disturbance observer (FDO) is proposed to estimate the mismatched disturbances. Compared with the existing works, a more practical controller is proposed based on the asynchronous premise variables. Utilizing the common quadratic Lyapunov function, appropriate conditions are derived to verify that the tracking error is robust from the initial moment. Furthermore, by adopting a decaying triggering threshold, it is guaranteed that the system is Zeno-free during the process. To verify the effectiveness of the suggested event-triggered ISMTC, a practical system including continuous stirred tank reactor (CSTR) is simulated and the results are compared.

Optimal constrained integral sliding mode control design for fuzzy-based nonlinear systems

This study introduces a novel H∞ optimal constrained integral sliding mode control (OCISMC) for nonlinear systems due to the matched/unmatched external disturbances based on Takagi–Sugeno (TS) fuzzy models. Based on the Lyapunov function, the appropriate conditions are provided to reach the sliding mode from any initial condition and robustness against the matched disturbances is guaranteed. The optimal nominal part of the proposed OCISMC is designed based on an online optimization problem. To reach robustness against the unmatched disturbances and constrained controller, the H∞ performance and the limitations of the control signal are included in the design procedure of the suggested OCISMC. Furthermore, by considering a non-quadratic Lyapunov function (NQLF), a new linear matrix inequality problem with less conservatism is derived. Finally, two examples are simulated and compared with the existing works to illustrate the capability of the proposed OCISMC.

Design of Robust Control for Vehicle Steer-by-Wire System

This study presented the design of a robust controller based on Integral Sliding Mode Control (ISMC) for controlling the Vehicle Steer-by-Wire (VSbW) system. The dynamic model of the VSbW system is first developed and then the design of ISMC has been conducted via the states of the system. The VSbW system has been described by two terms; one term represents the nominal model, which is free from nonlinearities, and the other term lumps the uncertainties in system parameters. The integral sliding mode controller has been designed for controlling the VSbW system. The control design consists of two parts. The first control part has addressed the nominal term of the system, while the second control part tackles and eliminates the effects of uncertainties and perturbation due to the uncertain term of the system. The numerical simulation has been conducted to show the robustness of ISMC and its capability to reduce the chattering effect in the control signal. In addition, a comparison study in performance has been conducted between the proposed controller and other controllers in the literature. We also carry out bibliometric analysis to see research trends. Based on our analysis, the number of publications regarding the keywords "controller", "steer", and "wire system" changes every year (25 (2018), 56 (2019), 51 (2020), 71 (2021), and 61 (2022)).

Design of Super Twisting Integral Sliding Mode Control for Industrial Robot Manipulator

In the present work, integral sliding mode based continuous control algorithm is extended to multi input multi output system. The typical integral sliding mode control (ISMC) contains nominal control with discontinuous feedback control due to which overall control becomes discontinuous in nature. The proposed controller is a fusion of two continuous terms and one of which is able to handle, estimate and reject the disturbance successfully. A proposed robust ISMC technique is applied for industrial robot manipulators which utilizes interactive manipulation activity. Here, robust position tracking control obtained via ISMC principle for two link IRM scheme influenced by parametric uncertainties and external disturbances. The proposed ISMC design replaces the discontinuous part by continuous control, which super twisting control is able to handle the disturbance rejection completely. The effectiveness of the proposed control technique is tested under uncertain conditions and comparison study with other controllers has been done. The simulation result shows that the tracking error is effectively minimized by the proposed technique in presence of uncertain conditions.

Fixed-time integral sliding mode control design for a class of uncertain nonlinear systems based on a novel fixed-time stability condition

This paper develops a different approach to fixed-time controller design by introducing a totally novel fixed-time stability condition formulated according to the Lyapunov function technique. Based on this condition, a fixed-time sliding mode control law is derived for a class of uncertain nonlinear systems. This controller assures complete robustness of the closed-loop system against matched uncertainties and exogenous disturbances from the beginning owing to the elimination of the reaching phase by benefiting from a novel integral terminal sliding surface. This surface constructed in accordance with the proposed condition determines whole dynamics of the closed-loop system and guarantees its fixed-time stability. Numerical simulations are reported to validate the effectiveness of the theoretical results.

