Linear Sliding Mode Control Research Articles

Adaptive Sliding Mode Control of Quadrotor System with Elastic Load Connection of Unknown Mass

During quadrotor load transport, the cable’s elasticity exacerbates load fluctuations, which may result in platform instability or a potential crash. This paper introduced a model of the connecting cable as a spring-damper system and established the dynamic model of the suspension system based on Newton’s law. Nonsingular fast terminal sliding mode control (NFTSMC) was employed for attitude, position, and anti-swing controller design. Adaptive controllers were integrated into altitude control to address uncertainties related to load mass and cable length. The inclusion of an anti-swing controller into the position control loop effectively dampens load oscillations while ensuring accurate position tracking. Numerical simulations demonstrated that the proposed controller outperforms both the energy-based controller and the conventional linear sliding mode controller.

Electromechanical coupling modeling and fractional-order control of the seeker stabilization platform

To address the electromechanical coupling and multi-source disturbance problems of the seeker stabilized platform, this paper constructs an electromechanical coupling model of the seeker stabilized platform based on the Lagrange-Maxwell equation. To mitigate the influence of electromechanical coupling on the control performance of the seeker, a super-twisting controller based on a fractional-order terminal sliding mode surface (FOSTSMC) is proposed. Additionally, to handle various disturbances in the system, this paper introduces a method that combines the extended state observer (ESO) with the proposed controller to enhance the system’s stability and anti-disturbance performance. The Lyapunov function is designed to prove that the proposed controller can reach a convergence state within finite time. Finally, the proposed control method is compared with PID control, fuzzy PID control, linear sliding mode control, and super spiral control combined with a disturbance observer (DOB). Multiple simulation experiments demonstrate that, under the influence of electromechanical coupling and multi-source disturbance, the FOSTSMC-ESO significantly improves the stability and anti-disturbance performance of the seeker stabilization platform.

Stability analysis of flying wing layout aircraft based on radial basis function neural network model

PurposeTo ensure the stability of the flying wing layout unmanned aerial vehicle (UAV) during flight, this paper uses the radial basis function neural network model to analyse the stability of the aforementioned aircraft.Design/methodology/approachThis paper uses a linear sliding mode control algorithm to analyse the stability of the UAV's attitude in a level flight state. In addition, a wind-resistant control algorithm based on the estimation of wind disturbance with a radial basis function neural network is proposed. Through the modelling of the flying wing layout UAV, the stability characteristics of a sample UAV are analysed based on the simulation data. The stability characteristics of the sample UAV are analysed based on the simulation data.FindingsThe simulation results indicate that the UAV with a flying wing layout has a short fuselage, no tail with a horizontal stabilising surface and the aerodynamic focus of the fuselage and the centre of gravity is nearby, which is indicative of longitudinal static instability. In addition, the absence of a drogue tail and the reliance on ailerons and a swept-back angle for stability result in a lack of stability in the transverse direction, whereas the presence of stability in the transverse direction is observed.Originality/valueThe analysis of the stability characteristics of the sample aircraft provides the foundation for the subsequent establishment of the control model for the flying wing layout UAV.

Development and Experiment of Semi-Physical Simulation Platform for Space Manipulator.

To address the extended development cycle, high costs, and maintenance difficulties associated with existing microgravity simulation methods, this study has developed a semi-physical simulation platform for robotic arms tailored to different gravity environments and loading conditions. The platform represents difficult-to-model joints as physical objects, while the easily modeled components are simulated based on principles of similarity. In response to the strong coupling, nonlinearity, and excess force disturbance issues in the electric variable load loading system, a fractional-order linear active disturbance rejection control algorithm was employed. The controller parameters were tuned using an improved particle swarm algorithm with modified weight coefficients, and experimental results demonstrate that a fractional-order linear active disturbance rejection control improves response speed and disturbance rejection performance compared to linear sliding mode control. The study investigated the differences in the drive force of joint motors in space robotic arms under varying gravity environments and loading conditions. Experimental results indicate that load torque is the primary influencing factor on joint motor drive force, while radial force serves as a secondary influencing factor. Additionally, when the axis of the joint motor is perpendicular to the ground, it can, to some extent, simulate microgravity conditions on the ground.

