Permanent magnet synchronous motor active disturbance rejection control method based on enhanced expansion state observer

Abstract

The invention discloses a permanent magnet synchronous motor control method based on an enhanced expansion state observer, and the method comprises the following steps: carrying out the preliminary estimation of disturbance through a rapid linear expansion state observer, introducing an estimation result into a nonlinear expansion state observer through a designed weight coefficient, and estimating a residual disturbance result, and the weight coefficient is used for adjusting the weight coefficient. Introducing the result into an error feedback control law, and calculating a reference current instruction; the output of the inverter is controlled through the current controller and the space vector modulation module so as to control the motor. Compared with traditional active-disturbance-rejection control, under the condition that the bandwidth is fixed, the response speed of the system is increased, and the anti-interference capacity is improved.

Description

Technical Field

[0001] The invention discloses a permanent magnet synchronous motor control method based on an enhanced extended state observer, belonging to the field of permanent magnet synchronous motor control. Background Art

[0002] Permanent magnet synchronous motor (PMSM) uses permanent magnets to replace the excitation winding of wound synchronous motors. It is widely used in various occasions due to its simple control, high power density, high precision and high efficiency. The permanent magnet synchronous motor is a multivariable, strongly coupled, time-varying nonlinear system. Its application environment is generally complex and is subject to external interference to varying degrees, including motor parameter changes, load disturbances and other uncertain factors. Therefore, the choice of control strategy is very important for the performance of the permanent magnet synchronous motor control system.

[0003] At present, most advanced control strategies have different degrees of dependence on motor parameters. In order to achieve good dynamic and static performance, traditional proportional integral control (PI) also needs to use motor parameters to calculate proportional and integral gains. Under complex operating conditions, permanent magnet synchronous motor drive systems cannot avoid the problem of frequent parameter changes, which affects the overall operating performance of the system and makes it difficult to meet high performance requirements.

[0004] With the application of modern control theory and the rapid development of digital controllers, active disturbance rejection control (ADRC) has been widely studied in the field of motor control due to its advantages such as fast dynamic response, strong anti-disturbance, good reliability and model independence. The extended state observer (ESO) is the core of ADRC, which can estimate state variables and disturbances without relying on the parameters of the permanent magnet synchronous motor. Increasing the bandwidth of the ESO can improve the rapidity of convergence and the accuracy of disturbance estimation, but the measurement noise will be amplified by the large bandwidth ESO, which will lead to system instability. Summary of the invention

[0005] The purpose of the present invention is to provide a permanent magnet synchronous motor anti-disturbance control method based on an enhanced extended state observer in view of the deficiencies of the above-mentioned prior art. First, a linear fast extended state observer (ESO) is used to perform a preliminary observation of the total disturbance, and then the estimated result is introduced into the nonlinear extended state observer using a designed weight function. Without increasing the bandwidth of the observer, the ability of disturbance observation is improved, the response speed of the speed step command is increased, and at the same time, the adjustable parameters are increased, so that the system can adjust the weight coefficient according to the actual disturbance size, and flexibly balance the disturbance observation and tracking performance.

[0006] The present invention adopts the following technical solutions to achieve the above-mentioned purpose:

[0007] A permanent magnet synchronous motor active disturbance rejection control method based on an enhanced extended state observer, characterized by comprising the following steps:

[0008] Step 1), according to the torque equation and mechanical motion equation of the permanent magnet synchronous motor, the motor rotor speed ω is used as the state variable x1, the total disturbance of the permanent magnet synchronous motor is modeled, the internal and external disturbances are regarded as a whole, the total disturbance f is defined as the state variable x2, and a second-order state equation is established.

[0009] Step 2), based on the second-order state equation, a fast linear extended state observer and a nonlinear extended state observer are built and cascaded, a proportional gain of the observation error is introduced into the disturbance loop of the linear extended state observer, and a weight function is designed to adjust the estimated disturbance value after the two are cascaded.

[0010] Step 3), design the state error feedback law, calculate the error between the observed speed and the given speed of the motor through the proportional link, compensate the differential of the given speed to the proportional link, and then feedback the total disturbance observed by the enhanced extended state observer to obtain the current command value i q .

[0011] Step 4), according to the current command value i q , using i d = 0 vector control, the current loop controller gives u q and u d The value of is used to control the inverter through SVPWM, so that the permanent magnet synchronous motor can operate normally and realize closed-loop control.

[0012] Compared with the prior art, the present invention adopts the above technology and has the following technical effects:

[0013] (1) The enhanced extended state observer permanent magnet synchronous motor self-disturbance rejection control method adopts a cascade of a fast linear extended state observer and a nonlinear extended state observer to improve the speed response speed and anti-interference performance.

