Sliding Mode Algorithm Research Articles

Fixed-Time Distributed Time-Varying Optimization for Nonlinear Fractional-Order Multiagent Systems with Unbalanced Digraphs

This paper investigates the problem of fixed-time distributed time-varying optimization of a nonlinear fractional-order multiagent system (FOMAS) over a weight-unbalanced directed graph (digraph), where the heterogeneous unknown nonlinear functions and disturbances are involved. The aim is to cooperatively minimize a convex time-varying global cost function produced by a sum of time-varying local cost functions within a fixed time, where each time-varying local cost function does not have to be convex. Using a three-step design procedure, a fully distributed fixed-time optimization algorithm is constructed to achieve the objective. The first step is to design a fully distributed fixed-time estimator to estimate some centralized optimization terms within a fixed time T0. The second step is to develop a novel discontinuous fixed-time sliding mode algorithm with nominal controller to derive all the agents to the sliding-mode surface within a fixed time T1, and meanwhile the dynamics of each agent is described by a single-integrator MAS with nominal controller. In the third step, a novel estimator-based fully distributed fixed-time nominal controller for the single-integrator MAS is presented to guarantee all agents reach consensus within a fixed time T2, and afterwards minimize the convex time-varying global cost function within a fixed time T3. The upper bound of each fixed time Tm(m=0,1,2,3) is given explicitly, which is independent of the initial states. Finally, a numerical example is provided to validate the results.

Sliding-mode control of electro-hydraulic positioning tracking system combining K-observer and nonlinear disturbance observer

High-precision position control of hydraulic systems is of great significance in industrial applications. However, unknown external force disturbance, measurement noise, and other uncertain nonlinearities widely exist in electro-hydraulic servo systems, which severely degrade the system performance. To handle this problem, a sliding-mode controller based on K-observer with nonlinear disturbance observer is proposed for electro-hydraulic position systems in this article. The nonlinear disturbance observer is to estimate and eliminate the time-varying external force disturbance. The sliding-mode controller based on K-observer is to reach low gain observation of states and improve the system performance by reducing the chattering of the sliding-mode algorithm. The proposed controller is proved to be stable by the Lyapunov stability criterion. Comparative experiments support that the controller has high precision and strong robustness.

Sensorless Control Method for SPMSMs Based on Improved Sliding Mode Reaching Rate

Due to the advantages of simple structure, small size, and high power density, permanent magnet synchronous motors (PMSM) have attracted the research interest of many scholars both domestically and abroad. However, traditional PMSM equipped with sensors, encoders, and other devices tend to have high equipment costs and rely heavily on the accuracy of the sensors for control effectiveness. Therefore, sensorless control has become a hot trend in the PMSM control field. In response to the chattering problem in sliding mode algorithms, this study first optimized the sliding mode reaching rate of a sensorless control system and applied it to construct a sliding mode observer and speed controller. Next, the improved sliding mode reaching rate-based sensorless control system was modeled and simulated in Matlab/Simulink, and its control performance was compared and analyzed with that of the traditional sliding mode reaching rate and replicated sliding mode reaching rate. Finally, comparative experiments were conducted on a test bench, and the results showed that, under the action of the improved sliding mode reaching rate, the chattering range of the output speed of the motor was +2%~+5%, which optimized the output speed of the PMSM and achieved the purpose of weakening the chattering.

Integral Fuzzy Sliding Mode Controller for Hydraulic System Using Neural Network Modelling

In this paper, a hydraulic motor controller is designed with a fuzzy supported integral sliding mode algorithm. The hydraulic system used in the study was modeled using artificial neural networks. Ability of handling nonlinearity of systems makes sliding mode controller to be a good choose for this system. The integral sliding mode controller can supply the robustness the system against the uncertainties. The basic idea of the proposed control method is to use fuzzy logic for the adaptation of the integral sliding mode control switching gain. Such adjustment reduces the chattering that is the most problem of classical sliding mode control. The equivalent control is computed using the radial basis function neural network. Simulation results of the presented method were compared with conventional PID controller results. It proved that it is more efficient to control the hydraulic system with integral fuzzy sliding mode control using neural network.

