Intelligent robust control of inverted pendulum using hierarchical sliding mode and ELM-based estimator

There are various uncertain factors such as parameter perturbation and external disturbance during the steering process of a permanent magnet slip clutch electronically controlled hydraulic power steering system (P-ECHPS) of medium and heavy duty vehicles, which is an electronically controlled hydraulic power steering system based on a permanent magnetic slip clutch (PMSC). In order to avoid the immutable single assistance characteristic of a hydraulic power steering system, a PMSC speed-controlled model and P-ECHPS of each subsystem model were studied. Combined with non-singular terminal sliding mode and fast terminal sliding mode, an Adaptive Non-singular Fast Terminal Sliding (ANFTS) mode control strategy was proposed to control precisely the rotor speed of the PMSC in P-ECHPS, thus achieving better power control for the entire P-ECHPS system. The simulation results show that adaptive nonsingular fast terminal sliding mode control enables PMSC output speed to track the target speed. Compared with the non-singular terminal sliding mode control and the ordinary sliding mode control, the convergence speed has been improved by 66.7% and 84.2%, respectively. The rapid control prototype test of PMSC based on dSPACE (dSPACE is a development and verification platform based on MATLAB/Simulink software.) was carried out. The validity of the adaptive NFTSM algorithm and the correctness of the offline simulation results are validated. The adaptive NFTSM algorithm have better robustness and can realize variable assist characteristics and save energy.

Robotics have been substituting humans increasingly and effectively to operate repeated, dangerous, heavy, complicated works in human life, production industry, and discovery missions. This work designs a Neural Integral Non-singular Fast Terminal Synchronous Sliding Mode Control (NINFTSSMC) approach for 3-DOF parallel robotic manipulators with uncertain dynamics, using synchronous nonlinear sliding surface, where this sliding surface is formed through the integration of the Synchronization Control (SC) and the Integral Non-singular Fast Terminal Sliding Mode Control (INFTSMC). Accordingly, position errors and synchronization errors quickly converge to the sliding surface at the same time. Next, a Feed-Forward Neural Network (FNN) is applied to estimate uncertain dynamics, whose novelty, compared to a classic FNN, is that they utilize a Non-singular Fast Terminal Sliding Mode (NFTSM) error filter to replace a classic error filter. Thanks to this procedure, the lumped uncertain dynamics are compensated more quickly and more accurately, thus, the malfunction in the reaching phase of state variables approaching the sliding surface is handled thoroughly. Finally, the control approach is designed for a robotic system to achieve the prescribed performance, obtaining rapid error convergence, robustness with uncertain dynamics, minimum chattering, synchronization, and high precision. The stability of the control loop is secured according to the Lyapunov theory. To test the robustness and confirm the effectiveness of the suggested controller for a 3-DOF parallel manipulator, computer simulations and performance comparisons are conducted.

Aiming at the characteristics of nonlinearity, strong coupling and unknown perturbation in the dynamics model of Delta robot under high-speed operation, this paper designs a new Global Non-singular Fast Terminal Sliding Mode Control (GNFTSMC), which avoids the singularity of the traditional terminal sliding mode control. On this basis, Fuzzy Global Non-singular Fast Terminal Sliding Mode Control (FGNFTSMC) is proposed by combining Global Non-singular Fast Terminal Sliding Mode Control with fuzzy system, which is a method of eliminating the chattering of sliding mode controller by using fuzzy logic outputs instead of the reaching control law. To improve the trajectory tracking accuracy, the Adaptive Fuzzy Global Non-singular Fast Terminal Sliding Mode Control (AFGNFTSMC) is proposed by adjusting output gain online through the adaptive fuzzy system. The Sparrow Search Algorithm (SSA) is proposed to optimize the Adaptive Fuzzy Global Non-singular Fast Terminal Sliding Mode Control (AFGNFTSMC) sliding surface parameters and select the optimal sliding surface parameters. Experiments show that applying the Adaptive Fuzzy Global Non-singular Fast Terminal Sliding Mode Control optimized based on the SSA (SSA-AFGNFTSMC) to the Delta robot improves the tracking accuracy, reduces the convergence time and eliminates the controller output chattering.

