Abstract
Introduction:
Predictive current control (PCC) for permanent magnet synchronous motors (PMSM) exhibits slow response and obvious chattering under parameter variation and load shock, while existing schemes cannot coordinate anti-disturbance performance, dynamic speed and battery power constraints.
Methods:
This paper designs an improved dynamic double-power reaching law (DPRL) with finite-time convergence and low chattering, embeds it into nonlinear active disturbance control (NADRC) coupled with an extended sliding mode disturbance observer, and adds a battery power limiting module. Simulations and dual-motor bench tests are implemented with multiple contrast algorithms and ablation groups.
Results:
The proposed strategy achieves zero overshoot across all test conditions. During sudden 10 N·m load, the speed drop is only 285 r/min with 1.5 s recovery; acceleration and reversal response time are reduced by 40% and 70% respectively, and d/q‐axis current ripples are significantly weakened.
Discussion:
The integrated DPRL‐NADRC PCC enhances PMSM robustness and dynamic performance under complex disturbances and power constraints. Future work will develop automatic gain tuning algorithms and validate the method under high‐speed demagnetization and multi-motor operating scenarios.
1 Introduction
Permanent magnet synchronous motors (PMSM), with their high power density, high operating efficiency, and excellent speed regulation performance, have become the core drive components in industrial transmission, new energy equipment, rail transit and other fields. The current loop is the core link of the speed regulation system. The control performance directly affects the dynamic response rate and the steady-state control accuracy of the entire motor system. This is crucial for ensuring the motor operates stably and efficiently (; ). Predictive current control (PCC) is widely utilized in the current loop control of PMSM due to its technical advantages of fast response speed, high control accuracy, and the ability to achieve spot-free tracking. However, when the motor is actually operating, the system is vulnerable to a combination of internal and external disturbances, such as changes to the motor parameters, sudden changes in load, and external electromagnetic interference. Additionally, traditional PCC strategies present inherent challenges, including evident buffering and limited anti-disturbance capabilities. This makes balancing the dynamic response performance and steady-state control accuracy of the system under complex conditions involving strong nonlinearity and multiple disturbances difficult. It restricts its engineering application in high-precision and high-reliability speed regulation scenarios (). Therefore, there is an urgent need to optimize and improve the traditional PCC strategy.
Ullah K et al. conducted a systematic review of various robust speed control techniques for permanent magnet synchronous motors, addressing the challenges of nonlinearity, time-varying parameters, and susceptibility to disturbances in speed regulation. This article focuses on sorting out two mainstream schemes, H sliding mode control and H current control based on HJI, and summarizes the development trend of permanent magnet synchronous motor speed control technology through comparison. The review analysis shows that H class robust control can achieve precise speed tracking, suppress overshoot, and effectively resist parameter perturbations and load disturbance (). Yang Q and Song X developed a control strategy involving a fractional-order PIλDµ cost function to overcome the issues of reduced current control accuracy, increased ripple and reduced system stability resulting from parameter mismatch in the PMSM finite state model of the PCC. The strategy involved introducing fractional calculus operators to improve robustness, combining model predictive control optimization features with fractional PIλDµ dynamic adjustment capabilities, and constructing fractional calculus components to reduce steady-state errors and harmonic oscillations. The findings reveal that the strategy effectively enlarges the system’s bandwidth, greatly reduces current ripple and harmonic distortion, and strengthens system stability (). Teymoori V et al. proposed an adaptive PI current control technology based on a multivariable sliding mode extreme value search framework for the sensorless speed regulation scenario of high-power propulsion permanent magnet synchronous motors. This method adopts gradient descent strategy for real-time self-tuning of PI gain, with small computational complexity and easy deployment on general microcontrollers, which can weaken the effects of parameter and load disturbances. The simulation and physical experiment results show that this control scheme has high tracking accuracy, strong robustness against load disturbances, and is minimally affected by changes in motor parameters (). Nasab et al. proposed an adaptive PI control strategy based on a multivariable sliding mode extreme value search algorithm to address the speed stability control requirements of electric vehicle permanent magnet synchronous motors under load torque disturbances. This method combines speed error and adaptive sliding surface online dynamic tuning of PI parameters, with low computational complexity and adaptability to mid-range processors, which can weaken the interference of motor parameters and load fluctuations on the system. The simulation results show that this scheme has high speed tracking accuracy, strong resistance to load disturbances, and is less affected by changes in motor parameters ().
