Sensorless vector control approach for the interior PM synchronous machine with DC-offset compensation loop

Two different DC offset compensators for sensorless PMSM, motor drives with wide speed range flux linkage observers, are introduced and compared. The first one is an improved flux observer with PI correction and no need for mover speed and phase adaptation. The second one is a novel flux observer with an active disturbance rejection controller (ADRC) compensator without mover speed adaptation. The ESO built into ADRC is able to detect and compensate for both internal model disturbance and external load disturbance, resulting in a controller with superior dynamic responsiveness and robust regulation. In both scenarios, an injected direct current (DC) offset is calculated and maintained by the PI integral part and ADRC, which effectively compensates for the DC biases and drifts caused by the sampling channels. Compared to the PI controller, ADRC demonstrates greater transient performance and disturbance robustness. The results of theoretical analysis and Matlab simulations have confirmed the feasibility and efficiency of the proposed strategy.


Introduction
Interior PM Synchronous machines are utilized in various applications due to their potential benefits, including a high torque-to-weight ratio and excellent efficiency.Present transmission technology often employs vector control as well as DTC based on the orientation of the stator or rotor's magnetic field, and the key to accomplishing control is the precise observation of flux linkage.The current, voltage and hybrid observation models are common flux observation approaches [1].Nonetheless, the current and hybrid models depend heavily on the rotor parameters and rotational frequency, which leads to observation inaccuracies, especially the case whenever the motor operates at moderate and high frequencies [2].In addition, the voltage-type rotor flux observer (VRF) is insensitive to the rotor side variables of the machine, and it doesn't require speed information; hence its parameter resilience is rather strong.Simultaneously, this method is straightforward to execute and frequently utilized in engineering research methods.In modern engineering application fields, the DC drift and integral saturation challenges caused by the VRF pure integrator would be compounded by influences including electromagnetic interference, sensor inaccuracy calibration, and analog to digital sampling signal error [3].Closed-loop stator flux estimators, enhanced-integrator technology, and correction error using reference rotor flux/stator flux magnitude [4][5] have been established by a community of scholars utilizing various compensation strategies.These methods modify the stator flux magnitude to counteract the DC offset.Unfortunately, they do not eliminate the DC component entirely, and they cause a phase delay, especially at low speeds.The performance of a PMSM-controlled system is highly dependent on its control.To regulate PMSMs, numerous controllers, such as PID control, SMO, adaptive control, ADRC, and intelligent control, have been developed [6][7][8][9].PID control is most commonly utilized.

Conventional flux observer analysis
Sensorless stator flux estimate using the stator voltage reference model ( 1 Where; Substituting the pure integral linkage with a first-order low-pass filtering link will mitigate integral saturation issues to some extent, but it will introduce additional phase and amplitude errors.The issue of DC bias caused by sensor measurement in practical contexts cannot be addressed by employing lowpass filtering due to the low frequency of DC bias.

Design of novel observer
In this section, an improved flux observer is presented in order to achieve a more precise rotor position.
The improved flux observer uses the PI and ADRC compensation using the stator-flux reference in the correction loop without introducing phase lag and rotor speed adaptation.Figure 2 depicts the improved flux observer's structure.

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The estimated stator flux linkage is obtained under synchronous rotating coordinates After 2r/2s transformation, the estimated stator flux linkage values sα \ and sβ \ in the two-phase stationary coordinate system are obtained.
. Block diagram of the proposed rotor position estimation system.

DC offset error correction
The observed stator currents are utilized in estimating the flux linkage sα \ and sβ \ .Since currents are detected by physical sensors, instead of the typical observer based back EMF or flux linkage, sensorless control performance can be enhanced in the starting and low-speed ranges without the need for integration; therefore, there will be no integral drift.Another common method is to estimate the flux linkage, which is the integration of back-emf.The harmonic flux-linkage vector sh \ in stator reference follows a circular path in the case of constant-magnitude flux control.In the presence of a DC-offset vector sdc \ , the resulting flux vector s For the purpose of disturbance compensation, a PI compensator with parameters p k i k is used to make an approximation of the DC-drift input vector ^p i . Estimation of the closed-loop flux is provided by To suppress the integral drift, the correction term applied to the PI compensator or ADRC compensator consists essentially of the imbalance between the estimated flux as well as the projected reference flux respectively.This method forces a circular trajectory with asymptotic phase convergence on the flux vector.The DC-estimation dc e is retained by the PI integral component, which eliminates the DC drift entirely.The flux estimator functions as an integrator with zero lag and high dynamics.
The new control technology of active disturbance rejection control (ADRC) offers the advantages of a simple control structure and robustness to plant uncertainty and external disturbances.The ADRC evaluates and adjusts for plant uncertainty and external disruptions actively.It is straightforward to apply in practical applications and robust against unmodeled physical properties and external disruptions.
The control parameters of the ADRC are observer bandwidth .Moreover, the anti-peaking feature is disabled.Figure 4 illustrates the proposed method for a DC Offset error compensator, which can be divided into two phases.In the first step of the calculation, the DC offset error was determined by taking the estimated stator flux and subtracting it from the actual stator flux Conventionally, phase-locked loops (PLLs) are used to determine the phase and frequency from input signals.Using the vector cross product of the aforementioned two flux linkages as the deviation signal, the PI controller is used to estimate the speed, and a speed integral is used to estimate the position of the mover.The position will be tracked after the position estimate error is zero ˆ0 T T T ' and sdcD '\ and sdcE '\ .When the rotor position estimate variation is very small for the phase-locked loop architecture shown in Figure 3.

