1. Introduction
As the core component for controlling the flow of fluid in the pipeline, electric valves are widely used in petroleum, metallurgy, environmental protection, water treatment and other industries [
1,
2]. Under high-temperature and high-pressure conditions, in order to solve the problem of high-temperature dynamic sealing, an integrated electric valve structure is adopted. The integrated structure of the traditional canned electric valve is mainly composed of an induction motor, an independent gear, coupling and a stroke control mechanism. In the limited installation space, the existence of the reducer greatly increases the axial length of the induction motor, which makes it difficult to achieve precise start/stop, and the control accuracy is insufficient. Permanent magnet synchronous motors (PMSM) have the advantages of a high power factor, a high torque density, and strong robustness [
3,
4], which can meet the harsh working environment and bring new opportunities to the valve field.
Although there are many studies [
5,
6] describing vector control and direct torque control techniques of permanent magnet motors under different load types, the research in the field of valves is still blank. The valve motor is limited by the size of the space, but it is still hoped that the stator current will be small during operation to reduce heat generation and extend the operating time of high-temperature systems. In order to achieve a larger torque under a smaller current, the MTPA control strategy is regarded as an effective way to improve the ability of output torque [
7,
8,
9,
10,
11,
12,
13]. The MTPA method is mainly divided into three categories, the look-up table method, the signal injection method, and the formula method. The look-up table method includes the experimental method and the finite element analysis (FEA) method. The look-up table method is complicated and cannot accurately track the MTPA point dynamically. Instead of finding
iq,
id using polynomials or lookup tables, some studies proposed using a proportional-integral (PI) controller to describe the relationship between
id and
iq. In reference [
7], Angelo Accetta et al. proposed an analytical formulation of the MTPA technique considering the magnetic saturation of the iron core for synchronous reluctance motors, and proved that the proposed technology can increase the torque per ampere. In reference [
9], T. Inoue et al. established a MTPA mathematical model of PMSM under the stator flux reference system, and optimized the stator flux for MTPA control based on the motor operating conditions. In reference [
10], the dynamic performance of MTPA is obtained by injecting virtual signals. In order to obtain the MTPA control accurately, Ke Li et al. proposed the MTPA method based on variable equivalent parameters, which is intended to accurately solve the MTPA control under different loads [
13]. Due to the introduction of a new topology, the MTPA model considering the parameters of the canned sleeve is analytically derived to truly reflect the control performance of the canned electric valve.
To implement vector control, sensors such as optical encoders and resolvers are used to provide a rotor position, which will increase the cost and complexity. However, in some special environments (e.g., dust, underwater, high-temperature, etc.), the application of this type of sensor is limited. The existence of the encoder will reduce the reliability of the electric valve under high temperature and high pressure. Therefore, the sensorless control of PMSM has always been a research hotspot in academia and industry [
14,
15]. In the control strategy of PMSM, common sensorless control technologies include open-loop estimation based on a mathematical model, the high-frequency signal injection method, the adaptive position observer method, the sliding mode observer method, and the extended Kalman filter. Among them, the accuracy of the open-loop estimation [
16] method is greatly affected by the motor parameters. When the motor is running, the motor parameters are always changing dynamically, and the system accuracy is poor. Although the closed-loop estimation methods such as model reference adaptive control [
17], state observer method [
18], and extended Kalman filters [
19] have good performance, they are only suitable for medium- and high-speed industrial applications, since the back EMF is too low and distorted to detect the flux position at low or zero speed. The high-frequency (HF) signal injection method uses its salient pole characteristics to estimate the rotor position under low speed or even at zero speed, which has nothing to do with the back EMF at the fundamental frequency and motor parameters [
20,
21,
22,
23]. Because this article focuses on the salient-polarity permanent magnet synchronous motor for valves, and the valve system has a low speed, the high-frequency signal injection method is adopted. According to the form of the injected signal, it is divided into voltage signal injection and current signal injection. High-frequency voltage signal injection is divided into rotating voltage injection [
20], pulsating sinusoidal voltage injection [
21], and square-wave voltage injection [
22].