Editorial: Sliding‐mode algorithms for state estimation and fault diagnosis

SummaryThe purpose of this Special Issue on “Sliding–mode algorithms for state estimation and fault diagnosis” is to present a collection of articles showing novel developments and results in the theory and practice of sliding–mode algorithms for state estimation and fault diagnosis. This collection also includes some advanced and non–standard methods to deal with the fault–tolerant control problem.

A New Approach to Selecting Optimal Parameters for the Sliding Mode Algorithm on an Automotive Suspension System

Stimuli from the road surface cause car vibrations. The suspension system ensures the vehicle’s stability and smoothness when moving. In this research, the author introduces the use of active suspension with a hydraulic actuator to improve the comfort of cars. Car oscillations are described based on a quarter-dynamics model with five state variables. Besides, the nonlinear system’s SM (sliding mode) control algorithm is used to control the system. The SM algorithm’s parameters are optimally selected using the multiple loop algorithm. The multiple loop algorithm allows the values to vary within a predefined limit and provides an optimal parameter based on the vehicle’s vibration conditions. This is a new point in the paper compared to previous studies. The output of the simulation problem includes displacements and accelerations of both the sprung and unsprung masses. In addition, the change of dynamics force at the wheel is also considered when evaluating the interaction between the wheel and the road surface. According to the paper’s results, the vehicle body’s acceleration and displacement values are strongly reduced when using the SM algorithm, compared with cars with only traditional suspension. In addition, the change in dynamics force at the wheel is not significant when using this algorithm. As a result, the car’s smoothness has been improved while the vehicle’s stability has not been lost. The phenomenon of “chattering” still occurs in some cases; however, its effect is negligible.

Path following control for large inland ships in a restricted waterway using the nonlinear terminal sliding mode method

In order to solve the problem of path following for large ships travelling in restricted waterways, an adaptive Line-Of-Sight (LOS) guidance with the Nonlinear Terminal Sliding Mode (NTSM) algorithm is proposed in this paper. Compared to classical Sliding Mode Controller (SMC) and Adaptive Sliding Mode Controller (ASMC), the proposed system enables large ships to track the desired path much faster, meanwhile, the course stability can also be achieved with the controller saturation and environmental disturbance. To solve the problems of high nonlinearity and uncertainty of ship motion in restricted waters, the mathematical model with Extended state observer (ESO) is proposed to linearize problem. A drift angle observer is established to observe the drift angle during the vessel's navigation, and the LOS guidance law is used to achieve accurate tracking of the desired trajectory. The simulation results show that the inland ships under the control of the proposed scheme can accurately track the desired trajectory in a restricted waterway. The proposed algorithm has good robustness under the effect of environmental disturbances.

Earthquake Control: An Emerging Application for Robust Control. Theory and Experimental Tests

This article addresses the possibility of using robust control theory for preventing earthquakes through fluid injections in the Earth’s crust. The designed robust controllers drive aseismically a fault system to a new equilibrium point of lower energy by tracking a slow reference signal. The control design is based on a reduced-order nonlinear model able to reproduce earthquake-like instabilities. Uncertainties related to the frictional and mechanical properties of the underlying physical process and external perturbations are considered. Two types of controllers are derived. The first one is based on the sliding-mode theory and leads to local finite-time convergence of the tracking error and rejection of Lipschitz w.r.t. time perturbations. The second controller is based on linear quadratic regulator (LQR) control and presents global exponential stability of the tracking error and rejection of Lipschitz w.r.t. state perturbations. Both the controllers generate a continuous control signal, attenuating the chattering effect in the case of the sliding-mode algorithms. The developed controllers are tested extensively and compared on the basis of numerical simulations and experiments in the laboratory. The present work opens new perspectives for the application of the robust nonlinear control theory to complex geosystems, earthquakes, and sustainable energy production.

Development of an Adaptive Fuzzy Sliding Mode Controller of an Electrohydraulic Actuator Based on a Virtual Prototyping

The EHA (electro hydraulic actuator) has a notable advantage over conventional hydraulic actuators as it uses a closed-loop circuit, reducing the size and volume of oil, and eliminates pressure losses caused by valve orifices. However, accurate control performance of EHA is difficult to achieve using a traditional PID (proportional integral derivative) controller due to the strongly nonlinear, time-varying, and unknown dynamics of the system. Hence this paper seeks to address this problem by proposing a design of an intelligent controller for the EHA. The proposed adaptive fuzzy sliding mode controller (AFSMC) is developed as a hybrid of the adaptive, fuzzy logic, and sliding mode algorithms. To reduce costs and time, a virtual prototype approach is also proposed instead of experimentations to evaluate the performance of the proposed controller. The virtual model of the EHA is built in Amesime software, and then embedded into Matlab/Simulink where the AFSMC is developed and tested to obtain the position responses of the EHA. The results show that the AFSMC is highly successful and more efficient than the traditional PID at controlling the position of the piston accurately.