Sensorless HSPMSM Control of an Improved SMC and EKF Based on Immune PSO

Here, for controlling a high-speed flywheel permanent magnet synchronous motor (HSPMSM), a position sensorless control method for estimation of motor rotor position and speed is proposed to address the problems faced by mechanical position sensors of high cost, large size, and poor interference immunity. The extended Kalman filter (EKF) has difficulty obtaining the optimal covariance matrix when performing state estimation. Therefore, the particle swarm algorithm (PSO) with an immune mechanism is used to optimize the covariance matrix of the EKF. However, the EKF algorithm makes the system less robust due to its delay effect. Based on the traditional sliding mode control rate, the exponential convergence law is improved, and the continuous function sat(s) is used instead of the symbolic function sgn(s). This improves the convergence law and proves the asymptotic stability of the designed sliding mode variable structure controller based on Lyapunov’s stability theorem. Then, the novel control law is applied to the sliding mode surface (SMS). An ordinary sliding mode controller (OSMC) using a linear sliding mode controller (LSMC), a global sliding mode controller (GSMC) using a global sliding mode surface (GSMS), and an integral sliding mode controller (ISMC) using an integral sliding mode surface (ISMS) are designed for improving control. Joint simulation in MATLAB and Simulink verifies that the optimized EKF based on the immune PSO can improve precision and accuracy for controlling the electronic rotor position and speed. Comparing the new sliding mode controller with a traditional PI controller reveals that the proposed system has stronger resistance to load disturbance and better robustness.

Speed Stability and Anti-Disturbance Performance Improvement of an Interior Permanent Magnet Synchronous Motor for Electric Vehicles

To enhance the speed stability and anti-interference performance of the interior permanent magnet synchronous motor (IPMSM) in electric vehicles, a composite control strategy, incorporating sliding mode control (SMC) and extended state observer (ESO), was implemented to regulate the IPMSM’s speed. Firstly, three simulation analysis models of the IPMSM were established based on its electrical parameters. The current-loop regulator was a PI regulator, while the speed-loop regulators consisted of a basic SMC regulator, a linear SMC–ESO regulator, and a nonlinear SMC–ESO regulator. The simulation analysis results demonstrated that all three speed-loop regulators effectively ensured the speed stability of the IPMSM. However, the nonlinear SMC–ESO regulator exhibited superior performance in terms of enhancing the IPMSM’s resistance to disturbances. Secondly, a hardware testing platform was constructed to validate the simulation analysis findings. The hardware testing results, when compared to the simulation analysis results, revealed the need for optimization of the PI regulator’s control parameters to maintain the speed stability of the IPMSM. Moreover, contrary to the simulation analysis results, the hardware testing results indicated minimal difference in the anti-disturbance performance of the IPMSM between the linear SMC–ESO regulator and the nonlinear SMC–ESO regulator. Finally, the differences between the simulation analysis results and the hardware testing results are thoroughly discussed and analyzed, providing valuable insights for the practical implementation of IPMSM in electric vehicle drive systems.

Asynchronous event-triggered linear sliding mode control for T-S fuzzy singular systems

This paper investigates an asynchronous event-triggered linear sliding mode control (SMC) problem for T-S fuzzy singular systems with external disturbances. The generalized regular form of T-S fuzzy singular systems is presented to obtain the reduced-order sliding motion, which removes the constraints that all the subsystems share the same input matrix. Based on the generalized regular form, the singular matrix and the state variables are used to design the triggering function, which fully employs the characteristics of singular systems compared with the related results. Furthermore, an asynchronous event-triggered SMC (ETSMC) law is designed to guarantee the existence of the practical sliding mode, and the controller gains can be obtained via the admissibility analysis of the reduced-order sliding motion. Based on the designed singular-matrix-dependent event triggering mechanism and the asynchronous ETSMC law, the positive lower bound of the inter execution time can be guaranteed. Finally, two simulation examples are presented to verify the effectiveness of the obtained results, and some comparison results with the relevant methods are presented to illustrate the advantages of the proposed method.