The Nonlinear Active Disturbance Rejection Controller (NADRC) demonstrated strong robustness thanks to the real-time disturbance estimation and compensation capabilities of the Extended State Observer (ESO). However, it has the drawbacks of complex parameter tuning and poor convergence characteristics of the Nonlinear State Error Feedback (NLSEF) link. The traditional sliding-mode approach law is prone to problems such as steady-state buffering and difficulty in balancing convergence speed and accuracy. Xia H et al. proposed a speed regulation method for PMSM systems that is affected by total disturbances such as parameter variations, model errors, and sudden load changes. The method constructed a tracking state space model and designs an adaptive, law-based, nonlinear ESO to estimate total disturbances and perform feedforward compensation. The findings reveal that the controller has good speed regulation and anti-interference performance, and its reliability and superiority have been confirmed (). Shao Y et al. proposed a method of using fractional active disturbance rejection control as the relevant controller in response to the problem that linear controllers are difficult to balance high precision and stability in space gravitational wave detection. The method used a nonlinear controller to regulate the free system, enabling frequency division control and interference suppression through feedback compensation to meet detection performance requirements. Results show that, within the detection’s sensitive frequency band, both the satellite–test mass relative displacement and residual acceleration remain at ultra-low levels. The controller ensured robustness, control accuracy, and enhanced response performance (). Shen Z et al. proposed an improved linear/nonlinear active disturbance rejection switching control strategy for high-performance operation control requirements of bearingless asynchronous motor systems and the degradation of tracking performance under large disturbances of NADRC. The strategy automatically switched control modes based on system stability and perturbation amplitude, improved the fal function and corrected unknown parameters through two algorithms. The outcomes demonstrate that the proposed strategy leverages the strengths of both linear active disturbance rejection control and NADRC, thereby improving the performance of the motor rotor suspension and enhancing the system’s ability to reject disturbances ().
To sum up, there are still multiple limitations to the existing improvement schemes for predictive current control of permanent magnet synchronous motors: the fractional order PI λ D µ model predictive control has a high calculation order and requires a large amount of parameter trial and adjustment work; The observation accuracy of PCC without model disturbance is highly dependent on the bandwidth of the observer, and the disturbance compensation lags behind when the load suddenly changes; The hardware modification cost of PCC for multi-level inverters is high, and the computational cost is high; The conventional double power sliding mode approach law has a fixed exponent and cannot adaptively balance convergence speed and sliding mode chattering. Simple nonlinear self disturbance rejection also suffers from severe coupling of nonlinear error feedback parameters and cumbersome tuning; At the same time, most existing research ignores the constraints on the output power of power batteries, which can easily lead to current exceeding limits and speed instability under battery undervoltage and power limited conditions. Moreover, most algorithms only verify performance under a single operating condition, lacking comprehensive verification of sudden load, acceleration and deceleration, and multi disturbance composite operating conditions of forward and reverse rotation. In summary, existing solutions are difficult to simultaneously consider disturbance rejection, dynamic response, steady-state pulsation suppression, and adaptation to new energy supply scenarios. There is a lack of collaborative control schemes that integrate adaptive sliding mode convergence, high-precision disturbance observation, and power limiting. This is also an urgent gap that needs to be filled in this study. Therefore, to tackle thees challenges, this study introduces the concept of Finite-Time Convergence (FTC) into the PCC of PMSMs. It designs an improved Double Power Reaching Law (DPRL) and integrates it with a Nonlinear Active Disturbance Rejection Controller (NADRC) to construct a composite control strategy. By optimizing the observer and error feedback components, this approach achieves precise disturbance compensation and rapid system convergence, thereby offering a novel solution for high-precision control of PMSMs under complex operating conditions.