Online parameters estimation schemes to enhance control performance in DC microgrids

This paper addresses the problem of achieving current sharing and voltage balancing in DC microgrids when the filter parasitic resistances of the Distributed Generation Units (DGUs) are unknown and potentially time-varying. Two schemes are proposed for current sharing and voltage balancing, which use only generated current and voltage measurements. The first scheme is a novel distributed adaptive control utilising the principles of back-stepping and passivity-based control design, intended for the case of constant parasitic resistances. The second scheme alters an existing stabilising controller for current sharing and voltage balancing by incorporating the estimation of the unknown, possibly time-varying, parasitic resistance. A Super-Twisting Sliding Mode Algorithm (STA) estimates the parasitic resistance and its bounded variations in finite-time. The simulation results using a DC microgrid composed of 4 DGUs demonstrate the performance of the proposed schemes.

Frequency-multiplying synchronous control of the multiple counter-rotating exciters in vibration system

Frequency-multiplying synchronization vibration system is beneficial to diverse the material screening and improve the screening efficiency. In order to solve the problems of insufficient frequency-multiplying synchronous theory and low synchronization precision of the multiple exciters in vibration systems, the dynamic model of the frequency-multiplying synchronous vibration system with multi-vibration exciters is first established. A combined control strategy including the master-slave control and the adjacent cross-coupling control strategy is then proposed, together with the adaptive sliding mode algorithm to realize the frequency-multiplying synchronous control for the multiple exciters in vibration system. The stability of the proposed multiple exciters under frequency-multiplying synchronous control is proved by Lyapunov theorem and Barbalat Lemma. The performance of the proposed controller of frequency-multiplying synchronization is illustrated by comparing the simulation analysis with the vibration synchronization method at double frequency. The results show that the proposed controller of frequency-multiplying synchronization can effectively control the multiple exciters in vibration system to achieve the frequency-multiplying synchronous motion with improved control precision. The influence of different parameters on the performance of the frequency-multiplying synchronization is discussed, which shows that the controller of frequency-multiplying synchronization has good robustness against the system parameter disturbance. On this basis, the synchronization performance of the multiple exciters under different multiplied frequencies are analyzed and explained. The proposed combined control strategy can control the frequency-multiplying synchronization of the multiple exciters in the vibration system to achieve the required stable vibration trajectory.

Robust temperature tracking and estimation for resistive heater circuit board with implementation

SummaryResistive heating is an efficient method for temperature control in many applications that need robust control designs. Very few attempts have been reported in this direction to deal robustness issues like parametric variations, disturbances and uncertainties. Moreover, there are hardly any laboratory scaled setups available, that are of low cost and provide ease of implementation for such applications to test various algorithms. To that end, lately a resistive heater circuit board (RHCB) setup has become a benchmark setup for testing. For which, available control schemes largely use PID based schemes so far that are not robust. Besides, they employ numerical derivatives of measurements, resulting in the added noise. To circumvent these issues and to address the mentioned literature gap, this paper reports new experimental and simulation studies by developing new robust control and estimation designs for temperature tracking. We design via sliding mode algorithms, a sliding mode observer (SMO) and discrete‐time sliding mode controller (DTSMC) for an uncertain system of RHCB. The proposed controller outperforms the existing PID schemes and tracks the temperature reference accurately, despite the uncertainties. Moreover, SMO robustly estimates the temperature measurements and provide accurate signal for the control purpose. In addition, this study also reports a first of its kind application of such DTSMC and SMO, for which the idea of using different temporal designs for each of them is employed and integrated together for the ease of implementation on RHCB. Thus, the novelty also lies in how to judicially stitch these approaches and showcase their efficacy through simulation and experimental validations.

