Permanent magnet synchronous motor control system

Abstract

The invention relates to a permanent magnet synchronous motor control system, which comprises a position ring, a speed ring and a current ring, the position ring and the speed ring are connected in parallel to serve as a system outer ring, the current ring is a system inner ring, and an output value after the position ring and the speed ring are connected in parallel is an input value of the current ring; and performing parameter setting on the controllers of the position loop and the speed loop through a frequency domain method. A series connection structure of a position ring and a speed ring in a traditional vector control system is changed into a parallel connection structure, system model simplification is carried out on the parallel connection structure, a system block diagram and a transfer function of the parallel connection structure are obtained, and meanwhile parameter setting is carried out on controllers of the position ring and the speed ring through a frequency domain method. The control system has better steady-state performance and dynamic performance; meanwhile, a higher system type is achieved, and steady-state errors do not exist when ramp signals are input; in addition, the control structure has a simpler optimization scheme, and has greater advantages in subsequent performance optimization.

Description

Technical Field

[0001] The present invention relates to the technical field of motor control, and in particular to a permanent magnet synchronous motor control system. Background Art

[0002] In the permanent magnet synchronous motor servo control system, the traditional three-loop vector control system is a three-loop series (cascade) control structure of position, speed and current. The purpose of the series control structure is to simplify the design and analysis of the control system, to consider a certain dynamic process and achieve specific performance in one loop, and to ignore the influence of other loops, thereby converting the relatively high-order object control system design into the control system design of multiple low-order objects. However, in order to ignore the influence of the inner loop control system, the bandwidth of the inner loop needs to be much larger than the bandwidth of the outer loop, and only in this way can the outer loop control command be perfectly tracked by the inner loop. Based on the above content, it can be seen that the position loop bandwidth of the traditional three-loop vector control system is limited by the speed loop bandwidth, and its dynamic performance cannot be fully released; at the same time, the position loop in the traditional three-loop vector control system is generally adjusted to a type I system, and when the input is a high-order desired signal, there will be a steady-state error, which makes it difficult to cope with high-precision application scenarios; in addition, the traditional three-loop vector control system has the difficulties of strong system coupling and complex optimization. Summary of the invention

[0003] The present invention provides a permanent magnet synchronous motor control system to solve the above technical problems.

[0004] In order to solve the above technical problems, the present invention provides a permanent magnet synchronous motor control system, including a position loop, a speed loop and a current loop.

[0005] The position loop and the speed loop are connected in parallel as the outer loop of the system, the current loop is the inner loop of the system, and the output value of the position loop and the speed loop after being connected in parallel is the input value of the current loop;

[0006] The controllers of the position loop and the speed loop are parameterized using a frequency domain method.

[0007] Preferably, both the position loop and the speed loop adopt PID controllers.

[0008] Preferably, the open-loop transfer function of the control system is:

[0009]

[0010] Among them, K pa_sp、 K pa_si , K pa_pp They are the proportional coefficient, integral coefficient of the speed loop controller and the proportional coefficient of the position loop controller respectively.

[0011] Preferably, the open-loop transfer function of the control system is converted into two integral links and one first-order differential link by performing an equivalent transformation on the open-loop transfer function of the control system.

[0012] Preferably, the coefficient H of the integral link is i and the coefficient of the differential element H d They are:

[0013]

[0014] Preferably, H i >H d , the controller parameters of the control system are as follows:

[0015]

[0016] Among them, ω pa_sc represents the desired open-loop cutoff frequency of the position loop.

[0017] Preferably, performing parameter tuning on the controllers of the position loop and the speed loop by using a frequency domain method includes: performing stability analysis by using a root locus cluster method.

[0018] Preferably, a regulating controller is provided before the current loop.

[0019] Preferably, the regulation controller adopts a second-order Butterworth filter.

[0020] Preferably, the cutoff frequency ω of the second-order Butterworth filter is cb Need to meet: 8ω pa_sc ≤ω cb .