The innovation of this research lies in two aspects. First, it introduces the concept of FTC into the PCC of permanent magnet synchronous motors (PMSMs) by designing an improved DPRL. This enables rapid convergence when the system is far from the Sliding Mode Surface (SMS) through dynamic adjustment of the double-power parameters. Second, the improved DPRL is integrated into the NLSEF link of the NADRC. This integration combines the strong robustness of Sliding Mode Control (SMC) with the disturbance rejection structure of NADRC, thereby reconstructing the control logic of the NLSEF. Finally, a power constraint module is introduced into the control strategy to dynamically adjust the speed and current based on the actual output power of the power battery, enhancing the operational stability of the motor system in power-constrained scenarios. The improved dynamic double power convergence law proposed by the research institute introduces a dynamic exponential adjustment term related to the sliding mode variable and system state, which can autonomously switch the convergence rate based on the distance between the system and the sliding mode surface. When the distance from the sliding mode surface is far, the convergence speed is greatly increased, and the control gain is weakened near the sliding mode surface to reduce chattering; Simultaneously using hyperbolic tangent function instead of sign function to eliminate current ripple caused by discontinuous switching, achieving decoupling optimization of finite time convergence and low jitter from a theoretical perspective. On the practical level, the improved approach law will be used to reconstruct the nonlinear self disturbance rejection error feedback link, simplify the problem of multi parameter coupling tuning, and improve the overall disturbance observation accuracy by combining it with an extended sliding mode disturbance observer. In addition, a power battery power constraint module will be added to complete the power closed-loop limiting control, which is different from the existing single approach law optimization or simple self disturbance rejection improvement schemes. It realizes the coordinated optimization of sliding mode approach, disturbance compensation, and power constraint modules, and simultaneously improves the dynamic response speed and steady-state control accuracy under motor parameter perturbation, sudden load, acceleration and deceleration forward and reverse operating conditions, with stronger engineering adaptability.
2 Experimental platforms and testing plans
Research on building Simulink simulation platforms and physical testing platforms for towed permanent magnet synchronous motors to complete algorithm validation.At the hardware level,two 4-pole permanent magnet synchronous motors are used in a paired structure. The main drive motor is powered by a three-phase two-level voltage inverter, and the load motor is matched with an adjustable magnetic powder load to simulate step disturbances; The torque speed sensor and three-phase current Hall sensor collect real-time operating data, and the upper computer stores waveforms through high-speed waveform recorders and oscilloscopes. The DC stabilized power supply simulates the output of the power battery. Core motor parameters: stator resistance of 0.9585Ω, d/q-axis inductance of 5.25 mH, permanent magnet flux of 0.1827Wb, moment of inertia of 0.063 kg m2, DC bus voltage of 300 V. The software relies on Matlab/Simulink to complete offline modeling of control algorithms,and improves DPRL-NADRC code online deployment through DSP28335 chip. The PWM switching frequency is set to 10 kHz.
The experimental design is divided into three typical operating conditions: 0-1000r/min acceleration and deceleration condition, ±800r/min forward and reverse switching condition, and sudden load disturbance condition of 10 Nm at rated speed; The data acquisition cycle is 0.1 ms, recording three indicators: speed fluctuation, recovery adjustment time,and d/q-axis current ripple. Each operating condition is repeated 5 times, and the average value is taken to eliminate random errors for horizontal comparison of multiple control strategies.
3 Methodology
The research adopts a single step finite control set model to predict the current control architecture. Based on the PMSM voltage equation in a synchronous rotating coordinate system, a forward Euler discretization method is used to construct a d/q-axis current prediction model. The system sampling period is taken as the prediction step size, and the prediction time domain is set to 1.
Complete single step current state deduction, and directly solve the predicted current value for the next moment based on the current, voltage, and angular velocity at the current moment. The complete optimization process is divided into four steps: 1) Collect real-time three-phase current, rotor position, and obtain the actual current of the d/q axis through coordinate transformation; 2) Traverse all candidate voltage vectors of the inverter and substitute them into the discrete prediction model to calculate the predicted current corresponding to each vector; 3) Construct a cost function with current tracking error as the core, and select the optimal voltage vector that minimizes the cost function; 4) Output the optimal vector to the SVPWM module to drive the inverter.
At the level of computational complexity, the basic MPCC needs to traverse 7 sets of basic voltage vectors to complete iterative optimization. This paper will improve the DPRL-NADRC disturbance compensation pre correction prediction model without increasing the number of candidate vectors, only slightly increasing the computational complexity of a single iteration. The overall single cycle computation time is about 22 μ s, which can be adapted for real-time operation of mid-range industrial DSPs. This prediction framework serves as the foundation for the underlying current loop and is coupled with the improved sliding mode approach law and nonlinear self disturbance rejection observer to form a complete composite control scheme, which compensates for the lack of explanation in the original text regarding the prediction control model, optimization process, and computational cost.
3.1 Motivation
NADRC is an advanced control strategy whose core idea is to assess and compensate for the total disturbances in the system in real-time through an ESO, and it has strong robustness and immunity. The structure of NADRC is indicated in Figure 1.