Adaptive Stability Control Based on Sliding Model Control for BEVs Driven by In-Wheel Motors

High-speed and complex road conditions make it easy for vehicles to reach limit conditions, increasing the risk of instability. Consequently, there is an urgent need to solve the problem of vehicle stability and safety. In this paper, adaptive stability control is studied in BEVs driven by in-wheel motors. Based on the sliding model algorithm, a joint weighting control of the yaw rate and sideslip angle is carried out, and a weight coefficient is designed using a fuzzy algorithm to realize adaptive direct yaw moment control. Next, optimal torque distribution is designed with the minimum sum of four tire load rates as the optimization objective. Then, combined with the road adhesion coefficient and the maximum motor torque constraint, the torque distribution problem is transformed into a functionally optimal solution problem with constraints. The simulation results show that the direct yaw moment controller based on the adaptive sliding mode algorithm has a good control effect on the yaw rate and sideslip angle, and it can effectively improve vehicle adaptive stability control. In the optimal torque distributor based on road surface recognition, the estimated error of road adhesion is within 10%, and has a greater margin to deal with vehicle instability, which can effectively improve vehicle adaptive stability control.

Active adaptive continuous nonsingular terminal sliding mode controller for hypersonic vehicle

An active adaptive continuous nonsingular terminal sliding mode algorithm (ACNTSM) is designed for hypersonic boost glide vehicle to achieve higher control accuracy and faster response speed. Firstly, a continuous nonsingular terminal sliding mode controller is presented to make the tracking error and sliding variable converge to zero under the effect of time-varying disturbance in finite time. Compared with traditional terminal sliding mode control using exponential approach law, the ACNTSM algorithm can generate continuous control signal, which effectively reduces chattering. Secondly, a novel active adaptive law is proposed to reduce convergence error, to avoid excessive gain, and to attenuate chattering by adjusting the gain of ACNTSM. The adaptive scheme includes sliding variable and disturbance estimation. The disturbance estimation is obtained by using the integral term of generalized super twisting sliding mode algorithm. The method takes less computational resources and reduces complexity of algorithm. In addition, the gain can automatically increase to shorten convergent time until the sliding mode is reached and then decrease to reduce chattering until the sliding mode is lost. The novel adaptive law ensures the finite-time convergence to a neighborhood of origin for sliding variable without overestimation of gain. Finally, numerical simulations are carried out to demonstrate the effectiveness and superiority of ACNTSM.

Attitude Fault-Tolerant Control of Aerial Robots with Sensor Faults and Disturbances

In this paper, sensor fault diagnosis and fault tolerant control strategy are investigated for quadcopters under sensor faults and disturbances. We propose the fault diagnosis estimation system and the fault-tolerant control (FTC) method. The fault diagnosis system provides time-varying sensor fault estimation under an unknown bound of disturbances. Moreover, the fault-tolerant control eliminates disturbance that is estimated through the associated disturbance observer. Overall, the proposed FTC guarantees the finite-time tracking convergence using nonsingular fast terminal sliding mode algorithm. Stability of the closed-loop system is validated through the Lyapunov theory. Finally, conventional nonsingular fast terminal sliding mode and adaptive neural network sliding mode control are compared with the proposed method through simulations under sensor faults and disturbances with different scenarios.

Performance evaluation of iterative learning control with different sliding mode algorithms for the slip‐ratio control of an electric vehicle

AbstractDeveloping a control strategy that can handle model uncertainties, external disturbances, and parameter fluctuations is essential for the desired operation of a nonlinear system. An attempt is made to develop such a control algorithm using the Learning Variable Structure Control technique. The proposed controllers have the advantages of both iterative learning control (ILC) and sliding mode control (SMC) such that they can compensate both structured and unstructured uncertainties. They are made comprised of modified‐twisting algorithm and super‐twisting algorithm respectively with the ILC technique. In this article, the performance of the two developed controllers is compared to a traditional SMC‐based ILC approach. Based on simulation results, the super‐twisting algorithm based ILC is found to be superior with reference to speed of convergence and tracking accuracy. This method is used to control the slip‐ratio of an electric vehicle as a specific application in this paper.