[0021] Compared with the prior art, the permanent magnet synchronous motor control system provided by the present invention has the following advantages:

[0022] 1. The present invention changes the series structure of the position loop and the speed loop in the traditional vector control system into a parallel structure, simplifies the system model of the parallel structure, obtains its system block diagram and transfer function, and simultaneously adjusts the parameters of the controllers of the position loop and the speed loop by the frequency domain method, so that the control structure system has better steady-state performance and dynamic performance, and has a higher system type, and there is no steady-state error when a ramp signal is input;

[0023] 2. The present invention improves the defects of the parallel structure system by adding a regulating controller for compensation before the current loop, so that the control system has greater advantages in subsequent performance optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1It is a control structure equivalent block diagram of a permanent magnet synchronous motor control system in a specific implementation manner of the present invention;

[0025] Figure 2 A Bode diagram of an open-loop transfer function of a permanent magnet synchronous motor control system in a specific implementation manner of the present invention;

[0026] Figure 3 A root locus cluster of a permanent magnet synchronous motor control system in a specific embodiment of the present invention;

[0027] Figure 4 This is an error comparison diagram of a ramp signal of a permanent magnet synchronous motor control system in a specific implementation manner of the present invention;

[0028] Figure 5 Bode diagrams for the existing series structure and the parallel structure proposed in this application;

[0029] Figure 6 This is the control structure block diagram of the improved (adding a regulating controller) permanent magnet synchronous motor control system;

[0030] Figure 7 It is a comparison diagram of the Bode diagrams of three structural systems (series structure, parallel structure, and improved parallel structure);

[0031] Figure 8 These are the response curves of three structural systems (series structure, parallel structure, and improved parallel structure) under step signal input. DETAILED DESCRIPTION

[0032] In order to describe the technical solution of the above invention in more detail, specific embodiments are listed below to demonstrate the technical effects; it should be emphasized that these embodiments are used to illustrate the present invention but not to limit the scope of the present invention.

[0033] The permanent magnet synchronous motor control system provided by the present invention comprises a position loop, a speed loop and a current loop.

[0034] The position loop and the speed loop are connected in parallel as the outer loop of the system, the current loop is the inner loop of the system, and the output value of the position loop and the speed loop after being connected in parallel is the input value of the current loop;

[0035] The controllers of the position loop and the speed loop are parameterized using a frequency domain method.

[0036] The present invention changes the series structure of the position loop and the speed loop in the traditional vector control system into a parallel structure, simplifies the system model of the parallel structure, obtains its system block diagram and transfer function, and simultaneously adjusts the parameters of the controllers of the position loop and the speed loop through the frequency domain method, so that the control structure system has better steady-state performance and dynamic performance, and has a higher system type, and there is no steady-state error when a ramp signal is input.

[0037] This application takes the surface-mounted permanent magnet synchronous motor as the research object, and the voltage equation established in the dq axis rotating coordinate system is:

[0038]

[0039] where u d 、u q Respectively represent the stator voltage of dq axis; i d 、i q Respectively represent the stator current of dq axis; ψ f represents the rotor flux; ω e Indicates the rotor electrical angular velocity; L s Represents the stator equivalent inductance; R s is the phase resistance of the stator winding.

[0040] The electromagnetic torque equation and motion equation of the permanent magnet synchronous motor can be expressed as:

[0041]

[0042] Where T e Represents electromagnetic torque; T L represents load torque; J represents moment of inertia; B represents viscous friction coefficient; ω r It represents the mechanical angular velocity of the rotor; P represents the number of pole pairs of the motor.

[0043] Compared with the traditional three-loop series control system, the parallel control system proposed in this application uses the original position loop and speed loop as the outer loop of the system and connects them in parallel. The output value after parallel connection is the input value of the current loop. The equivalent block diagram of the three-loop parallel connection is as follows: Figure 1 As shown, the proportional and integral coefficients of the parallel structure speed loop controller and the proportional coefficient of the position loop controller are represented by K pa_sp、 K pa_si , K pa_pp express.

[0044] The open-loop transfer function of the parallel control system is:

[0045]

[0046] Equation (3) is transformed equivalently and decomposed into several standard forms of basic links, as shown below:

[0047]

[0048] From formula (4), it can be obtained that the open-loop transfer function of the system is mainly composed of two integral links and one first-order differential link. For simplicity, the coefficients of the two links are defined as follows:

[0049]

[0050] Among them, H i , H d Respectively represent the coefficients of the parallel structure integral link and the first-order differential link. i It is determined by the integral coefficient of the speed loop controller and the coefficient of the position loop controller; H d It is determined by the three coefficients of the speed loop and position loop controller. Therefore, we can first determine H i Then determine H d , and the two do not interfere with each other.