PSO-Based Integral Sliding Mode Controller for Optimal Swing-Up and Stabilization of the Cart-Inverted Pendulum System

An integral sliding mode controller (ISMC) which employs particle swarm optimization (PSO) algorithm to search for optimal values of the parameters of the integral sliding manifold as well as the gains of the controller is proposed in this work. We considered the swing-up and stabilization of the cart-inverted pendulum system which is assumed to be affected by uncertainties. First, we determined the swing-up and stabilization conditions of the control system by using the internal dynamics of the cart-inverted pendulum system and sliding mode dynamics. A PSO algorithm is then used to search for the optimal values of the ISMC design parameters that satisfy the stabilization condition with the aim of improving the transient performance of the control system. To mitigate the chattering phenomenon, a saturation function of the integral sliding variable was used in the discontinuous control law. Simulation results on swing-up and stabilization of the cart-inverted pendulum system revealed improvement in transient behaviour by reducing settling time (by 52.61%), overshoots (by 45.56%) and required track length for cart movement (by 68.34%).

A descriptor regular form‐based approach to observer‐based integral sliding mode controller design

AbstractThis article establishes a descriptor regular form and shows its applications in observer‐based integral sliding mode controllers design of descriptor systems. A reduced‐order linear observer and a full‐order descriptor sliding mode observer are, respectively, designed to estimate the state variables of the descriptor system under consideration. Necessary and sufficient conditions for the existence of the proposed descriptor regular form and observers are derived. With the descriptor regular form, it is revealed that the separation principle holds for the proposed observer‐based integral sliding mode control methods. This means that the proposed observers can be designed independently and when using the estimation of state variables obtained from them to replace the state variables in a stabilizing state‐feedback integral sliding mode controller, the resulting observer‐based integral sliding mode controller can still stabilize the descriptor system. Finally, a constrained mechanical system is numerically simulated to verify the methods proposed.

Neuro-adaptive backstepping integral sliding mode control design for nonlinear wind energy conversion system

The electrical power extracted from a wind energy conversion system (WECS) tends to be inconsistentdue to the intermittent nature of the wind. This issue is addressed by formulating a maximum power point tracking(MPPT) control strategy that optimizes the power extraction from the WECS under a wide range of wind speed profiles.This research article focuses on the formulation of a nonlinear neuro-adaptive backstepping integral sliding mode control(NABISMC) based MPPT strategy for a standalone, variable speed, fixed-pitch WECS equipped with a permanentmagnet synchronous generator (PMSG). The proposed paradigm is a hybrid of the conventional backstepping andthe integral sliding mode control (ISMC) based MPPT schemes. The effectiveness of the control strategy devised isguaranteed through numerical simulations carried out in Matlab/Simulink for a 3kW PMSG-WECS under a stochasticwind speed profile. Further validation is guaranteed by giving a detailed performance comparison analysis of the proposedMPPT control strategy with the conventional feedback linearization control (FBLC), proportional integral derivative(PID) control, sliding mode control (SMC), and standard neuro-adaptive integral sliding mode control (NAISMC) basedMPPT strategies, where the proposed strategy is found superior to all the stated strategies in terms of offering moreaccurate MPPT, lower steady state error, faster dynamic response and lesser chattering.

Adaptive Integral Second-Order Sliding Mode Control Design for Load Frequency Control of Large-Scale Power System with Communication Delays

Nowadays, the power systems are getting more and more complicated because of the delays introduced by the communication networks. The existence of the delays usually leads to the degradation and/or instability of power system performance. On account of this point, the traditional load frequency control (LFC) approach for power system sketches a destabilizing impact and an unacceptable system performance. Therefore, this paper proposes a new LFC based on adaptive integral second-order sliding mode control (AISOSMC) approach for the large-scale power system with communication delays (LSPSwCD). First, a new linear matrix inequality is derived to ensure the stability of whole power systems using Lyapunov stability theory. Second, an AISOSMC law is designed to ensure the finite time reachability of the system states. To the best of our knowledge, this is the first time the AISOSMC is designed for LFC of the LSPSwCD. In addition, the report of testing results presents that the suggested LFC based on AISOSMC can not only decrease effectively the frequency variation but also make successfully less in mount of power oscillation/fluctuation in tie-line exchange.