[0014] (2) The enhanced extended state observer proposed in the present invention can have a smaller phase lag and faster tracking capability for disturbance observation under a certain bandwidth.

[0015] (3) Compared with the second-order linear extended state observer, it has a better effect on suppressing disturbances in the medium and low frequency bands, and can improve the speed response speed by adjusting the two weight coefficients.

[0016] (4) The system maintains strong robustness, is less affected by motor parameters, and has flexible parameter configuration. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1The structure diagram of the enhanced active disturbance rejection control permanent magnet synchronous motor active disturbance rejection control system

[0018] Figure 2 The specific structure diagram of ADRC based on enhanced ESO

[0019] Figure 3 Bode diagram comparison of the anti-interference capabilities of the traditional LADRC and the ADRC based on the enhanced ESO proposed in the present invention.

[0020] Figure 4 The figure is a speed waveform simulation comparison between the traditional LADRC and the enhanced ESO-based ADRC proposed in the present invention under a step speed command.

[0021] Figure 5 The figure shows the speed waveform simulation comparison between the traditional LADRC and the enhanced ESO-based ADRC proposed in the present invention under step load disturbance. DETAILED DESCRIPTION

[0022] The present invention is further described below in conjunction with the accompanying drawings, as shown in the drawings:

[0023] The present invention discloses a permanent magnet synchronous motor self-disturbance rejection control method based on an enhanced extended state observer. Figure 1 Please follow the steps below to implement:

[0024] According to the torque equation and mechanical motion equation of the permanent magnet synchronous motor, the motor rotor speed ω is taken as the state variable x1, the total disturbance of the permanent magnet synchronous motor is modeled, the internal and external disturbances are regarded as a whole, the total disturbance f is defined as the state variable x2, and the second-order state equation is established.

[0025] The mechanical motion equation of the surface-mounted permanent magnet synchronous motor is:

[0026]

[0027] Where B is the viscous friction coefficient, θ is the rotor angular displacement, Where ω is the mechanical angular velocity.

[0028] The torque equation is:

[0029]

[0030] Where p is the pole pair number, is the magnetic link, i q is the q-axis current, T e is the load torque.

[0031] The state equation for the mechanical motion of the motor is constructed as follows:

[0032]

[0033] In the formula, i q * is the given value of the electromagnetic torque of the controller; b n is the gain factor f is the sum of the internal and external disturbances of the system, n n (t) is the unmodeled dynamic term.

[0034] Establish a mechanical angular velocity ω as the output, q-axis current i q The speed loop anti-disturbance controller is the input variable. If the state variable x1 is x1, the state space form is expressed as:

[0035]

[0036] Build a second-order extended state observer based on the second-order state equation.

[0037] First, a linear extended state observer is used to perform a preliminary observation of the total disturbance on the system disturbance, which can be expressed as:

[0038]

[0039] In the formula, β 11 , β 12 , β2 is the gain coefficient of fast LESO; is the estimated characteristic gain, which is different from the true value b n There may be deviations, and the impact of the deviations between the two is classified as unknown disturbances.

[0040] Then the nonlinear extended state observer is established, which is expressed as:

[0041]

[0042] Among them, the nonlinear function is expressed as:

[0043] Where: β 1n , β 2n is the gain coefficient of the nonlinear ESO, a1, a2, δ are the parameters of the nonlinear function; f 1n To divide τf 0n External observation results.

[0044] The enhanced active disturbance rejection control law is designed as:

[0045]

[0046] In the formula, ξ, τ are weight coefficients; It is the differential link of the given speed, used to compensate for oscillation and overshoot during the speed step process.

[0047] The enhanced extended state observer is tuned using the bandwidth method as follows:

[0048]

[0049] Where n1 and n2 are the coefficients of the observation error proportional link, their values ​​are positive numbers, and their sum is equal to 2.

[0050] The following function is used to design the weight adjustment value:

[0051]

[0052] In the formula, τ max , max and τ min , min Respectively refer to the maximum and minimum values ​​of the weight coefficient, e max and e min Select the upper and lower limits for the error.

[0053] Due to the difficulty of stability analysis in nonlinearity, the equivalent gain method can be used for analysis, and its expression is:

[0054]

[0055] In this way, the nonlinear ESO can be regarded as a variable gain ESO, whose gain is inversely proportional to the error.