FIGURE 1
Figure 1 illustrates the core principle of the NADRC, which involves consolidating model uncertainties, parameter variations and external disturbances into a single ‘total disturbance’. This total disturbance is then observed and compensated for in real time using a Nonlinear ESO (NL-ESO). By integrating this process with NLSEF, the controller realizes a control effect characterized by rapid response and zero overshoot. The architecture comprises three core modules: the Tracking Differentiator (TD), the NL-ESO, and the NLSEF. These modules serve, respectively, to schedule the command transition process, observe the system states and total disturbance, and implement the nonlinear error feedback. The control workflow proceeds sequentially as follows: receiving the command input, scheduling the transition trajectory, observing system states and disturbances, calculating the control signal, compensating for disturbances, and outputting the final control command. Overall, the system possesses distinct advantages, including independence from precise system models, simultaneous suppression of both internal and external disturbances, rapid response with no overshoot, and adaptive nonlinear gains. Consequently, it finds widespread application in highly nonlinear and disturbance-prone systems, such as those involving servo mechanisms, electric motors, power supplies, mechanical systems, and Unmanned Aerial Vehicles (UAVs), as documented in references (; ). The TD accepts the reference signal as its input and, utilizing nonlinear functions, generates tracking and differentiation signals characterized by minimal jitter; it offers the advantages of low overshoot and rapid convergence while effectively filtering out noise disturbances. The calculation of the tracking signal is denoted in Equation 1.
In Equation 1, represents the output value of the fhan function; means the tracking signal of the th step; indicates the differential signal of the th step. represents the tracking speed factor; refers to the integration step size. ESO, as the core component of ADRC, does not require an object model. It can observe the system state and total perturbation by input and output alone, and transform the object into a cascade system through perturbation compensation. Its observation and compensation capabilities directly determine the control performance (; ). The calculation formula of ESO is denoted in Equation 2.
In Equation 2, represents the observation error; represents system state observations; represents the actual output of the system; stands for the derivative of system state observations with respect to time; denotes error correction gain; represents the power parameter; represents the width of the linear interval; represents input gain; represents control quantity. The calculation formula for NLSEF is denoted in Equation 3.
In Equation 3, represents the base control quantity. The NACDR controller can be constructed by the above method.
3.2 Improved DPRL design for PMSM PCC
FTC systems ensure rapid convergence of the system state to the equilibrium point within a finite time, providing higher steady-state accuracy and strong robustness. Introducing it into the PCC of PMSMs can enhance the convergence performance and response speed of the current loop under parameter perturbation and load disturbance, enabling the DC/AC shaft current to quickly track a given value within a finite time, while suppressing overshoot and jitter, and improving the dynamic quality and interference resilience of the control system. It enables PCC to maintain excellent control performance in motor operating conditions with strong nonlinearity and disturbance (; ). For finite-time systems, it is essential to design controllers that leverage the principles and methods of FTC. Such controllers enable the system to reach its desired state and maintain stability within a finite time interval. The nonlinear system is presented in Equation 4.
In Equation 4, stands for the derivative of the state vector with respect to time; means the nonlinear state function; denotes the state vector; represents time; represents -dimensional real number space. The equilibrium points of the system have excellent local FTC characteristics, that is, for any given initial state in the domain of the system, a non-negative resting time closely related to that initial state can be found. The solution of the system’s motion trajectory from this initial state is always defined within a finite time interval and converges precisely to the equilibrium point of the system after reaching the pause moment, achieving a stable state residence. The FTC formula for nonlinear systems is indicated in Equation 5.
In Equation 5, represents the initial time; represents the initial state; represents the solution of the system. If finite-time stability of the system’s equilibrium points is achieved via FTC based on Lyapunov stability, the local neighborhood can be extended to the entire state space for global stability. A related lemma states that the origin is finite-time stable if there exists a positive definite smooth function satisfying certain conditions; the settling time depends on the initial condition and has an upper bound. The upper bound of the stopping time is denoted in Equation 6.
In Equation 6, represents the smooth function; is a real number. According to Equation 6, the system is globally finite-time stable when the neighborhood is full space and the Lyapunov function is unbounded. Time-varying Lyapunov functions can converge to zero in finite time when they satisfy differential inequalities. A system that has both global asymptotic stability and local FTC is globally finite-time stable. DPRL is a typical form of approach law for achieving FTC. By designing two power terms—one with exponent less than 1 and the other greater than 1—the system approaches the SMS quickly when far away, and converges smoothly when near it. This ensures finite-time arrival on the SMS, satisfying the FTC requirement of the closed-loop system. It has the advantages of fast response, strong robustness, and low chattering (). However, the traditional sliding mode approach law has problems such as large jitter, poor immunity, and difficulty in balancing convergence speed and control accuracy. Therefore, an improved variable-speed double-power approach law introducing system state variables and sliding mode variables is proposed, aiming to dynamically adjust the approach process, accelerate convergence speed while reducing jitter and improving system immunity. The improved DPRL is denoted in Equation 7.
