Non-Singular Fast Terminal Sliding Mode Control for PMSM Based on Sliding Mode Disturbance Observer

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

ABSTRACTThe control performance of a permanent magnet synchronous motor (PMSM) is significantly deteriorated when faced with unknown disturbances, such as model uncertainties, parameter variations, and external interferences. This paper proposes a model‐free fast integral terminal sliding mode control (MFITSMC) approach based on an extended super‐twisting sliding mode disturbance observer (ESTSMDO), referred to as the ESTSMDO‐based MFITSMC approach. First, a unique ultra‐local model (NULM) of the PMSM is developed that accounts for unknown disturbances. Then, the MFITSMC is formulated by integrating a fast integral terminal sliding mode surface with a switching control law. The speed loop controller is designed using the MFITSMC. The ESTSMDO is meant to precisely estimate unknown disturbances and subsequently input them into the MFITSMC controller. The ESTSMDO‐based MFITSMC approach mitigates chattering and improves the system's robustness to unanticipated disturbances. Finally, the simulation and experimental validation demonstrate that the dynamic response of the PMSM system is markedly enhanced, and the chattering associated with SMC is effectively reduced.

This paper presents a sensorless speed control method of permanent magnet synchronous motor (PMSM) applying sliding-mode control theory, to enhance the observation precision and improve robustness of control system. Firstly, an improved full-order sliding mode observer (FSMO) with sigmoid function is gifted to weaken the high-frequency (HF) chattering caused by conventional sliding mode observer (SMO). The quadrature phase-locked loop (PLL) is used to calculate high-precision rotor location and speed, avoiding the use of filter. Then the nonsingular fast terminal sliding mode controller (NFTSMC) in speed controller is introduced to replace traditional proportional integral (PI) controller to improve the dynamic performance of control system. The outcomes verify that the presented control method enhances the overall observation precision, suppresses HF chattering, and increases dynamic and stable state response of PMSM.

Diseases such as cerebral palsy can lead to lower limb dysfunction in children. Lower limb rehabilitation exoskeletons have been clinically validated as effective interventions for gait rehabilitation of children. This study proposes a novel lower-limb gait rehabilitation exoskeleton design and its corresponding control method for pediatric applications. A dynamic model was established, and a nonsingular fast terminal sliding mode control (NFTSMC) strategy was developed to achieve precise trajectory tracking. The curve fitting was performed on a publicly available children’s gait dataset to generate reference hip and knee joint trajectories. The Lagrange method was subsequently employed to derive the dynamic model of the lower-limb exoskeleton. Control simulations were conducted using the proposed NFTSMC algorithm. Comparative analysis with traditional sliding mode control (SMC) demonstrated that NFTSMC reduced root mean square error (RMSE) by 75% (hip) and 67.4% (knee), while integral of time-weighted absolute error (ITAE) decreased by 77.3% and 92.3%, respectively. These results confirm that NFTSMC significantly enhances joint trajectory tracking accuracy, system response speed, and tracking precision.

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.

An important function of the steer-by-wire (SBW) system is to follow a desired steering angle accurately. However, it is impossible to avoid transmission backlash in the servo system, which will aggravate the mechanical vibration and cause delays and fluctuations in control system responses. A composite controller for permanent magnet synchronous motor (PMSM) servo system is proposed in this paper to solve the adverse effects resulting from backlash of the SBW system. To mitigate the effects of backlash nonlinearity, the dead-zone backlash model is identified utilizing the particle swarm optimization (PSO) algorithm, and its influence is compensated in the controller. Additionally, to address the model declination and unpredictable disturbances, a nonsingular fast terminal sliding mode controller (NFTSMC) combined with a super-twisting extended state observer (STESO) is designed. In simulation experiments, a SBW control system model is built to evaluate the performance of the disturbance observer and the angle following controller. In hardware-in-loop (HIL) experiments, the angle tracking control capability of the novel method is further evaluated under the double lane change condition. Finally, the results of simulation and HIL experiments are offered to validate the excellence of the novel method.

This paper proposes a non-singular fast terminal sliding mode control (NFTSMC) method for micro gyroscopes with unknown uncertainty based on gated recurrent fuzzy neural networks (GRFNNs). First, taking advantage of non-singular fast terminal sliding control, a sliding hyperplane is designed with a nonlinear function to ensure that the tracking error of the system converges to zero within a specified finite time. Then, the unknown model parameters of the micro gyroscope are estimated using a GRFNN. Since the GRFNN can adaptively adjust the base width, center vector, gated recurrent unit parameters, and outer gains, it can achieve accurate approximation to unknown models, enhancing the robustness and accuracy. In addition, due to the introduction of gated recurrent units, The GRFNN can effectively utilize the previous data and avoid the problem of gradient disappearance. The comparison of the simulation results with traditional neural sliding mode control shows that the proposed method can achieve better tracking performance and more accurate estimation of unknown models.

A Global Fast Terminal Sliding Mode Controller (GFTSMC) is proposed for n-link robotic manipulators by employing the Fast Terminal Sliding Mode (FTSM) control concept in both the reaching phase and the sliding phase. Under the control, the system states will reach FTSM in desired finite time and then converge to the origin along the FTSM in specified finite time, resulting in a reduced steady tracking error in comparison with the conventional sliding mode controller. The proposed controller is continuous and therefore chattering-free. An example is presented to demonstrate its effectiveness.