[0051] The open-loop transfer function of the parallel structure is simpler than that of the series structure. The open-loop transfer function of the parallel structure can be analyzed in the frequency domain through the Bode plot and the parameters can be adjusted.

[0052] Figure 2 is the Bode diagram of the open-loop transfer function of the parallel structure system. Figure 2 It can be seen that when H i <H d When H i =H d When H i >H d When the logarithmic amplitude-frequency characteristic curve passes through 0dB at an attenuation slope of -20dB / dec, the corresponding phase margin is greater than 45°. In order to ensure good dynamic performance of the system, it is usually required that the logarithmic amplitude-frequency characteristic curve passes through 0dB at an attenuation slope of -20dB / dec. At the same time, a larger phase margin can also ensure good steady-state performance of the system. In summary, the link coefficient is selected as H i >H d , and the controller parameters of the parallel control system can be obtained as follows:

[0053]

[0054] Among them, ω pa_scRepresents the desired open-loop cutoff frequency of the parallel structure position loop.

[0055] Firstly, the stability of the parallel vector control structure is analyzed.

[0056] Stability analysis of linear continuous steady-state systems is usually divided into time domain analysis methods (such as the root locus method, Routh criterion, etc.) and frequency domain analysis methods (such as Bode plots, Nyquist criterion, etc.). The research objects of the above methods are mostly systems with a certain or variable parameter, but the parallel structure system in the present invention contains three variable parameters. Although the stability conditions of the two structural systems can be solved by the Routh criterion, the correlation between the changes in each parameter and the changes in system stability cannot be obtained. The root locus cluster method is different from the above method. This method can clearly obtain the changes in system stability when each parameter changes. Therefore, this application uses the root locus cluster method for stability analysis.

[0057] According to formula (3), the characteristic equation of the parallel structure system is as follows:

[0058] s 2 +uK pa_sp s+u(K pa_si +K pa_pp )=0 (7)

[0059] From the above formula, we can see that K pa_si and K pa_pp The change of has the same effect on the root locus cluster, so the two parameters can be combined:

[0060] K pa_t =K pa_si +K pa_pp (8)

[0061] a. Let K pa_sp =0, the characteristic equation is simplified to:

[0062] s 2 +uK pa_t =0 (9)

[0063] To convert it into 1+G pa_k1 = 0, using a parameter term without a variable (i.e. s 2 ) divided by the terms on both sides of equation (9), we can get the equivalent open-loop transfer function G pa_k1 (s):

[0064]

[0065] According to the above formula, K pa_t From 0 to ∞ The root locus of the equivalent open-loop transfer function when changes.

[0066] b. Restore K pa_sp is a variable parameter, and step a is repeated to obtain the final parallel structure system equivalent open-loop transfer function G pa_k2 (s):

[0067]

[0068] According to the above formula, the root locus cluster of the equivalent open-loop transfer function of the parallel structure system is obtained, such as Figure 3 shown.

[0069] exist Figure 3 In, take K pa_sp =1,4,9,16. The dotted line is drawn by step a. It is always on the imaginary axis as the starting point of the root locus cluster, and as K pa_t As K increases, the root locus cluster shows an expansion trend, and the double roots of the system gradually move away from the imaginary axis; the solid line is drawn by step b. Since the starting point is always on the imaginary axis, the system can always remain stable. pa_sp As the damping increases, the system will gradually change from an underdamped state to an overdamped state.

[0070] Secondly, the steady-state error of the parallel vector control structure is analyzed.

[0071] From equation (3), we can see that the parallel structure system is a type II system. Whether the input signal of the position loop is a step signal or a ramp signal, the output of the system can perfectly track the input without any steady-state error.

[0072] according to Figure 1 The error transfer function E of the position loop of the parallel structure system can be obtained pa (s) is:

[0073]

[0074] Only when the order of the input signal is greater than 2, the position loop has a steady-state error greater than 0.

[0075] In order to verify the accuracy of the analysis results, simulation verification is required. This application uses Matlab / Simulink simulation software to build models of permanent magnet synchronous motor vector control systems based on series structure and parallel structure, respectively. The specific simulation parameters of the motor are shown in Table 1.