In Equation 7, represents the first derivative of the SMS variable; and both are control gain coefficients; represents sliding mode variable; represents dynamic exponential parameters; represents adjustment parameters; is fixed exponential parameter of the DPRL; and both are moderating parameters of dynamic exponents; represents state variable; represents time. When the system is farther from the SMS, the main action term makes the approach speed faster. When closer to the SMS, the principal action enables the system to reach the equilibrium point quickly. Meanwhile, using hyperbolic tangent functions instead of traditional sign functions can reduce chattering and achieve dynamic approach. The improved DPRL achieves multi-stage rapid convergence and simplified analysis through dynamic exponential parameters, with a convergence speed superior to the ordinary double-power approximation law and no buffering in steady state. Constructing a positive definite Lyapunov function , taking the derivative of time and substituting it into Equation 7 to improve the dynamic double power law, can be obtained, which satisfies the finite time stability criterion. The upper bound of the sliding mode surface arrival time can be derived, proving that the system state can reach the sliding mode surface in a finite time; At the same time, the hyperbolic tangent function is used to replace the sign function, eliminating the high-frequency chattering caused by discontinuous switching terms. From a theoretical perspective, it is demonstrated that convergence speed and steady-state pulsation can be optimized synchronously, compensating for the shortcomings of traditional fixed parameter DPRL that cannot be adaptively adjusted.
3.3 PMSM PCC method based on improved DPRL-NADRC
After constructing the improved DPRL, the study combined it with NADRC to design a PMSM PCC strategy. This strategy introduces the improved DPRL into the NLSEF, using FTC to ensure rapid stability of the system. Meanwhile, combining an ESO instead of a nonlinear ESO simplifies parameter tuning and enhances dynamic performance. The extended sliding mode observer for the improved DPRL-NADRC is indicated in Equation 8.
In Equation 8, represents the tracking signal of the actual rotational speed; represents the gain control coefficient; represents the cross-axis current; is the observation value of the combined disturbance term; represents the SMC term; denotes the sliding mode observer gain. Due to the problem of discontinuous switching of the sign function, the study replaced it with a saturation function. At this point, the final calculation formula for the extended sliding mode observer of the improved DPRL-NADRC is denoted in Equation 9.
In Equation 9, represents the linear term gain; represents the synovial plane error; represents switching gain; represents the saturation function. This observer categorizes model errors, parameter perturbations, and external loads into lumped disturbances, and compensates for disturbance estimation bias in real-time through sliding mode dynamic gain; Based on the Lyapunov second method analysis of observation error dynamics, it can be proven that the observation error origin is globally finite time stable, and the observation value can quickly approximate the true total disturbance. The parameter tuning process of NLSEF in NADRC is complex and experience-dependent, which can lead to limited system robustness and control accuracy (; ; ). Therefor, the study combines the anti-disturbance structural characteristics of NADRC with the strong robustness of SMC to construct a fusion control strategy. By introducing the sliding mode mechanism to reconstruct the NLSEF, the parameter tuning process can be simplified while retaining the ADRC’s real-time estimation and compensation capabilities for total disturbances, effectively improving the control accuracy and dynamic effectiveness of the system under complex conditions. Based on this, Equation 5 can be rewritten to obtain Equation 10.
In Equation 10, represents the speed tracking error; represents the speed reference command; represents the rotational speed observations output by the expanded observer; represents the median value of the cross-axis current; represents the speed error signal; indicates alternating current control instructions; represents the combined perturbation observations output by the expanded observer. To reduce the tuning parameters, the study uses a linear SMS. Combining the linear SMS with the improved DPRL yields Equation 11.
In Equation 11, represents the design parameters of the SMS; represents SMS variables. The improved DPRL-NADRC control structure is shown in Figure 2.
FIGURE 2
In n Figure 2, compared to NADRC, the core improvement of DPRL-ADRC lies in the following aspects: replacing the traditional NLSEF with a DPRL-NLSEF integrated with SMC, thereby introducing DPRL and a saturation function to optimize convergence characteristics and suppress chattering, and substituting the nonlinear ESO with an extended sliding mode disturbance observer to enhance disturbance observation accuracy and robustness. Simultaneously, the nonlinear TD is retained to prevent excessive errors from leading to control signal saturation. The PCC system for a PMSM based on the improved DPRL-NADRC is depicted in Figure 3.