Quantized-data resource allocation for reinforcement learning cooperative control of networked Euler-Lagrange agents with input saturation

This paper investigates the resource allocation problem of networked Euler-Lagrange agents (NELAs) with quantized-data interactions and input saturation in the framework of reinforcement learning (RL). We propose a hierarchical control strategy that includes a distributed resource allocation estimator (DRAE) and a local RL linear sliding mode controller (RL-LSMC). Specifically, the DRAE based on the gradient descent and state feedback is proposed, which aims to achieve optimal resource allocation by estimated states. The local RL-LSMC is designed through utilizing the feedback of critic neural network and the approximation capacity of actor neural network, which prompts the states of the NELAs to track the optimal estimated states. Several sufficient conditions are established with the help of Lyapunov stability argument. Finally, the effectiveness of the proposed hierarchical control algorithm is verified by the two simulation examples.

Attitude Tracking Adaptive Control of a Geocentric Polar Displaced Solar Sail

To deal with the attitude tracking control problem of a struck or pierced geocentric polar displaced solar sail (GPDSS), an attitude adaptive control strategy is proposed in this paper under the complex conditions of unknown inertial parameters, external disturbance and input saturation. First, on the basis of a flexible solar sail spacecraft attitude dynamics model with damping terms and vibration initial values, an integrated disturbance term, including inertial parameter uncertainties and external disturbance, is constructed. Second, a radial basis function neural network is applied to design a disturbance estimator with an adaptive law to estimate the integrated disturbance in real time. Then, a sliding-mode controller with fixed-time convergence in the reach phase and finite-time stability in the sliding phase is designed, and stability analysis is conducted by using the Lyapunov theory. Finally, comparative simulations with a linear sliding-mode controller and numerical simulations under various workings are performed. The results show that the designed adaptive control strategy can effectively achieve the attitude tracking control of the GPDSS.

Analysis and Control of Chaos in Voltage Mode Control Superbuck Converter for Photovoltaic Systems

Superbuck converter is a high-order converter with complex nonlinear dynamic characteristics, such as bifurcation and chaos, which will affect the stability of photovoltaic power generation systems. In this paper, the nonlinear dynamics of the voltage mode control Superbuck converter are studied. Taking reference voltage, input voltage, and output voltage error amplification factor as bifurcation parameters, the evolution process of the system from a stable state to bifurcation to a chaotic state is analyzed. The bifurcation forms of the converter under three bifurcation parameters are all period-doubling bifurcations. In this paper, the linear sliding mode control method is used to suppress and clear the nonlinear phenomenon of the system so that the converter in the chaotic state and unstable operation state can be restored to a stable single-cycle state in about 0.6ms.

Implementation and Performances Evaluation of Advanced Automotive Lateral Stability Controls on a Real-Time Hardware in the Loop Driving Simulator

This study concerns the comparative investigation of two advanced lateral stability automotive controllers with respect to a commercial solution. The research aims to improve the stability performances achieved by a combined tracking of yaw rate and side-slip angle through the application of optimal efforts. The proposed solutions are based on Linear Quadratic Regulation and Sliding Mode Control, respectively. Both rely on the same approach for the control objective definition but differ from the action perspective. This solution involves the adoption of a differential braking actuation technique to deliver a desired yaw moment to the car body to track controlled states. Indeed, a sliding controller can also traction torques of hub-motor configurations as well as steering corrections, achieving vehicle stability and a driving response in accordance with the pilot’s intentions. Calibration and validation of the controllers are performed through a Hardware-in-the-Loop simulation rig, along with a real-time static simulator, performing different close-loop maneuvers to assess achievements in terms of lateral stability. Results show that both solutions ensure higher handling performances if compared to Non-controlled or Commercial-controlled vehicle scenarios.