Aiming at the problem that the single-degree-of-freedom controller cannot take into account both tracking and disturbance rejection, reference [
24] introduced 2-DOF control to improve the system’s disturbance rejection. In order to enhance the current regulation bandwidth and robustness of permanent magnet linear motor, a 2-DOF current controller is designed in reference [
25], which is combined with predictive current control (PCC) to obtain better dynamic and static performance. In order to achieve fast response and high-precision control of the bearingless permanent magnet synchronous motor, reference [
26] combines the neural network inverse (NNI) method with a 2-DOF internal model controller to enhance system tracking and disturbance rejection performance. Reference [
27] combines finite set model predictive control (FS-MPC) with 2-DOF control, and compared with conventional PI controller, it has better dynamic performance and enhances system robustness. In this paper, a 2-DOF control algorithm is used to improve the speed loop, and a position sensorless control system based on 2-DOF control is established.
The remaining contents of this paper are organized as follows. In
Section 2, the new topology of CEV-PMSM is proposed, and the integrated structure and operating characteristics are analyzed. In
Section 3, as an original contribution, the new MTPA model considering the canned sleeve parameters was developed. In
Section 4, sensorless control for CEV-PMSM is implemented. In
Section 5, the 2-DOF design of the speed loop PI controller is carried out to improve system robustness. Finally, some conclusions are provided in the last section.
2. Structure and Principle of the New Canned Electric Valve
2.1. Integrated Structure and Characteristics
The integrated structure of the electric valve removes the dynamic sealing structures such as the stuffing box, packing pressure plate, and packing pressure sleeve added in the high-temperature valve. The valve cavity contains a high-temperature, high-pressure liquid medium, so the canned sleeve is introduced into the air gap to form an integrated sealing structure with the housing. If the canned induction motor + reducer structure is adopted, due to the presence of the rotor copper bars, the stator and rotor double-layer canned sleeves are required to isolate high-temperature, high-pressure liquids, which greatly increases the reactive current required to establish the magnetic field, and shortens the running time of the high-temperature system. Moreover, the slip rate is greatly affected by the high-temperature liquid, and it is difficult to ensure accurate position control at low speeds. Special working conditions place higher requirements on the valve motor. The valve motor must have the properties of high temperature and high pressure resistance, accurate tracking and positioning, sealing reliability, and miniaturization advantages.
In order to solve the above problems, this article adopts the integrated structure of CEV-PMSM, as shown in
Figure 1. The CEV-PMSM does not need a rotor canned sleeve, which shortens the air gap length and reduces the air gap reluctance. Permanent magnets are used as the excitation source to generate magnetic field instead of stator current armature reaction, so the power factor and torque density are greatly improved. The taper sleeve is used to withstand the pressure on the top of the stator canned sleeve. As the valve stem moves up and down, the valve completes the operation of opening and closing.
2.2. Valve Operation Principle
Among them, Q refers to the flow through the valve, in m3/h. H refers to the differential pressure before and after the gate, in Pa. Q1, Q2 and Q3 represent the flow percentage, H1, H2 and H3 are the differential pressure at the corresponding flow positions, H0A, H0B, H0C are the flow resistance curves at the corresponding flow positions. Closing the valve gradually from the fully open position, the flow resistance characteristic curve of the pipeline changes from curve H0A to H0B, the operating point changes from A to B, and the flow rate decreases from Q1 to Q2. When the flow rate of valve reaches 20%, the operating point becomes point C, and the flow resistance characteristic curve is H0C. Because of the throttling of the fluid, the differential pressure between the front and rear of the gate increases. This differential pressure acts on the gate plate, which makes the stem need a large axial force to drive the gate. h = f(Q) is the differential pressure-flow rate characteristic curve.
The variation of differential pressure with flow rates is illustrated in
Figure 2.
According to engineering application and space size constraints,
Table 1 lists the main parameters of the CEV-PMSM.
The control analysis flow chart is shown in
Figure 3. Whether the new MTPA control or the sensorless control with 2-DOF is adopted, the cycle is terminated when the control performance required by the electric valve system is satisfied.
In this paper, we establish the new MTPA model considering the eddy current loss resistance of the canned sleeve. On this basis, the position sensorless algorithm is combined with the 2-DOF control to achieve optimal control of CEV-PMSM.