Adaptive generalized super twisting sliding mode control for PMSMs with filtered high-gain observer

This paper proposes a novel adaptive-gain generalized super twisting algorithm for permanent magnet synchronous motors. The stability of this algorithm is strict proof using the Lyapunov method. Both controllers of the speed-tracking loop and the current regulation loop are designed according to the proposed adaptive-gain generalized super twisting algorithm. Dynamically adjusted gains in the controllers can improve the transient performance and system’s robustness while reducing chattering. A filtered high-gain observer is applied in the speed-tracking loop to estimate the lumped disturbances, including parameter uncertainties and external load torque disturbances. The estimates feeding forward to the controller further improve the robustness of the system. Meanwhile, the linear filtering subsystem reduces the sensitivity of the observer to the measurement noise. Finally, experiments are constructed using the adaptive gain generalized super twisting sliding mode algorithm and the fixed gain one, showing the effectiveness and advantages of the proposed control scheme.

Composite Finite-Time Resilient Control for Cyber-Physical Systems Subject to Actuator Attacks.

Cyber-physical systems (CPSs) seamlessly integrate communication, computing, and control, thus exhibiting tight coupling of their cyber space with the physical world and human intervention. Forming the basis of future smart services, they play an important role in the era of Industry 4.0. However, CPSs also suffer from increasing cyber attacks due to their connections to the Internet. This article investigates resilient control for a class of CPSs subject to actuator attacks, which intentionally manipulate control commands from controllers to actuators. In our study, the supertwisting sliding-mode algorithm is adopted to construct a finite-time converging extended state observer (ESO) for estimating the state and uncertainty of the system in the presence of actuator attacks. Then, for the attacked system, a finite-time converging resilient controller is designed based on the proposed ESO. It integrates global fast terminal sliding-mode and prescribed performance control. Finally, an industrial CPS, permanent magnet synchronous motor control system, is investigated to demonstrate the effectiveness of the composite resilient control strategy presented in this article.

Cascade sliding mode maximum power point tracking controller for photovoltaic systems

Introduction. Constant increases in power consumption by both industrial and individual users may cause depletion of fossil fuels and environmental pollution, and hence there is a growing interest in clean and renewable energy resources. Photovoltaic power generation systems are playing an important role as a clean power electricity source in meeting future electricity demands. Problem. All photovoltaic systems have two problems; the first one being the very low electric-power generation efficiency, especially under low-irradiation states; the second resides in the interdependence of the amount of the electric power generated by solar arrays and the ever changing weather conditions. Load mismatch can occur under these weather varying conditions such that maximum power is not extracted and delivered to the load. This issue constitutes the so-called maximum power point tracking problem. Aim. Many methods have been developed to determine the maximum power point under all conditions. There are various methods, in most of them based on the well-known principle of perturb and observe. In this method, the operating point oscillates at a certain amplitude, no matter whether the maximum power point is reached or not. That is, this oscillation remains even in the steady state after reaching the maximum power point, which leads to power loss. This is an essential drawback of the previous method. In this paper, a cascade sliding mode maximum power point tracking control for a photovoltaic system is proposed to overcome above mentioned problems. Methodology. The photovoltaic system is mainly composed of a solar array, DC/DC boost converter, cascade sliding mode controller, and an output load. Two sliding mode control design strategies are joined to construct the proposed controller. The primary sliding mode algorithm is designed for maximum power point searching, i.e., to track the output reference voltage of the solar array. This voltage is used to manipulate the setpoint of the secondary sliding mode controller, which is used via the DC-DC boost converter to achieve maximum power output. Results. This novel approach provides a good transient response, a low tracking error and a very fast reaction against the solar radiation and photovoltaic cell temperature variations. The simulation results demonstrate the effectiveness of the proposed approach in the presence of environmental disturbances.

Chatter-Free Non-Singular Fast Terminal Sliding Mode Control of Interleaved Boost Converter

In this brief, a global non-singular fast terminal sliding mode controller (NSFTSMC) is proposed to stabilize the output voltage of an interleaved boost converter which is affected by disturbances such as variations in supply voltage, load resistance, and system parameter uncertainties. First, the converter model is transformed into a simplified form to make the controller design process simple. Second, the two-time scale disturbance estimation technique is adopted to estimate the matched, unmatched disturbances, and un-modeled system dynamics. Then, a nonlinear controller based on the sliding mode algorithm is developed to achieve guaranteed large-signal stability. Unlike other controllers, the proposed one ensures global stability and features a fast dynamic response with accurate output voltage tracking ability over wide variations in operating range. Both simulations and experimentations verify the robustness and feasibility of the proposed controller.