[0076] Table 1 Permanent magnet synchronous motor simulation parameters

[0077] parameter Numeric <![CDATA[Stator resistance R s / Ω]]> 0.331 <![CDATA[Stator inductance L s / H]]> 0.0021 <![CDATA[Rotor flux linkage ψ f / Wb]]> 0.3537 <![CDATA[Moment of inertia J / (kg·m 2 )]]> 0.00252 Pole pair number P 4 Motor speed n / (r / min) 500 <![CDATA[Open-loop cut-off frequency ω of the series speed loop se_sc / (rad / s)]]> 300 <![CDATA[Open-loop cut-off frequency ω of the parallel position loop pa_sc / (rad / s)]]> 300

[0078] Set the input signal to a ramp signal and take the position loop error as the output of the oscilloscope to obtain Figure 4 .Depend on Figure 4 It can be seen that under the input of the ramp signal, the systems of both structures can quickly reach stability. At the same time, both are overdamped systems and there is no overshoot oscillation. However, for the series structure system, the system reached a stable state at 0.15s, and there was a steady-state error of 0.7rad; for the parallel structure system, the system reached stability at 0.11s, and the steady-state error was 0rad.

[0079] Finally, the dynamic and anti-disturbance performance of the parallel vector control structure is analyzed.

[0080] The dynamic performance and anti-disturbance performance of the system are analyzed in the frequency domain through the Bode plot. According to the three-band theory, the mid-frequency band of the Bode plot (i.e., the area near the cutoff frequency) reflects the dynamic performance of the system. The slope of the open-loop amplitude-frequency characteristic curve in this interval should generally not be less than -20db / red; the high-frequency band (i.e., the area with a frequency greater than 10 times the cutoff frequency) reflects the system's ability to resist high-frequency disturbances. The lower the decibel value of the high-frequency characteristic, the stronger the attenuation of the high-frequency interference signal. According to the open-loop transfer functions of the two structural systems, their Bode plots can be obtained respectively, as shown in the figure below: Figure 5 shown. Figure 5 In the figure, the green line represents the Bode diagram of the series structure system, and the blue line represents the Bode diagram of the parallel structure system. The middle and high frequency bands are analyzed by the three-band theory.

[0081] In the mid-frequency band, the open-loop cutoff frequency of the parallel structure system is 300rad / s, and the phase margin is 80°. The open-loop cutoff frequency of the series structure system is only 80rad / s, and the phase margin is 70°. The parallel structure has a higher open-loop cutoff frequency and phase margin than the series structure. At the same time, the slope of the open-loop amplitude-frequency characteristic curve of the two systems is -20dB / red, so the dynamic performance of the parallel structure system will be better.

[0082] In the high frequency band, the slope of the parallel structure system is -20dB / red, while the slope of the series structure system is -40dB / red. Therefore, the series structure system has a stronger ability to resist high-frequency disturbances.

[0083] Aiming at the defect that the high-frequency anti-interference performance of the parallel structure system is weaker than that of the series structure system, the present application improves the above-mentioned parallel vector control structure, namely:

[0084] Add a regulating controller G in front of the current loop of the parallel structure system pa_ex , the improved parallel structure system open-loop transfer function G is obtained pa_oL :

[0085]

[0086] From the above formula, it can be seen that after adding the regulating controller to the parallel structure system, the performance of its open-loop transfer function is simply to directly multiply the original open-loop transfer function by the transfer function of the added regulating controller, which will cause the designed regulating control performance to be directly reflected in the open-loop transfer function, simplifying the design difficulty. Therefore, a regulating controller that can be used to compensate for the defects of the parallel structure system is designed separately, and it is added before the current loop, which can improve the high-frequency anti-interference performance of the parallel structure system.

[0087] In some embodiments, the regulation controller can use a second-order Butterworth filter, which has good high-frequency suppression capability and a frequency response curve that is as flat as possible within the passband without fluctuations. This characteristic is very suitable for parallel structure systems. Therefore, it is considered to add a second-order Butterworth filter G in front of the current loop. LPF (s) is used to suppress high-frequency interference signals while maintaining better dynamic performance. The block diagram of the improved parallel structure system is as follows: Figure 6 shown.

