Vector Control of PMSM Based on Improved Sliding Mode Observer and Controller

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

This paper proposes an improved Sliding Mode Observer (SMO). Compared with the traditional SMO, it can estimate position and speed information of the rotor more accurately. Its stability is proved by Lyapunov Stability. A control scheme of Permanent Magnet Synchronous Motor (PMSM) under Direct Torque Control (DTC) is designed, using the improved SMO as the feedback of speed information. The results show that the proposed method works well without position encoder. The improved SMO guarantees DTC scheme quick response and strong robustness.

To address the issue of reduced speed tracking accuracy in permanent magnet synchronous motors (PMSM) under variable-speed conditions, this paper proposes a non-singular fast terminal sliding mode controller (NFTSMC) that mitigates the chattering problem inherent in sliding mode control (SMC). For handling external disturbances where the controller exhibits poor convergence, a sliding mode disturbance observer (SMDOB) is designed to ensure effective convergence of the proposed control strategy under disturbed conditions. The superiority of the integrated control approach combining the NFTSMC with the SMDOB was ultimately validated through simulations.

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 study introduces a sensorless control approach for permanent magnet synchronous motors (PMSMs) that employs an Improved Non-Singular Fast Terminal Sliding Mode Controller (IMNFTSMC) and an Improved Non-Singular Fast Terminal Sliding Mode Observer (IMNFTSMO). The IMNFTSMC employs a novel hybrid reaching law and a continuous piecewise square root switching function to achieve faster convergence and effective chattering reduction over the conventional Sliding Mode Controller (SMC). This design successfully replaces two critical components: the discontinuous constant velocity term (a key component of the traditional SMC reaching law that is a primary source of control chattering in PMSM torque regulation) and the high-gain exponential term (which tends to induce overshoot during transient speed adjustments and degrade steady-state control precision). In the IMNFTSMO, a hybrid approach combining linear and non-singular terminal sliding modes eliminates phase lag associated with low-pass filtering in traditional sliding mode observers, improving rotor position and speed estimation accuracy. Stability of both IMNFTSMC and IMNFTSMO is rigorously proven using Lyapunov stability theory.Validation through extensive simulations and hardware experiments, including challenging zero-speed start, speed stepping, and load disturbance tests, confirms the proposed strategy provides improved dynamic response, effective anti-disturbance capability, and high accuracy for rotor position and speed estimation compared to established benchmark methods, demonstrating its feasibility for mid-to-low speed sensorless PMSM drives.

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.

Based on the application of sensorless control for permanent magnet synchronous motors(PMSM), this paper put forward an improved sliding mode observer(SMO). The conventional SMOs use discontinuous step sign functions as switching functions, which cause chattering problems in the estimation of back electromotive force. Therefore, a smooth activation function is adopted as the switching function. An adaptive reaching law is devised to enhance stability of observing. To address the delay of phase issue caused by low-pass filters(LPF), an adaptive cut-off frequency is designed. The speed and angle information are estimated by using a phase-locked loop(PLL) in the place of of the arctan function, and phase compensation is implemented. Finally, the system of controlling motor is simulated in Matlab to verify that the sensorless control method according to the improved SMO has the effect of reducing chattering and improving the control accuracy of the system.

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 an improved Sliding-Mode Observer (SMO) for the sensorless control of a five-phase induction motor, which substitutes a sigmod function for the sign function. The conventional SMO is robust against parameter variations and disturbances, however, it has serious chattering problem in the steady state. The proposed method is utilized to reduce the chattering, and the rotor flux is also obtained from SMO for direct field oriented control. The convergence of the improved SMO is analyzed, and sufficient conditions are given to prove the stability. Simulation and experimental results are verified the effectiveness of the proposed method.

In high-speed permanent magnet synchronous motor (PMSM) drive systems, low switching frequencies increase discretization errors in conventional sliding mode observers (SMOs). This results in greater harmonics in the estimated stator currents and back electromotive force (EMF), thereby degrading the accuracy of speed and position estimation. This paper investigates steady-state position errors of conventional SMOs under low carrier ratios. The analysis reveals that the primary causes are model discretization errors and quasi-sliding mode motion errors. To address these issues, exact discrete voltage equations are derived in the two-phase stationary reference frame. Subsequently, an improved discrete-domain SMO is developed, incorporating a redesigned back-EMF computation method to enhance speed and position estimation accuracy. Furthermore, to improve dynamic performance under high-speed operating conditions, an adaptive quadrature phase-locked loop (AQPLL) is introduced. This method employs a stochastic gradient descent (SGD) algorithm for online parameter tuning, expanding the bandwidth for faster transient response while maintaining noise immunity at low speeds. The proposed method is validated through experiments on a low-inductance PMSM, demonstrating high estimation accuracy, reduced transient errors, and robust performance under parameter mismatches at a carrier ratio as low as 7.

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.

Sinusoidal Permanent Magnet synchronous motors have become more popular for new drives. Advantages of PMSMs includes high torque to inertia ratio, high efficiency and high power density. For the PMSMs it is necessary to estimate the rotor position and speed as well. A good error filtering, low angle error and dynamic performance can be obtained with feedback observers. The sliding mode observer (SMO) is one of the observers with a system model suitable for PM synchronous motors. The study deals with the analysis based on simulation of PMSM with space vector pulse width modulation in MATLAB environment. In this paper sensorless estimation of speed and position using SMO with tan hyperbolic function achieved. The result is compared with SMO using sigmoidal function. The simulation results shows that sliding mode observer with tan hyperbolic function gives smooth performance. Keywords: PMSM, Sliding Mode observer,Sigmoidal function, tan hyperbolic function

Anti-disturbance speed control of low-speed high-torque PMSM based on second-order non-singular terminal sliding mode load observer

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