Integral Sliding Mode Controller Design for the Global Chaos Synchronization of a New Finance Chaotic System with Three Balance Points and Multi-Stability

This paper conveys new results of a new finance chaotic system with three unstable balance points of which one balance point is a hyperbolic saddle while the other balance points are saddle-foci. The new finance chaotic system involves three nonlinearities of which one is quadratic, the other is quartic and the third is absolute function nonlinearity. As an application of the new finance chaotic system, integral sliding mode control is invoked to achieve synchronization of master-slave finance chaotic systems. MATLAB simulations are carried out to explain the main results of this research report.

Dimensional-varying integral sliding mode controller design for uncertain Takagi–Sugeno fuzzy systems

An integral sliding mode control method for uncertain Takagi–Sugeno fuzzy systems is investigated in this paper. Considering the time-varying property of the fuzzy system control matrix, a dimensional-varying integral sliding mode controller is proposed. With a membership function piecewise linearization technique, the gain matrices of equivalent control law are derived. Then a dimension switching sliding model control scheme is designed to close the control loop. As a result, traditional restrictions on input matrix can be further relaxed. Finally, a numerical and a Diesel Engine Air-Path control examples are provided to certificate the merits and effectiveness of the proposed approach.

Integral Sliding Mode Control Based on Barrier Function for Servo Actuator with Friction

This paper proposes the use of the integral sliding mode control (ISMC) based on the barrier function to control the servo actuator system with friction. Based on the barrier function, the main features of the ISMC design were preserved, additionally, the proposed control design is done without the need to know the bound on the system model uncertainty, accordingly, the overestimation of the control gain doesn’t take place and the chattering is eliminated. Moreover, the steady-state error can be adjusted via selecting the barrier function parameter only. The simulation results demonstrate the performance of the proposed ISMC based on the barrier function where the system angle successfully follows the desired angular position with a small pre-adjusted steady-state error. Additionally, the obtained results clarify superior features compared with a traditional ISMC designed to the same actuator.

Integral Sliding Mode Control Design for a Quarter-Car Active Suspension System

This paper utilizes the design of a robust integral sliding mode control (ISMC) for a quarter-car active suspension system. The main goal is to increase the ride comfort, whilst the road holding and rattle space remain within the safety bound. According to ISMC, the system state starts at the switch surface where the system nonlinearity, parameter changes, and road disturbances are rejected by a discontinuous control term present strongly in the suspension dynamics. This feature allows the design of a continuous controller, i.e. ideal controller during sliding motion from the first instant. Consequently, the car body is isolated from the wheel unit to perform the desired suspension requirements characteristics. The ISMC shows a high robustness control design of the suspension system, and can suppress chattering in the high-frequency band. The effectiveness of the proposed controller is performed by simulating the 2- DOF quarter car system with controlled and uncontrolled cases. The Matlab 2019a software is used to simulate the suspension models with bump road profiles as excitation disturbance.

Robust integral sliding mode controller design of a bidirectional DC charger in PV-EV charging station

Robust integral sliding mode controller design of a bidirectional DC charger in PV-EV charging station

Robust integral sliding mode controller design of a bidirectional DC charger in PV-EV charging station

The charging infrastructure is developed and extended simultaneously with the considerable growing of electric vehicle fleet. In this paper, the problem of controlling an energy storage unit used in the photovoltaic charging station for electric vehicles is considered. The purpose is to design a robust control of a bidirectional DC-DC converter in order to ensure a perfect tracking of the battery current to its reference, and an asymptotic stability of the closed-loop system. For this reason, a robust integral sliding mode control is designed to regulate the current considering the output voltage of DC bus is regulated. The vehicle to grid concept is guaranteed using the bidirectional converter that interface between the energy storage unit and the EV battery. The formal analysis and simulation results are shown that the designed integral sliding mode controller was found to be robust and stable without steady-state errors, which matches all the objectives.