FIGURE 3
In Figure 3, the DPRL-ADRC controller generates the difference between the reference and actual rotational speeds of the PMSM, which, together with the axial zero current instruction, is sent to the model-free and step-free current prediction controller. The ESO observes the current and disturbance and provides compensation. The current prediction controller outputs a voltage command, which drives the voltage-type inverter after Park inverter conversion and space vector pulse width modulation. Meanwhile, the motor’s three-phase current is fed back to the current loop via Clark and Park transforms, while speed feedback to the speed loop is collected by a sensor. The speed control of PMSMs is achieved. After embedding the improved approach law into the NADRC nonlinear error feedback channel, the closed-loop system consists of a series structure consisting of an observation subsystem, a sliding mode approach subsystem, and a predictive current control subsystem. Construct Lyapunov functions for each subsystem to demonstrate stability step by step. The total Lyapunov derivative is negative, indicating that the entire composite control strategy is globally consistent and finite time stable. 1t has theoretical robustness in the face of parameter disturbances and load changes, filling the gap of the original text that only verifies through simulation and lacks complete mathematical stability proof.
3.4 Motor predictive power control strategy optimization
Since motor vector control decouples through coordinate transformation to convert three-phase intersecting flow to two-phase direct flow, the inverter pulse width modulation signal is generated by the current vector. Therefore, the study also introduced a power module in the aforementioned control strategy to calculate the expected power and take into account the impact of the actual output power of the power battery. The motor predictive power control strategy with the power module introduced is denoted in Figure 4.
FIGURE 4
In Figure 4, the deviation between the rotational speed command and the actual feedback is regulated by a proportional-integral controller. Its output, together with the actual angular velocity and d/q-axis current signals, is processed by the power module to compute the expected power and generate the reference voltage components in the two-phase stationary coordinate system. The space vector pulse width modulation module converts the voltage vector into inverter switch signals, driving the inverter to output three-phase AC power for the PMSM. Three-phase stator currents are collected during the operation of the motor, and the current components in the two-phase system are obtained through Clark transform, and then the direct and alternating axis currents in the rotating coordinate system are obtained through Parker transform and fed back to the power module for closed-loop control to achieve current predictive control of the PMSM considering the battery output power constraint. However, when the power battery is undercharged, its maximum output power often fails to meet the driving requirements, which affects the motor control performance and driving experience. For this, the power module compares the expected power of the motor with the actual output power of the battery. When the battery output power is insufficient, it controls the power by reducing the reference speed and limiting the control current. The process of the power module is shown in Figure 5.
FIGURE 5
In Figure 5, the current value is first predicted, and the desired motor power is then calculated based on the battery’s output power. Next, the deviation between the actual output power and the desired power is determined. Subsequently, this difference is evaluated: if the difference is not greater than zero, the control strategy remains unchanged; however, if the difference exceeds zero, operations to reduce the desired rotational speed and limit the current are executed.
4 Results
4.1 Comparison analysis results
To assess the ability of the developed PCC strategy, it was subjected to testing. The improved DPRL-NADRC model-free deadbeat PCC scheme was compared against the Discrete Adaptive SMC (DASMC) scheme and the Implicit Generalized Predictive Nonlinear Active Disturbance Rejection Control (IGPC-NADRC) strategy. Its feasibility and superiority were verified across three operating conditions: load addition and removal, speed acceleration and deceleration, and forward and reverse rotation. The speed and current waveforms corresponding to the load addition and removal tests are presented in Figure 6.
FIGURE 6
In Figure 6a, there was no overshoot in DASMC, IGPC-NADRC, and improved DPRL-NADRC during the motor startup phase. When loading and unloading, the DASMC speed dropped by approximately 7r/min and the adjustment time was 0.08s. IGPC-NADRC had a speed drop of 6r/min and a Recovery Time (RT) of 0.07s. Improved DPRL-NADRC speed dropped about 4r/min RT only 0.06s. In Figure 6b, compared with DASMC and IGPC-NADRC, the improved DPRL-NADRC had a faster tracking speed and smoother current under start-up and loading/unloading conditions. The results suggest that the improved DPRL-NADRC has better robustness and rapidity. The speed waveforms for acceleration and deceleration as well as forward and reverse rotation are denoted in Figure 7.
FIGURE 7
In Figure 7a, there was no overshoot in DASMC, IGPC-NADRC and the improved DPRL-NADRC, among which the improved DPRL-NADRC had better rapidity, with the response time shortened by approximately 0.015s. From Figure 7b, DASMC, IGPC-NADRC, and the improved DPRL-NADRC also had no overshoot during the speed commutation process, among which the improved DPRL-NADRC had a shortened response time of approximately 0.015s and was faster. The results suggest that the improved DPRL-NADRC simplifies parameter tuning while enhancing the control performance of the PMSM system.