Power supply circuit model and sliding mode control of supercritical unit boiler system commissioning

AbstractIn the process of power control and commissioning of supercritical unit boiler system, there are some problems such as large steady‐state error and slow response speed. In order to optimize the control performance of supercritical unit boiler system, the power supply loop model and sliding mode control method of supercritical unit boiler system debugging power supply are proposed. Firstly, the power supply circuit model is established according to the data of voltage doubling rectifier circuit, inverter circuit, high frequency transformer and LC resonant circuit. Secondly, the capacitance voltage value and the inductance current value are calculated in the power supply circuit model. Finally, based on the numerical results, a terminal sliding mode controller and a linear sliding mode controller are established to complete the double closed‐loop terminal sliding mode control and realize the power control of the debugging power supply. The experimental results show that when the input voltage is 50 V and the current is 14 V, the input voltage and current waveforms remain stable. When the input voltage is between 40 and 50 V, the change of switching frequency is small, only increasing from 22 to 26 kHz. The steady state of the power supply is high, and when the input voltage increases, the DC offset is 21.2. The convergence time in the calculation process is less than 200 ms. The instantaneous change of inductance is 0.7 A. The steady‐state error is less than 0.005 V. The output voltage distortion rate is less than 4%. It is proved that this method has strong control performance in the supercritical unit boiler system.

Distributed fixed-time sliding mode control of time-delayed quadrotors aircraft for cooperative aerial payload transportation: Theory and practice

This paper investigates a cooperative fixed-time control for networked-delayed and disturbed quadrotors in payload transportation missions. First, the input time-delayed tracking error system is adequately transformed into a delay-free system via Artstein’s reducing transformation. Second, a novel Distributed Cooperative Fixed-Time Stable Control Protocol (DCFTSCP) is proposed for the multi-quadrotor system to stabilize the geometrical spatial formation while carrying the payload. Furthermore, a disturbance observer is incorporated into the control framework to counteract the lumped disturbances and achieve the transportation task with a minimal swing. Overall, the designed DCFTSCP is able to stabilize the delayed tracking states at the origin in fixed-time uniformly to the Initial Conditions (ICs). It is worth mentioning that the proposed controller belongs to the homogeneous sliding mode control class. The reported related works rely on the bi-limit approximation method to prove the fixed-time convergence of the states. Nevertheless, this method suffers from a crucial shortcoming where it is unable mathematically to provide an explicit expression on the settling (convergence) time. In contrast, in the present study, the stability analysis is thoroughly investigated based on the algebraic Lyapunov tools, namely, Algebraic Lyapunov Equation (ALE) and Lyapunov Quadratic Function (LQF). Consequently, the upper-bound on the convergence-time is explicitly derived for the first time for time-delayed quadrotors aircraft used in cooperative payload transportation. MATLAB® simulations and real flight experiments are conducted to corroborate the theoretical studies of the paper. Overall, the results show that the proposed control protocol yields performance improvement regarding fixed-time tracking stability featuring fast transient, strong robustness, and high steady-state precision. In addition, the undesirable chattering problem of regular linear sliding mode control is noticeably attenuated. Furthermore, unlike conventional terminal sliding mode control techniques, the control input is singularity-free. Finally, several challenging issues in cooperative fixed-time control for networked-delayed quadrotors are highlighted for future research.