Figure 4 is the CEV-PMSM model diagram, adopting the 10-pole/24-slot combination.
4. Sensorless Tracking of CEV-PMSM
In order to achieve sensorless control of CEV-PMSM in the low-speed range, this paper adopts a rotating high-frequency voltage injection method. Based on the salient pole effect of the CEV-PMSM, a high-frequency rotating voltage is injected into the stationary coordinate system, and the high-frequency response current signal is extracted by a filter. Finally, the rotor position can be detected by demodulating the negative phase sequence component.
4.1. Mathematical Model of CEV-PMSM under High-Frequency Excitation
Under the excitation of the high-frequency rotating voltage signal, the stator resistance Rs can be neglected compared to the high-frequency reactance. At this time, the model of the CEV-PMSM under high-frequency excitation can be equivalent to a pure inductance model. Under high-frequency excitation, the relationship between voltage and high-frequency reactance is:
The high-frequency circuit model is shown in
Figure 16.
In order to accurately estimate the position of the CEV-PMSM, the relationship between the estimated rotor synchronous rotation coordinate system
-
and the actual rotor synchronous rotation coordinate system
d-
q is established, as shown in
Figure 17.
Where:
udi,
uqi,
idi, and
iqi are the HF voltages and currents, respectively;
P is a derivative operator;
θr is the actual rotor position angle;
is the estimated rotor position; Δ
θ is the difference between the actual rotor position angle and the estimated rotor position angle.
Here, L = (Ld + Lq)/2 is the average inductance, and ΔL = (Ld − Lq)/2 is the half-difference inductance.
Define the inductance matrix as:
It can be observed from Equation (22) that the inductance matrix Lαβ contains rotor position information, and the switching frequency of the inverter is generally 10 kHz. In order to ensure the sine of the high-frequency voltage signal, the frequency ωi of the injected high-frequency voltage signal is generally 0.5–2 kHz.
4.2. HF Rotating Voltage Injection
In the two-phase stationary coordinate system, a high-frequency rotating voltage is injected into the CEV-PMSM. The injected voltage can be described as:
where:
Vi,
ωi represent the amplitude and the frequency of the injected vector voltage, respectively.
According to the high-frequency mathematical model of CEV-PMSM in the two-phase stationary coordinate system, the high-frequency response current equation in the coordinate system can be expressed as:
Transforming the above formula to the stationary coordinate system, the expression is:
It can be noticed from Equation (26) that the high-frequency current contains both positive and negative sequence components. The first component, called the positive-sequence component
Ip, is proportional to the average inductance, but does not contain information on the rotor position
θr. The second component, called negative-sequence component
In, is proportional to the half difference inductance and contains information on the rotor position
θr.
Therefore, it is necessary to filter out the fundamental frequency current, low-order harmonic current, PWM switching frequency harmonic current, and positive phase sequence high-frequency current in the terminal current of CEV-PMSM. Finally, the rotor position can be detected by demodulating the negative phase sequence component.
4.3. Synchronous Frame Filter (SFF)
Conventional filtering methods use band-pass filters and band-stop filters, which will cause problems such as larger phase shift and amplitude attenuation. In order to avoid the above problems, synchronous frame filters are used in this article.
The SFF transforms the high-frequency signal quantity (
α,
β) in other coordinate systems into the synchronous coordinate system (
d-
q) with the same frequency as the high-frequency signal. At this time, the current component of the positive phase sequence will become a direct component, and the component of the negative phase sequence will become a high-frequency component. After that, a high-pass filter is used to eliminate the positive phase sequence component.
Figure 18 shows the block diagram of the SFF.
Where ωc represents the carrier frequency.
After filtering, the remaining signal is the negative phase sequence high-frequency current component, which is a useful signal that can be used to track the salient pole, and its vector expression is:
4.4. Rotor Position Extraction by Heterodyne Method
The phase angle modulation is found by the heterodyne method to demodulate the negative phase sequence component, and obtain the tracking error signal, which can be expressed as:
As long as the tracking error signal Δθ is adjusted to approach zero, it can be ensured that the estimated rotor position angle converges to the actual rotor position angle. After this error signal passes through the loop filter of the first-order integral nature, the estimated value of the rotation speed can be obtained, and the estimated value of the rotor magnetic pole position can be obtained by further integrating the rotation speed.