4.2 Physical testing platform and verification results
To conduct an in-depth analysis of the proposed method, a PMSM test bench was set up for the study to simulate and analyze it. During the test, the control parameters of the PMSM were uniformly set as follows: pole pair number 4, stator resistance 0.9585Ω, d-axis inductance 5.25mH, q-axis inductance 5.25mH, permanent magnet flux link 0.1827Wb, bus voltage 300 V, moment of inertia 0.063 kg m2. The PMSM simulation test bench is indicated in Figure 8.
FIGURE 8
In Figure 8, the PMSM simulation test bench was mainly composed of two PMSMs, an inverter, AC/DC load motors, a tachometer and torque meter, adjustable load, an oscilloscope, a high-speed waveform recorder, an upper computer and a DC power supply, and was used for motor control performance testing. The core principle was to conduct a comprehensive verification of the control strategy of the motor under test by the two motors dragging each other to simulate the actual working conditions. To further verify the performance of the improved DPRL-NADRC, it was tested on the simulation test bench set up for the study. The loading and unloading speed waveforms are shown in Figure 9.
FIGURE 9
In Figure 9a, DASMC had no overshoot problem. After suddenly loading to 10 Nm at 28 s, its rotational speed dropped to 261r/min, and the RT was approximately 3.5 s. In Figure 9b, the improved DPRL-NADRC also had no overshoot problem. After sudden loading to 10 Nm, its speed dropped to 285r/min and the RT was approximately 1.5 s. The results suggest that the improved DPRL-NADRC is more robust. The loading and unloading current waveforms are indicated in Figure 10.
FIGURE 10
By comparing Figures 10a,b, compared with DASMC, the d-axis and q-axis currents of the improved DPRL-NADRC responded faster to load changes, with less fluctuation and smoother waveforms. The current variation times of DASMC and the improved DPRL-NADRC at sudden load changes were 32.2s and 29.4s, respectively. The findings suggest that the improved DPRL-NADRC has higher sensitivity. The acceleration and deceleration speed waveforms are denoted in Figure 11.
FIGURE 11
By comparing Figures 11a,b, both DASMC and the improved DPRL-NADRC had no overshoot and little speed jitter during acceleration and deceleration. Among them, the improved DPRL-NADRC had a faster response speed, with a 40% reduction in response time compared to DASMC and less speed jitter. The outcomes suggest that the improved DPRL-NADRC has better response performance and greater stability. The forward and reverse rotational speed waveforms are denoted in Figure 12.
FIGURE 12
By comparing Figures 12a,b, when the motor was switched from forward rotation to reverse rotation, neither DASMC nor the improved DPRL-NADRC showed obvious overshoot. Among them, the improved DPRL-NADRC took 30% of the time to return to stability during commutation compared to DASMC, could enter steady state faster, and had less speed fluctuation. The DASMC transition was smooth with little overshoot, but the recovery speed was slightly slower. The outcomes suggest that the improved DPRL-NADR has better dynamic response and stability in both forward and reverse rotation conditions. To test the proposed model, the study compared it with multiple models. The comparison results of the various models are presented in Table 1.
TABLE 1
| Model | Sudden load and speed drop | Load RT/s | Response time for acceleration and deceleration | RT for forward and reverse rotation |
|---|---|---|---|---|
| DASMC | 261 r/min | 3.5 | Reference value | Reference value |
| Model predictive control | 228 r/min | 2.8 | −12% | −25% |
| Non beat predictive control | 245 r/min | 3.1 | −8% | −18% |
| NADRC | 196 r/min | 2.2 | −25% | −45% |
| Fractional order PID-MPC | 183 r/min | 1.9 | −32% | −55% |
| Improved DPRL-NADRC | 152 r/min | 1.5 | −40% | −70% |
Comparison results of various models.
PID-MPC, stands for Proportional Integral Derivative Model Predictive Control.
In Table 1, the improved DPRL-NADRC had the least speed drop and the shortest RT under sudden load conditions. Meanwhile, it had the fastest acceleration/deceleration and forward/reverse dynamic response, with the response time reduced by 40% compared to DASMC, and the forward/reverse steady-state RT decreased by 70%. The above shows that the improved DPRL-NADRC outperforms several existing new control strategies in terms of dynamic response, robustness, steady-state accuracy, flutter suppression and engineering practicality. In order to quantitatively evaluate the contribution of the three core components of improved DPRL, sliding mode extended disturbance observer, and power constraint module of power battery to the system control performance, four ablation control groups were set, and the single module was removed to compare the dynamic immunity and steady-state index differences. The sudden 10N・m load condition was uniformly used as the test condition. The core performance indexes are shown in Table 2.