Robust fractional‐order fast terminal sliding mode control with fixed‐time reaching law for high‐performance nanopositioning

AbstractFor high‐performance trajectory tracking at the nanometer scales, this paper presents a new fast terminal sliding mode controller, which combines a recursive integer‐order non‐singular high‐order sliding manifold and a fractional‐order fast fixed‐time reaching law to ensure globally fast convergence, and adopts a time‐delay‐estimation (TDE) based disturbance estimator deeming the designed controller robust to parameter uncertainty. Stability of the designed controller is verified through the Lyapunov framework, where the full analyses of convergence region and settling time are also presented. The tracking performance is experimentally verified on a piezo‐stack driven nano‐positioning platform. To showcase the performance improvements, measured closed‐loop performance of the proposed controller is contrasted with those obtained using three benchmark control approaches namely the basic Proportional‐Integral‐Derivative (PID), the popular Positive Position Feedback with Integral action (PPF+I), and the traditional linear sliding mode controller (LSMC).

Implementation and Stabilization of a Quadcopter Using Arduino and the Combination of LQR and SMC Methods

This paper presents a combination of Linear Quadratic Regulator (LQR) and Sliding Mode Control (SMC) methods to control a four-rotor unmanned aerial vehicle (UAV) that takes off and lands vertically (VTOL). Although controlling UAVs is difficult due to their highly nonlinear characteristics, the controller successfully controlled and stabilized the quadcopter in altitude and attitude by combining the advantages of the nonlinear and linear controllers. The Newton-Euler method is employed to build the dynamic model of the quadcopter, which is divided into two subsystems: the under-controlled subsystem and the fully actuated subsystem. The entire controller model was demonstrated in MATLAB/Simulink, and results demonstrating the controller's performance in various scenarios were obtained.

Comparative study of post-impact motion control of a flexible arm space robot

Designing a controller to manipulate a flexible space robot is hampered by the inherent complex nonlinear dynamics. Furthermore, the collision of a space robot with an external object in the space environment often leads to degradation of the space robot system. Therefore, an effective control algorithm is necessary for a successful space robot mission to regulate the motion of the entire system after an impact. This paper presents a comparative study on the performance of two different composite controllers to control post-impact motion of the space robot with two-link flexible arms. A performance comparison study helps to choose a better controller to carry out specific tasks. The dynamics of a space robot with flexible manipulators are highly nonlinear and coupled, hence split into rigid and flexible motion to make the control design easier. In this paper, two different composite controllers, namely Nonlinear Model Predictive Control with a Linear Quadratic Regulator (NMPC-LQR) and Sliding Mode Control with Linear Quadratic Regulator (SMC-LQR) are developed. NMPC and SMC are used to control rigid motion of the system, while LQR is used to suppress the flexible motion. The objective of the proposed controllers is to regulate the motion of the entire space robot system, including the flexible manipulator, after impact with an external object. The effectiveness of the proposed composite controllers is demonstrated using numerical simulations. Simulation results confirm that, in the absence of uncertainties, the performance of the control system using the proposed NMPC-LQR is more accurate compared to using SMC-LQR. Furthermore, given uncertainties of mass and inertia of the system, we find NMPC-LQR provides a higher level of accuracy when compared to SMC-LQR.

Switching Neural Network Control for Underactuated Spacecraft Formation Reconfiguration in Elliptic Orbits

A switching neural network control scheme, consisting of the adaptive neural network controller and sliding mode controller, is proposed for underactuated formation reconfiguration in elliptic orbits with the loss of either the radial or in-track thrust. By using the inherent coupling of system states, the switching neural network technique is then adopted to estimate the unmatched disturbances and design the underactuated controller to achieve underactuated formation reconfiguration with high precision. The adaptive neural network controller works in the active region, and the disturbances composed of linearization errors and external perturbations are approximated by radial basis function neural networks. The adaptive sliding mode controller works outside the active region, and the upper bound of the approximation errors is estimated by the adaptation law. The stability of the closed-loop control system is proved via the Lyapunov-based approach. The numerical simulation results have demonstrated the rapid, high-precision and robust performance of the proposed controller compared with the linear sliding mode controller.