This paper proposes a nonsingular fast terminal sliding mode approach integrated with finite-time disturbance observer (DO-NFTSMC) for a magnetic levitation system exposed to uncertainties and external disturbances. A finite-time disturbance observer is first proposed to handle disturbances and modeling uncertainties. Then a nonsingular fast terminal sliding mode control (NFTSMC) approach is formulated relying on a newly constructed sliding surface to ensure fast transient convergence to the equilibrium. Overall stability and finite-time estimation were verified using the Lyapunov stability theory. Computer experiments using a highly nonlinear magnetic levitation (maglev) system showed promising results in terms of finite-time attainability, disturbance rejection and effective continuous control with reduced chattering. Additionally, performance comparison to that of a dynamic sliding mode control (DSMC) design was carried over and showed that the proposed controller outperformed the DSMC in all aspects.

A Non-singular Fast Terminal Sliding Mode Approach to Improve the Network Stability of Wind Rich Power Grids

Permanent Magnet Synchronous Motors (PMSMs) exhibit inherent symmetry in their electromagnetic structure yet behave as nonlinear and strongly coupled systems that are susceptible to internal parameter perturbations and external disturbances, posing challenges to effective control under dynamic operating conditions. To address these issues, this paper proposes a sliding mode control strategy for PMSMs that integrates a Novel Adaptive Reaching Law (NARL) and an Improved Terminal Fuzzy Sliding Mode Disturbance Observer (IFTSMDO), denoted as SMC-NARL-IFTSMDO. The NARL is designed with a state-dependent dynamic gain adjustment mechanism and terminal attractive factor characteristics: it increases the gain to ensure fast convergence when the system state is far from the sliding mode surface, and adaptively attenuates the gain to suppress chattering when approaching the sliding mode surface, thereby balancing the contradiction between convergence speed and chattering in traditional sliding mode control. The IFTSMDO constructs a composite sliding mode surface incorporating error derivatives, terminal power terms, and saturation functions, which enhances the sensitivity of disturbance estimation in the small-error stage, avoids high-frequency chattering caused by sign functions, and provides accurate feedforward compensation for the speed loop controller to improve the system’s anti-disturbance capability. Additionally, the asymptotic stability of the proposed control strategy is strictly proven using the Lyapunov stability theory, laying a solid theoretical foundation for its application. Experiments are conducted on a TMS320F28379D DSP-based platform, and quantitative results show that compared with the traditional sliding mode control (SMC-TRL), the proposed strategy reduces the no-load startup response time by 60%, the steady-state speed fluctuation by 60%, and the speed fluctuation under load disturbance by 81.5%, fully demonstrating its superiority in dynamic response and anti-disturbance performance.

A novel adaptive non-singular fast terminal sliding mode control (NFTSMC) scheme is developed for a highly nonlinear two-link robotic manipulator (TLRM) system subject to system uncertainties and unknown disturbances. First, to compensate for the system uncertainties, neural network (NN) is employed to approximate the unknown nonlinear dynamic function. Subsequently, to address the challenges of disturbance compensation and unmeasured joint angular velocity, a nonlinear NN-based extended state observer (NN-based ESO) is introduced. The NN-based ESO facilitates accurate disturbance estimation and compensation, while also enabling simultaneous estimation of the joint angular velocity. Through the integration of these techniques, the closed-loop system’s stability is proven using the direct Lyapunov method, demonstrating remarkable tracking performance within finite time. Simulation results validate the effectiveness of the NFTSMC with the NN-based ESO, showcasing superior performance compared to alternative control strategies.

This paper introduces a variable structure to regulate speed of PMSM system by a global fast terminal sliding mode control (GFTSMC) technique optimizing speed tracking performance of permanent magnet synchronous motor (PMSM) servo system. Firstly, a global fast terminal sliding mode control strategy is introduced. Compared with common sliding mode control strategy, this strategy eliminates the chattering phenomenon in that it does not contain switching terms. Also, it can make the output speed reach the reference value in finite time, along with a shorter convergence time and a better tracking precision. Due to the complexity of control equations, S-function in MATLAB is adopted to design the GFTSMC. The effectiveness and robustness of the proposed scheme are verified by MATLAB simulations.

In order to improve the anti-disturbance performance of permanent magnet synchronous motor (PMSM) servo system, a sliding-mode control strategy using a new reaching law (NRL) is proposed. The NRL incorporates power term and switching gain term of the system state variables into the conventional exponential reaching law (CERL), which can effectively suppress the sliding-mode chattering and increase the convergence rate of system state reaching sliding-mode surface. Based on this new reaching law, a sliding-mode speed controller (SMSC) of PMSM is designed. At the same time, to solve the chattering problem caused by the large sliding-mode switching gain, an anti-disturbance sliding-mode speed controller method with an extended sliding-mode disturbance observer (ESMDO), called SMSC+ESMDO method, is developed. The sliding-mode disturbance observer is designed to accurately estimate the motor speed and external load disturbances, and the disturbance estimator is used as a feed-forward to compensate the sliding-mode speed controller (SMSC) to improve the system robustness and reduce the system chattering. Simulation and experimental results show that the proposed compound sliding-mode control strategy can effectively improve the dynamic performance and robustness of the system compared with the PI controller.

A recursive terminal sliding mode controller (RTSMC) based on sliding mode disturbance observer (SMDOB) is proposed for the longitudinal dynamics of a generic hypersonic flight vehicles (HFVs) in the presence of parametric uncertainties, measurement noises and external disturbances. First, a sliding mode tracking controller is presented by introducing recursive terminal sliding mode manifolds, in which each manifold will reach zero subsequently in finite time as well as the usual singularity problem will not occur. The RTSMC embraces advantages of both nonsingular terminal sliding mode control and high-order sliding mode control. Next, for the sake of enhancing the robustness of controller for uncertainties, a SMDOB is proposed to estimate and compensate the disturbances. Then, a composite controller that is composed of RTSMC and SMDOB is designed, and its stability is analyzed utilizing Lyapunov function method. Finally, numerical simulation is conducted for cruise flight condition of HFV. Simulation results show the expected control performance.