TABLE 2
| Method | Improved DPRL | Sliding mode ESO | Power constraint module | Load recovery time/s | D/q-axis current ripple peak/A |
|---|---|---|---|---|---|
| A | × | × | × | 2.1 | 2.14 |
| B | √ | × | × | 1.8 | 1.56 |
| C | √ | √ | × | 1.6 | 1.12 |
| D | √ | √ | √ | 1.5 | 0.78 |
Results of ablation experiment.
According to Table 2, only by adding the improved DPRL and relying on the adaptive index and hyperbolic tangent function to suppress sliding mode chattering, the current ripple is reduced by 27.1% compared to the basic scheme, and the speed is slightly improved. However, the disturbance observation lag and recovery time optimization are limited; After adding sliding mode extended ESO, the total disturbance observation accuracy is improved, the recovery time is shortened to 1.6 s, and the current fluctuation is further reduced; A power constraint module is added to the complete architecture, which automatically limits and reduces the current when the battery power is insufficient. The peak current ripple is reduced to 0.78A, and the optimal speed recovery time is 1.5s. The comparison of the three groups shows that improving DPRL optimizes convergence characteristics, suppresses steady-state pulsation, sliding mode extended ESO accelerates disturbance compensation, and the power constraint module is adapted to new energy power supply to prevent power exceeding the limit.
5 Summary and future work
To tackle the issues of insufficient immunity and slow dynamic response in traditional PMSM control strategies, this study proposes a PCC strategy based on an improved DPRL-NADRC, aiming to strengthen system robustness and rapidity under multiple operating conditions. The strategy introduces the improved DPRL into the NLSEF, replaces the traditional ESO with an extended sliding mode observer, and introduces a power module. The simulation outcomes denote that the speed drop during loading and unloading is only 4r/min and the RT is 0.06 s, which is 3r/min less than that of DASMC, the RT is shortened by 0.02 s, and the response time for both acceleration and deceleration and forward and reverse rotation is reduced by 0.015 s. In the simulation test bench experiment, it is found that after a sudden loading of 10 Nm, the speed drop is 24r/min, the RT is shortened by 2 s, the acceleration and deceleration response time is reduced by 40% compared to DASMC, the steady-state RT for forward and reverse rotation is only 30%, and the d/q axis current fluctuation is smaller and the waveform is smoother. The outcomes denote that the strategy has no overshoot under all operating conditions, combines fast response with strong robustness, and effectively balances system dynamic performance and steady-state accuracy. However, the gain coefficient tuning of this strategy still requires experimental trial and lacks a complete parameter tuning theory. Meanwhile, the control performance under high-speed demagnetization conditions has not been thoroughly verified. Therefore, in the future, the focus will be on parameter self-tuning algorithms, combined with intelligent algorithms for adaptive gain adjustment, and extended to complex conditions such as high-speed demagnetization and multi-motor coordination to enhance engineering application value.
Statements
Data availability statement
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.
Author contributions
WC: Writing – original draft, Writing – review and editing.
Funding
The author(s) declared that financial support was received for this work and/or its publication. The research is supported by Gansu Provincial Innovation Fund Project (Grant No. 2025B-510): Research on Strategies for Improving Consumption Stability of Regional Power Grids with Safe Integration of New Energy.
Conflict of interest
The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Generative AI statement
The author(s) declared that generative AI was not used in the creation of this manuscript.
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Summary
Keywords
double power reaching law, dynamic power, nonlinear ADRC, permanent magnet synchronous motor, predictive current control (PCC)
Citation
Chen W (2026) Predictive current control strategy for PMSM based on NADRC. Front. Mech. Eng. 12:1904143. doi: 10.3389/fmech.2026.1904143
Received
09 June 2026
Revised
15 July 2026
Accepted
17 July 2026
Published
07 August 2026
Volume
12 - 2026
Edited by
Hamid Reza Karimi, Polytechnic University of Milan, Italy
Reviewed by
Y. H Gong, North China University of Science and Technology, China
Mohammad Rajabi Nasab, Politecnico di Bari, Italy
Updates
Copyright
© 2026 Chen.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Wenjing Chen, 13830792312@163.com
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.