Simulation results
The general block diagram of the ADRC and PI DC offset correction loop-based sensorless PMSM system is illustrated in Figure 5.This system uses the 0 d i control mechanism.MATLAB/Simulink was utilized in order to construct the simulation model of the PMSM control system; Table 1 contains information regarding the motor's parameters.6 and Figure 7 depicts dynamic characteristics of the ADRC controller and the PI controller in reference to the DC drift error portion.When a 0.5 V DC drift error is added at 0 s to the line-to-line back-EMF, the back emf maintains the severe pulsation.With no delay, the proposed strategy initiated DC offset error correction in real time.The DC-offset impact is reduced gradually initially by the PI compensator.Within fewer than two seconds, the PI integral part memorizes the DC-offset value, keeping the drive insensitive to DC-bias.While adopting the optimized ADRC compensator Suppresses the DC-drift influence within less than 1 second, less time is required to achieve stability and demonstrate robust interference suppression.The DC-drift error value is increased from 0.5V-0.6V at 5 s.The PI compensator gradually removes the DC drift effect within less than 1.3 seconds, while the ADRC compensator restricts the DC-bias impact within less than 0.5 seconds.Since compensation is conducted even if the DC-bias error part is applied, the flux linkage oscillation is efficiently eliminated by the DC-drift compensator, namely the PI controller and ADRC controller, and its stable value is maintained.Even though the amplitude of the DC drift error portion varies, it is possible to confirm that the real-time compensating functions are satisfactory.As can be seen in the simulation results, the new ADRC control algorithm offers excellent steady-state performance as well as dynamic performance.The simulation findings show that ADRC is superior to PI in its capacity to eliminate DC offset.Figure 8 compares the angle estimation error in PI and ADRC-based methods.The proposed adaptive approach smoothly decreases the theta-err position error to zero in both circumstances, the flux linkage constant converges to its true value.
As seen in Figure 9 the estimated flux linkage closely resembles the real flux linkage, and the calculated back emf does not contain high-frequency components.The proposed ADRC approach smoothly removes the DC-offset, and the flux linkage constant converges to its true value.The orthogonal property of the back-EMF value is restored with the help of the PI compensator as shown in Figure 10.After initialization, the residual error gradually diminishes, and the flux estimate centers at the origin.Figure 11 depicts the simulation results of speed for the two control methods.The algorithm for PI control oscillates and overshoots.When a 0.5-volt DC-offset is applied at 0 seconds.The ADRC returns to a steady state after 0.4 s, while the PI returns to a steady state after 1.7 s. when the DC-offset error value is changed to 0.6 V at 5 s.The ADRC returns to a steady state after 0.4 s, while the PI returns to a steady state after 1.7 s.The simulation findings indicate that the efficiency of ADRC in rejecting disturbances is superior to that of PI.It is simple to determine that the position sensorless control system featuring the ADRC controller is superior to the PI controller in terms of control speed and steady-state accuracy, demonstrating the developed controller's usefulness.

Conclusions
In this study, we present a real-time correction method for estimating flux with precision, despite the presence of an existing DC offset component.The suggested research promotes a straightforward pure integration with DC offset correction loop based on the motor voltage and current models.It demonstrates a precise flux estimation performance at low speed.The detailed analysis illustrates how a DC component error affects the estimation procedure.Following that, an observer-based estimate is presented as a potential method for removing the DC offset.In the presence of the voltage sensor error, it is confirmed that the proposed approach can effectively handle the problem of low-speed flux estimate.The ADRC DC offset regulator is intended to replace existing PI DC offset regulators, achieving superior response rates, reduced overshoot, and control impact.Control speed and steady-state accuracy are both improved with the position sensorless control system equipped with the ADRC controller, proving the effectiveness of the proposed controller.
) is an appealing solution for all ac machines exhibiting sinusoidal flux distribution.It integrates a projected emf s e .

Figure 1 .
Figure 1.Classical voltage-type flux observer.A structure diagram of the Classical voltage-type flux observer is shown in Figure 1.Recently, numerous sensorless flux-linkage estimators employing voltage-model with equivalent integrators have been studied.All of them tend to exhibit the same frequency characteristics as the pure integrator:

Figure 2 .
Figure 2. Block structure of improved flux observer: (a) with PI DC-offset compensator; (b) with ADRC DC-offset correction loop.

Figure 3
Figure 3 represents the basic block design of the mover position estimation mechanism presented in this work.The suggested approach for rotor position estimation is mainly based on flux linkage.The stator flux linkage calculation formula is derived from the voltage flux linkage in the motor's two-phase stationary coordinate system.

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follows a circular path, with the origin offset by sdc \ .Consequently, the estimate ^^ŝ dc s sh \ \ \ provides information regarding the circle's eccentricity.The DC-offset vector sdc \ at the integrator's output is the result of the input DC-drift vector dc e or initial flux errors 0 s \ .For flux-linkage estimation, a closed-loop integrator with PI correction and ADRC correction for DC offset is proposed in Figure 3.A feedback correction error based on the estimated DC-offset flux vector DC is employed to cancel the DC portion (4).At the integrator output, the estimated flux ^s \ is acquired and ^sh \ is approximated by the estimated reference flux * s \ with the same amplitude * s \ and phase ^s T \ as the ^s \ vector.

Figure 8 .
Figure 8.(a) Estimated position under ADRC and PI Controller mode; (b) Comparison of angle error (degree) waveform Set Point (SP) = 200 RPM without load under different DC offset injection.

Figure 9 .Figure 10 .
Figure 9. Simulation waves of dynamic flux linkage estimations using the ADRC DC-offset compensator.
Figure 11.Comparison of dynamic rotor speed estimation using the PI controller and ADRC controller under DC offset.