4.5. Zero Lag Position Tracking Observer
Estimate the rotor pole position from the negative sequence component, and use the Romberg observer to observe the rotor pole position.
The rotor position tracking observer can obtain an error signal tending to zero, as illustrated in
Figure 19. Since the position observer introduces the torque variable, the observer can achieve accurate observation without phase lag. According to the rotor position observer in
Figure 19, the transfer function between the rotor position and the estimated position is obtained, as shown in Equation (31).
4.6. Analysis of Sensorless Simulation
According to the above theory, the Simulink model shown in
Figure 20 is established.
Figure 21 shows the speed tracking waveform at no load, and the speed changes to 150 r/min at 0.5 s. It can be noticed that regardless of the speed-up stage or the rated speed, the actual speed and the estimated speed have good consistency. The control algorithm of high-frequency signal injection enables the motor to track the target speed in real time, which can meet the accuracy requirements of the CEV-PMSM system.
Figure 22 shows the speed estimation error curve. The speed estimation error has a larger value during the speed-up stage, and the speed estimation error gradually decreases as the speed runs stably. In general, the speed estimation error amplitude is small, and the tracking performance is better.
Figure 23a is the contrast waveform between the actual angle and the estimated angle when the motor speed changes suddenly.
Figure 23b is a partial enlarged view of the rotor position. It can be seen that the estimated speed and the actual speed are in good agreement.
According to
Figure 24, the position estimation error diagram shows that the rotor position error is less than about 0.01 rad. As the speed stabilizes, the rotor position estimation error is gradually reduced, and the tracking performance is good.
Figure 25a,b show the actual value and estimated value of the rotor position when the actual speed changes from 100 r/min to −100 r/min according to the slope law. When it reverses suddenly at 0.3 s, the rotor position tracking performance is still maintained during the deceleration process.
Figure 26 shows the speed estimated value and actual value change curve. It can be observed that this detection method can also track the actual speed of the rotor very well at low speeds, and has a good dynamic tracking performance.
The PI controller used in the sensorless tracking is a one-degree-of-freedom controller. The parameter adjustment of the PI controller will affect the tracking performance and anti-disturbance performance of the system at the same time. If the parameters are set according to the optimal anti-interference performance, the system tracking performance will deteriorate. If the parameters are set according to the optimal tracking performance, the anti-interference performance will deteriorate. Therefore, the design and parameter tuning of conventional PI controllers are usually solved by compromise or trial and error. The valve position control system has high requirements on the speed response of the control system, which is very sensitive to overshoot and does not allow overshoot. Therefore, a control system based on a two-degree-of-freedom (2-DOF) and position sensorless algorithm is studied.
5. Two-Degree-of-Freedom Control Strategy
Combining the position sensorless control theory described above with the 2-DOF control, a vector control system based on 2-DOF and position sensorless algorithm can be designed. It can not only have strong anti-interference and speed control ability, but also has a certain adaptive ability, solves the problem of speed overshoot, and achieves smooth transition of the valve transient process.
In order to solve the problem that the traditional PI control cannot meet the requirements of speed overshoot and response rapidity, the 2-DOF control strategy is proposed to design the speed loop PI controller.
5.1. 2-DOF Controller
For the speed loop controller, the tracking performance and anti-disturbance performance of the system are optimized, respectively.
Figure 27 is a 2-DOF control with set-value filtering, where
v is the control input,
w is the outer disturbance input,
kp and
ki are the gains of proportional and integral parts,
δn is the external noise input.
H(s) is the compensation link and
C(s) is the internal model controller. The transfer function of the control system under input is
Φr(s), and the transfer function under disturbance is
Φd(s), which is a high-frequency signal. The transfer function under measurement noise is
Φn(s).
The system model P(s) is determined, so the anti-interference performance and noise-measurement performance of the system are only related to C(s), while the tracking performance of the system is not only related to C(s), but also to H(s). Among the three transfer functions Φr(s), Φd(s), and Φn(s), two transfer functions can be adjusted independently, so the system is a 2-DOF control system. When designing a 2-DOF control system, the system should first meet the requirements of anti-interference performance and suppression of measurement noise performance by designing C(s), which is the advantage of the 2-DOF control system.