Control Strategy for a Quadrotor Based on a Memetic Shuffled Frog Leaping Algorithm

This work presents a memetic Shuffled Frog Leaping Algorithm (SFLA) based tuning approach of an Integral Sliding Mode Controller (ISMC) for a quadrotor type of Unmanned Aerial Vehicles (UAV). Based on the Newton–Euler formalism, a nonlinear dynamic model of the studied quadrotor is firstly established for control design purposes. Since the main parameters of the ISMC design are the gains of the sliding surfaces and signum functions of the switching control law, which are usually selected by repetitive and time-consuming trials-errors based procedures, a constrained optimization problem is formulated for the systematically tuning of these unknown variables. Under time-domain operating constraints, such an optimization-based tuning problem is effectively solved using the proposed SFLA metaheuristic with an empirical comparison to other evolutionary computation- and swarm intelligence-based algorithms such as the Crow Search Algorithm (CSA), Fractional Particle Swarm Optimization Memetic Algorithm (FPSOMA), Ant Bee Colony (ABC) and Harmony Search Algorithm (HSA). Numerical experiments are carried out for various sets of algorithms’ parameters to achieve optimal gains of the sliding mode controllers for the altitude and attitude dynamics stabilization. Comparative studies revealed that the SFLA is a competitive and easily implemented algorithm with high performance in terms of robustness and non-premature convergence. Demonstrative results verified that the proposed metaheuristics-based approach is a promising alternative for the systematic tuning of the effective design parameters in the integral sliding mode control framework.

Robust $\mathcal {H}_{\infty }$-Based Control for Uncertain Stochastic Fuzzy Switched Time-Delay Systems via Integral Sliding Mode Strategy

In this article, we investigate the problems of robust exponential stabilization in mean square and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> -based integral sliding mode controller design for uncertain stochastic Takagi–Sugeno (T-S) fuzzy switched time-delay systems with both matched and unmatched uncertainties under synchronous switching and asynchronous switching, respectively. In these systems, the control input is dependent on a switching signal. Under synchronous switching and asynchronous switching, sufficient conditions are developed to guarantee that the resulting closed-loop systems are robustly exponentially stable in mean square with a prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> -performance, respectively. The integral sliding mode surfaces and the sliding mode controllers are designed for the underlying systems under synchronous switching and asynchronous switching, respectively. By two examples stemming from the mass–spring–damper model and the single-link robot arm model under stochastic perturbation, the effectiveness of the results obtained is verified.

Characterization and Designing Integral Sliding Mode Controller for 2-Link Robot System with Coulomb Friction

The indemnification of uncertainty and disturbance which is added to non-linear systems by an Integral Sliding Mode Controller (ISMC) design. the key target of this paper is designing a sturdy controller to observe the performance of a 2-link robot. The nonlinearity in mechanical systems is a shared issue that the researchers are facing in formulating control systems for it. The best solution to this problem is a design Sliding Mode Controller (SMC) for controlling a nonlinear system. In the current paper, 2-link robot is studied which suffering from disturbances and parameter uncertainty and coulomb friction as additional to friction inertia of the system for each link. firstly, Classical Sliding Mode Controller (CSMC) is designed and then Integral Sliding Mode Controller (ISMC). As known, CSMC includes two phases: reaching phase and sliding phase. SMC is suffering from the known phenomenon as "chattering" which is supposed as a critical case and unsuitable characteristic. chattering is described as a curvy movement span the switching surface. In the current study, the chattering is attenuated by employing a saturation function alternative of a sign function. Although SMC can be considered as a good way of controlling nonlinear systems. Where it continues to suffer from the long settling time as undesired features. ISMC is a good method can be employed for reducing the settling time and controlling a nonlinear system. ISMC is easy, robust execution and supposes as an active and strong technique. The most significant advantage in ISMC designing, the reaching phase is canceled that considered a major part of designing classical SMC. The 2 link Robot system was used for proving the performance of CSMC and ISMC algorithms. The outcomes received from the simulations utilizing the ISMC and CSMC which fulfilled asymptotic stability for the system. In comparative between CSMC and ISMC. ISMC is better than CSMC in the good performance of tracking the desired position with less time. Finally, MATLAB2019a software package has relied upon this work.