This work proposes a non-singular fast terminal sliding mode control (NFTSMC) strategy based on the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm and a nonlinear disturbance observer (NDO) to address the issues of modeling errors, motion disturbances, and transmission friction in robotic manipulators. Firstly, a novel modular serial 5-DOF robotic manipulator configuration is designed, and its kinematic and dynamic models are established. Secondly, a nonlinear disturbance observer is employed to estimate the total disturbance of the system and apply feedforward compensation. Based on boundary layer technology, an improved NFTSMC method is proposed to accelerate the convergence of tracking errors, reduce chattering, and avoid singularity issues inherent in traditional terminal sliding mode control. The stability of the designed control system is proved using Lyapunov stability theory. Subsequently, a deep reinforcement learning (DRL) agent based on the TD3 algorithm is trained to adaptively adjust the control gains of the non-singular fast terminal sliding mode controller. The dynamic information of the robotic manipulator is used as the input to the TD3 agent, which searches for optimal controller parameters within a continuous action space. A composite reward function is designed to ensure the stable and efficient learning of the TD3 agent. Finally, the motion characteristics of three joints for the designed 5-DOF robotic manipulator are analyzed. The results show that compared to the non-singular fast terminal sliding mode control algorithm based on a nonlinear disturbance observer (NDONFT), the non-singular fast terminal sliding mode control algorithm integrating a nonlinear disturbance observer and the Twin Delayed Deep Deterministic Policy Gradient algorithm (TD3NDONFT) reduces the mean absolute error of position tracking for the three joints by 7.14%, 19.94%, and 6.14%, respectively, and reduces the mean absolute error of velocity tracking by 1.78%, 9.10%, and 2.11%, respectively. These results verify the effectiveness of the proposed algorithm in enhancing the trajectory tracking accuracy of the robotic manipulator under unknown time-varying disturbances and demonstrate its strong robustness against sudden disturbances.

This paper presents a new method for position estimation of the robotic manipulators, based on the principles of the Extended Kalman Filter (EKF). The standard EKF suffers from performance depreciation and may even diverge from the true estimation in case the statistics of the noises which affect the system were unknown. Hence an Adaptive EKF has been proposed that has better outcome than conventional EKF in terms of robustness, convergence speed and estimation accuracy. Furthermore, the position of each joint is estimated to use in a Non-singular Fast Terminal Sliding Mode (NFTSM) controller. This controller will makes the states to reach in finite time. It also solves the singularity problem of Terminal sliding mode control. Computer simulations given for 2-DOF robot manipulator demonstrate the outperformance of the AEKF in compared with EKF. It has also been shown that the NFTSM controller has the ability to track the trajectory path properly and accurately.

For accurate trajectory tracking of robotic manipulators with actuators, a novel nonsingular fast terminal sliding mode control (NFTSMC) strategy based on radial basis function neural network (RBFNN) is put forward and investigated in this paper. Because of the existence of nonsingular fast terminal sliding mode (NFTSM) manifold, the controller possesses high precision and fast convergence. Considering that it is difficult to obtain accurate model parameters owing to modeling errors or external disturbances, RBFNN is used to approximate the nonlinear uncertainties due to its simple structure and great generalization ability. A new adaptive law is designed to adjust RBFNN. In order to compensate the estimation errors and suppress other unstable factors, a robust term is introduced. A new adaptive law is developed to flexibly adjust the robust term. Then, Lyapunov theory is applied to prove the system stability and finite-time convergence. Finally, a small-sized industrial robotic manipulator Epson LS3-401S with its first two joints is taken as the simulation plant, and several simulations between the proposed controller and the other two controllers are performed. External disturbances and other two conditions are considered to simulate the real environment, and the corresponding results verify the effectiveness and superiority of the proposed controller.

Servomechanisms and motion stages often encounter many mechanical transmission problems such as friction, backlash, and structural resonance, as well as other factors such as system nonlinearity, servo lags, and unknown disturbances. In contour following applications, these problems are the main causes of deterioration in contour following accuracy. As a result, the issue of dealing with the above problems so as to reduce tracking error and contour error is crucial. The Dynamic Fast Nonsingular Terminal Sliding Mode Control (DFNTSMC) scheme proposed in this paper combines the advantages of Fast Nonsingular Terminal Sliding Mode Control (FNTSMC) and Dynamic PID Sliding Mode Control (DSMC) while avoiding their drawbacks. The proposed DFNTSMC has attractive features such as improvement of contour following accuracy, chattering effect suppression, enhancement of robustness, and finite time convergence. The convergence of the proposed DFNTSMC is proved based on Barbalat’s lemma. Several contour following experiments are performed to assess the performance of the proposed DFNTSMC. Experimental results suggest that the proposed DFNTSMC outperforms both FNTSMC and DSMC, two control schemes also tested in the contour following experiment.

In the paper, a new control system was proposed for nonlinear system control. A nonsingular fast terminal sliding mode controller based on state (NFTSM-S) was designed for nonlinear system. Analyzed nonsingular fast terminal sliding mode controller, NFTSM-S was designed. which reduced transition time between nonsingular fast terminal sliding mode controller (NFTSM) and linear sliding mode controller and combined merits of them. This algorithm reduced convergent time and ripple of input. Finally, simulation results show this method is validity in nonlinear system control.