[0088] The transfer function of the second-order Butterworth filter is expressed as:

[0089]

[0090] Among them, ω cb represents the cutoff frequency of the second-order Butterworth filter. According to equation (14), the filter tends to ∞ The amplitude at the time and the phase lag caused by the introduction into the original system are calculated:

[0091]

[0092] Formula (15) shows that the introduction of the Butterworth filter will not affect the position steady-state error of the original system, but will cause the system phase lag and reduce the stability margin of the system. Therefore, in order to take into account the stability problems caused by high-frequency noise suppression and phase lag, it can be stipulated based on experience that the phase margin lag caused by the filter is less than 10°, thus obtaining the filter cutoff frequency range: 8ω pa_sc ≤ω cb .

[0093] Figure 7This is a comparison of the Bode diagrams of the three structural systems. The red line represents the Bode diagram of the filter-type parallel vector structure. Comparing the Bode diagrams of the parallel system before and after the improvement (i.e., parallel structure 1 and parallel structure 2), it can be seen that the red line and the orange line are almost overlapped in the low and medium frequency bands, and their open-loop cutoff frequencies remain consistent. Therefore, it can be determined that the second-order Butterworth filter does not reduce the type and dynamic performance of the system; at the same time, the slopes of the parallel structures with and without low-pass filters in the high-frequency band are -40dB / dec and -20dB / dec attenuation, respectively, which improves the system's high-frequency noise suppression capability.

[0094] Figure 8 These are the response curves of the three structural systems under step signal input. From the figure, it can be seen that the response time of the parallel structural system before and after the improvement is almost the same, and both are faster than the series structural system.

[0095] In summary, the permanent magnet synchronous motor control system provided by the present invention changes the series structure of the position loop and the speed loop in the traditional vector control system into a parallel structure, simplifies the system model of the parallel structure, obtains its system block diagram and transfer function, and simultaneously adjusts the parameters of the controllers of the position loop and the speed loop through the frequency domain method, so that the control structure system has better steady-state performance and dynamic performance, and has a higher system type. When a ramp signal is input, there is no steady-state error; it can also improve the defects of the parallel structure system by adding a regulating controller for compensation in front of the current loop, so that the control system has greater advantages in subsequent performance optimization.

[0096] Obviously, those skilled in the art can make various changes and modifications to the invention without departing from the spirit and scope of the invention. Thus, if these modifications and variations of the invention fall within the scope of the claims of the invention and their equivalents, the invention is also intended to include these modifications and variations.

Claims

1. A permanent magnet synchronous motor control system, characterized in that: Including position loop, speed loop and current loop, The position loop and the speed loop are connected in parallel as the outer loop of the system, the current loop is the inner loop of the system, and the output value of the position loop and the speed loop after being connected in parallel is the input value of the current loop; The controllers of the position loop and the speed loop are parameterized using a frequency domain method.

2. The permanent magnet synchronous motor control system according to claim 1, characterized in that: The position loop and the speed loop both adopt PID controllers.

3. The permanent magnet synchronous motor control system according to claim 2, characterized in that: The open-loop transfer function of the control system is: Among them, K pa_sp、 K pa_si、 K pa_pp They are the proportional coefficient, integral coefficient of the speed loop controller and the proportional coefficient of the position loop controller respectively.

4. The permanent magnet synchronous motor control system according to claim 3, characterized in that: By performing equivalent transformation on the open-loop transfer function of the control system, the open-loop transfer function is converted into two integral links and one first-order differential link.

5. The permanent magnet synchronous motor control system according to claim 4, characterized in that: The coefficients of the integration link Hi and the coefficients of the differential element Hd They are:

6. The permanent magnet synchronous motor control system according to claim 5, characterized in that: Select H i >H d , the controller parameters of the control system are as follows: Among them, ω pa_sc represents the desired open-loop cutoff frequency of the position loop.

7. The permanent magnet synchronous motor control system according to claim 6, characterized in that: The controllers of the position loop and the speed loop are tuned for parameters by using the frequency domain method, including: performing stability analysis by using the root locus cluster method.

8. The permanent magnet synchronous motor control system according to claim 7, characterized in that: A regulating controller is also arranged before the current loop.

9. The permanent magnet synchronous motor control system according to claim 8, characterized in that: The regulation controller adopts a second-order Butterworth filter.

10. The permanent magnet synchronous motor control system according to claim 9, characterized in that: The cutoff frequency ω of the second-order Butterworth filter cb Need to meet: 8ω pa_sc ≤ω cb .

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