A Compound Control Method Based on the Adaptive Linear Extended State Observer and Global Fast Terminal Sliding Mode Control for Inertially Stabilized Platform

To realize high-performance control for the inertially stabilized platform, a compound control method based on the adaptive linear extended state observer and global fast terminal sliding mode control is proposed. For estimating the unknown disturbances of inertially stabilized platform, an adaptive linear extended state observer was developed. With the full use of the information of attitude and angular velocity, the adaptive bandwidth of an adaptive linear extended state observer can deal with the peaking phenomenon without introducing excessive noise. Furthermore, the adaptation law based on the global fast terminal sliding mode control for disturbance estimation compensation was developed, which can improve the disturbance estimation accuracy of the adaptive linear extended state observer, and the higher order terminal function in global fast terminal sliding mode control was replaced by the lumped disturbance estimation of adaptive linear extended state observer, which can improve the anti-interference ability of inertially stabilized platform, reduce the chattering problem, and improve the control performance. The asymptotic stability of the proposed control method has been proven by the Lyapunov stability theory. The effectiveness of the proposed method was validated by a series of simulations and experiments.

출력 예측 성능을 갖는 제어 입력 변환 터미널 적분 슬라이딩 모드 제어

In this note, the discontinuous and continuous control input transformation integral terminal sliding mode control(TSMC)s by using the integral sliding surface without the reaching phase and with the output prediction performance as the one approach are presented for second order uncertain plants. Theoretically discontinuous and practically continuous control input transformed TSMCs are proposed when Δb ≠ 0, while it is assumed that Δb=0 in most of the TSMCs for easy design. Applying the idea of [32] for the linear sliding mode control(LSMC), the integral sliding surface without the reaching phase is suggested for the TSMCs. The exponent of the power function can be any positive numbers satisfying q＞p＞0 such that 0＜p/q＜1. The ideal sliding dynamics of the integral sliding surface is derived and the real robust output can be predicted, predesigned, predetermined by means of the solution of the ideal sliding dynamics. The transformed control input is suggested for generating the sliding mode for the entire trajectory from any given initial condition to the origin based on defining a new auxiliary nonlinear state. The closed loop exponential stability together with the existence condition of the sliding mode on the predetermined sliding surface is investigated theoretically for the complete formulation of the TSMC design for the output prediction performance. As a remedy of the singularity, a certain limit is imposed on the new auxiliary nonlinear state. For practical applications, a continuous approximation of the discontinuous TSMC is made by means of the modified boundary layer function. In addition, the closed loop bounded stability together with the existence condition of the sliding mode by the continuous TSMC is analyzed. The discontinuity of the control input as the inherent property of the sliding mode control is much improved in view of the practical applications. Through a design example and simulation studies, the effectiveness of the proposed discontinuous and continuous control input transformed TSMCs is verified.

Application of an Improved STSMC Method to the Bidirectional DC–DC Converter in Photovoltaic DC Microgrid

In a photovoltaic DC microgrid, the intermittent power supply of the distributed generation and the fluctuation of the load power will cause the instability of the bus voltage. An improved super-twisting sliding mode control method based on the super-twisting algorithm is proposed to solve this problem. In this paper, a bidirectional half-bridge buck–boost converter was selected as the research topic. The proposed control method replaces the sign function with the saturation function to further mitigate the chattering effect. The stability of the proposed control method was proven to be finite-time convergent using the Lyapunov theory control. Compared with PI control, linear sliding mode control, and terminal sliding mode control, the proposed control method reduces the system overshoot by up to 33% and greatly improves the response speed; compared with the traditional super-twisting sliding mode control method, the system overshoot is reduced by 6.8%, and the response speed is increased by 38%. The experimental results show that the proposed control method can reduce the fluctuation range of the bus voltage, shorten the time of bus voltage stability, effectively stabilize the bus voltage of the photovoltaic DC microgrid, and maintain strong robustness.