The output of the 2-DOF PI control system with setting value filtering is:
In particular, when
a = 0, the output of the control system can be simplified as:
From the above analysis, it can be seen that the two-degree-of-freedom PI controller first designs PI control parameters through the requirements of anti-disturbance performance, and then designs function H(s) through the requirements of tracking performance. Adjusting the tracking performance by H(s) does not affect the disturbance rejection performance.
It can be seen from Equation (36) that in order to make the system track without error under time-varying setting, the transfer function of the system under input can be designed as:
At this time, the corresponding set-valued filtering function
H1 (s) is:
In order to make the step response of the system without overshoot, the transfer function of the system under input can be designed as a first-order or second-order low-pass filter.
The corresponding set-valued filter function
H2(s) is:
where
m is a positive constant.
5.2. Simulation Analysis of 2-DOF Control
In order to verify the effectiveness of the new system, its step-response and anti-disturbance performance are analyzed. The sampling period of the speed loop and the current loop and the calculation step of the system are both 0.02 ms.
Take
m = 0,
ωn is 30, 35, and 40, respectively, and
ωn is the speed loop bandwidth. The step is set to 100 rpm, and the waveform at no-load starting is shown in
Figure 28.
It can be seen from
Figure 28 that the speed waveform is no longer in overshoot and has faster tracking than
Figure 21 and
Figure 26. With the increase in the speed loop bandwidth, the faster the system response speed, and the better the speed tracking performance.
Take
ωn = 60,
m is 0, 0.5 and 1, respectively. The step is set to 100 rpm, and the waveform at no-load starting is shown in
Figure 29.
The simulation results show that the designed 2-DOF PI control can effectively reduce the overshoot of the speed, and improve the speed tracking performance and the anti-disturbance performance of the system. The smaller the m value, the smaller the overshoot. With an increase in m value, the overshoot increases gradually. When m is 1, it is a sensorless waveform without 2-DOF control. Therefore, it can be concluded that the position sensorless control based on 2-DOF further improves the anti-load disturbance performance of the system, and can achieve fast response and no overshoot control of the speed. The correctness and effectiveness of the proposed control strategy are verified.
6. Experimental Test
In this paper, TMS320F28335 is selected as the DSP product for motion control. The control algorithm model that can automatically generate code is established on the MATLAB/Simulink platform, and the functions of the hardware system are tested and corrected. The vector control system based on 2-DOF and the position sensorless algorithm proposed in this paper is verified by experiments.
The variation curve of the calculated and measured rotor position at 1.2 times the rated speed is shown in
Figure 30.
The step load disturbance is taken as an example to verify the anti-disturbance performance of the system. Firstly, 100 rpm is given to make the motor run without load, and then the influence of loading and unloading on speed fluctuation is tested. The loading and unloading curves are shown in
Figure 31.
Taking the unloading experiment as the assessment target, the 2-DOF control is systematically analyzed. Take
m = 0,
ωn is 30, 35 and 40, respectively, and the speed response curve is shown in
Figure 32a. Taking
ωn = 60,
m is 0, 0.5, and 1, respectively, the speed response curve is shown in
Figure 32b.
It can be observed from
Figure 32 and
Figure 33 that the anti-disturbance performance of the 2-DOF control system is only related to
ωn and independent of m. In summary, the tracking performance of the 2-DOF controller with set-value filtering is affected by
ωn and m at the same time, and the anti-interference performance is only affected by
ωn. It is proved that the vector control system based on 2-DOF and sensorless algorithm has good tracking performance and anti-interference performance, and has strong engineering practicability.
The experimental results show that the system can achieve accurate positioning and e fast response of the speed without overshoot, which meets the performance requirements of the servo system. The vector control system based on 2-DOF control and a sensorless algorithm has great improvements with regard to high precision, fast response, and strong robustness, which can enhance the system stability and the static as well as dynamic properties of the CEV-PMSM system significantly.
Figure 34 shows the main components and the experimental platform of CEV-PMSM.