Aims: external interference and slow localization response. The primary objective is to propose an algorithm that integrates admittance control and non-singular fast terminal sliding mode control, verifying its effectiveness through simulation experiments while exploring its potential for patent application. Background: Due to their versatility and efficiency, UAVs are increasingly utilized in various aerial operations. However, they are susceptible to external disturbances, which may affect their stability and accuracy during tasks such as contact operations. Additionally, inherent delays in localization response speed may impact their performance in dynamic environments. Addressing these issues is essential for improving the reliability and robustness of UAV-based systems. Methods: To achieve the objectives, the kinematics and dynamics of a hexacopter aerial carrier robotic arm system were initially modeled. Subsequently, an external admittance controller was designed to mitigate disturbances encountered during contact operations, achieving smooth control of the robotic arm end-effector by adjusting the desired position to enhance system stability and disturbance rejection. Additionally, to prevent performance degradation stemming from controller saturation, an internal position control mechanism utilizing a non-singular fast terminal sliding mode control algorithm was implemented. This approach enhances system robustness and convergence speed, ensuring accurate positioning. Results: To validate the effectiveness and feasibility of the proposed control algorithm, numerical simulations were conducted. The outer loop's admittance control exhibited a smoother control process, particularly during sudden stiffness changes when the actuator contacts the environment. The inner loop, employing Non-Singular Fast Terminal Sliding Mode Control (NFTSMC), improved joint angle tracking speed by 41%-58% compared to PID control, and by 20%-50% compared to traditional Sliding Mode Control (SMC). This algorithm demonstrated faster convergence rates and smoother transitions, significantly reducing steady-state errors in contact force while exhibiting robustness to environmental parameters. The findings indicate that the algorithm effectively addresses the issues of external interference and sluggish localization response encountered by UAVs during aerial operations. Conclusion: The algorithm based on admittance control and non-singular fast terminal sliding mode control demonstrates superior performance compared to traditional sliding mode control and PID control in mitigating external disturbances and enhancing the precision of UAV aerial operations. This ensures the resilience to disturbances and the speed of localization response of the rotary- wing flying robotic arm system during cleaning processes, thus enhancing its reliability and robustness in dynamic environments.

This paper proposes a fault tolerant control technique for uncertain faulty robotic manipulators when only position measurement is available. First, a neural third-order sliding mode observer is utilized to approximate the system velocities, the lumped uncertainties and faults, in which the radial basis function neural network is employed to approximate the observer gains. Then, the obtained information is applied to design a non-singular fast terminal sliding mode control to deal with the effect of the lumped uncertainties and faults. In addition, an adaptive law is used to approximate the sliding gain in switching control law. The controller-observer method can provide superior features such as high tracking precision, less chattering phenomenon, finite-time convergence, and robustness against the lumped uncertainties and faults without the requirement of its prior knowledge. The stability and finite-time convergence of the proposed technique are proved in theory by using the Lyapunov function. To verify the usefulness of the proposed strategy, computer simulations for a 2-link serial robotic manipulator are performed.

To facilitate the stabilization of nonlinear underactuated robotic systems under perturbation, a novel nonsingular fast terminal sliding mode control method is proposed. Based on the system transformation into an integrator chain, the combination of twisting-like algorithm and a nonsingular fast terminal sliding mode control technique is employed to achieve the stabilization of the studied systems, which can drive the robot states (joint positions and velocities) to the desired region and then maintain the system at the equilibrium point in finite time. The robustness of the proposed method is validated by the Lyapunov direct method. Finally, numerical simulation results further demonstrate that the proposed method has better performance on the convergent speed of the system state (robot joint positions and velocities) than state-of-the-art methods, especially for the underactuated joints.

Adaptive nonsingular fast terminal sliding-mode control for the tracking problem of uncertain dynamical systems

This Paper presents a chattering free non-singular fast terminal sliding mode controller for a Robot manipulator in the presence of parameter uncertainties and external disturbances and comparison of its response with Conventional Sliding Mode Control(SMC) & Terminal Sliding Mode Control(TSMC). Non-singular Fast Terminal Sliding Mode Control(NFTSMC) removes the singularity and slower convergence rate problem of Terminal Sliding Mode Control. Chattering is alleviated by applying the Super Twisting algorithm with NFTSMC without affecting tracking performance. The Effectiveness of the Controller is validated by simulation results.

Aimed at solving the slow convergence problem of traditional non-singular fast terminal sliding mode control algorithm, this paper develops a novel piece-wise non-singular fast terminal sliding mode control algorithm by introducing the nonlinear term of the one existed control algorithm into the traditional non-singular fast terminal sliding mode. In comparison with the traditional one, the proposed approach not only maintains the advantage of avoiding singularity, but also has a faster convergence performance around the local region of equilibrium.

To solve the problems that control performance of high torque traction interior permanent magnet synchronous motor (IPMSM) is degraded by parameter perturbation and unknown disturbance, this paper proposes a novel Improved Super-Twisting non-singular fast terminal sliding mode control strategy (IST-NFTSMC) for IPMSM based on Extended Nonsingular Fast Terminal Sliding Mode Disturbance Observer (ENFTSMDO). Firstly, the mathematical model of IPMSM under parameter perturbation is established; Then, an improved Super-Twisting nonsingular fast terminal sliding mode speed controller (IST-NFTSMC) based on extended nonsingular fast terminal sliding mode disturbance observer (ENFTSMDO) is designed, in which the improved Super-Twisting control law designed can effectively weaken the chattering of traditional NFTSMC, and ENFTSMDO can more accurately observe the unknown disturbance part of the system in real-time than ESMDO; Finally, compared with PI control and traditional NFTSMC control by simulations and experiments, the method proposed has merits of accelerating convergence, improving steady-state accuracy and minimizing the current and torque pulsation.