[0056] Here, the disturbance suppression capability of the system is analyzed. The closed-loop transfer function of the traditional ADRC system is expressed as:

[0057]

[0058] The system closed-loop transfer function of the enhanced ADRC is expressed as:

[0059]

[0060] Where n ij (i=1, 2; j=1, 2, 3, 4) is a simplified form, and the specific expression is:

[0061]

[0062] Here the parameters are uniformly selected as; ω o =200; k p =10. The weight coefficients are selected as; τ = 0.6; ξ = 0.8; n1 = 0.5; n2 = 1.5. The transfer function Bode diagram is plotted as Figure 3 As shown. Figure 3It can be seen that under the condition of the same bandwidth and a certain error, the enhanced ADRC proposed in the present invention has stronger anti-interference ability in the low frequency band than the traditional LADRC, and does not affect the noise suppression ability in the high frequency band.

[0063] In order to verify the superiority of the enhanced active disturbance rejection control method for permanent magnet synchronous motor proposed in this application, the traditional LADRC and the method proposed in this invention are simulated respectively, and the controller parameters are: K p =800;ω o =1000; α1=0.75; α2=0.5; δ=0.05; τ max =0.6; τ min =0.4;ξ max =1;ξ min =0.8, n1=0.5, n2=1.5, LADRC takes the same bandwidth and gain.

[0064] The motor parameters used in the simulation are shown in the following table.

[0065]

[0066] The speed comparison simulation is carried out. The speed command transformation process is as follows: the initial speed is 300r / min, it changes to 600r / min at 0.05s, and drops to 300r / min at 0.1s. The simulation results are as follows: Figure 4 The simulation data is shown in the following table:

[0067]

[0068] The speed is set to 600 rpm, a load of 5 N / m is suddenly applied at 0.05 seconds, and the load is stopped at 0.1 seconds. The simulation results are as follows: Figure 5 The simulation data is shown in the following table:

[0069]

[0070] The simulation results show that when adding or subtracting loads, the enhanced ADRC proposed in the present invention is superior to the traditional LADRC in terms of speed fluctuation and recovery time.

[0071] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein, including technical and scientific terms, have the same meaning as generally understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with the meanings in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless defined as herein.

[0072] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A permanent magnet synchronous motor active disturbance rejection control method based on an enhanced extended state observer, characterized by comprising the following steps: S1: According to the torque equation and mechanical motion equation of the permanent magnet synchronous motor, the motor rotor speed ω is taken as the state variable x1, the total disturbance of the permanent magnet synchronous motor is modeled, the internal and external disturbances are regarded as a whole, the total disturbance f is defined as the state variable x2, and the second-order state equation is established. S2: According to the second-order state equation, a fast linear expanded state observer and a nonlinear expanded state observer are built and cascaded. A proportional gain of the observation error is introduced into the disturbance loop of the linear expanded state observer, and a weight function is designed to adjust the estimated disturbance value after the two are cascaded. S3: Design the state error feedback law, calculate the error between the observed speed and the given speed of the motor through the proportional link, compensate the differential of the given speed to the proportional link, and then feedback the total disturbance observed by the enhanced extended state observer to obtain the current command value i q . S3: According to the current command value i q , using i d = 0 vector control, the current loop controller gives u q and u d The value of is used to control the inverter through SVPWM, so that the permanent magnet synchronous motor can operate normally and realize closed-loop control.

2. The method for enhanced active disturbance rejection control of a permanent magnet synchronous motor according to claim 1, characterized in that: The torque equation and mechanical motion equation of the surface mounted permanent magnet synchronous motor in step 1 are: Where p is the pole pair number, is the magnetic link, i q is the q-axis current, T e is the load torque, B is the viscous friction coefficient, θ is the rotor angular displacement, Where ω is the mechanical angular velocity. The state equation for the mechanical motion of the motor is constructed as follows: In the formula, i q * is the given value of the electromagnetic torque of the controller; b n is the gain factor f is the sum of the internal and external disturbances of the system, n n (t) is the unmodeled dynamic term.

3. The improved active disturbance rejection control method for a permanent magnet synchronous motor according to claim 1 is characterized in that ,The enhanced extended state observer in S2 has the following structure: In the formula, β 11 , β 12 , β2 is the gain coefficient of enhanced LESO; is the estimated characteristic gain, β 1n , β 2n is the gain coefficient of the nonlinear ESO, a1, a2, δ are the parameters of the nonlinear function; f 1n To divide τf 0n According to the bandwidth method, the enhanced observer parameters are configured as follows: Where n1 and n2 are the coefficients of the observation error proportional link, their values ​​are positive numbers, and their sum is equal to 2. The following function is used to design the weight adjustment value: In the formula, τ max , max and τ min , min Respectively refer to the maximum and minimum values ​​of the weight coefficient, e max and e min Select the upper and lower limits for the error.

4. The improved active disturbance rejection control method for a permanent magnet synchronous motor according to claim 1, characterized in that: The error between the speed given value and the actual value is calculated through the proportional link, and then the system disturbance observation value obtained in step 3 is compensated to obtain the reference current command:

Images