Magnetic lead screw motor linear speed control method based on improved active disturbance rejection controller

Abstract

The invention discloses a magnetic lead screw motor linear speed control method based on an improved active-disturbance-rejection controller, and the method comprises the following steps: building a magnetic lead screw motor model, designing an active-disturbance-rejection control law according to the motor model, carrying out the higher-order operation of an extended state observer in a controller, and introducing an acceleration error at a reasonable position of a state equation, thereby achieving the linear speed control of a magnetic lead screw motor. And the improved active disturbance rejection controller is obtained. Compared with the prior art, the improved method provided by the invention has the advantages that the observation capability of the expansion state observer on the disturbance error is improved, so that the anti-interference performance of the control system is improved, and the method has certain universality. Simulation and experiment results show that high-quality operation of the linear driving system of the magnetic lead screw motor can be realized by adopting the improved active-disturbance-rejection control strategy.

Description

Technical Field

[0001] The present invention belongs to the technical field of the control of linear actuators, and particularly relates to a high anti-interference control method for a magnetic screw motor. It is applicable to fields such as new energy vehicles, aerospace, and robotics that have relatively high requirements for the reliability of motors. Background Art

[0002] With the progress of control algorithms and motor designs, magnetic screw motors have been increasingly widely used and have become indispensable equipment in fields such as numerical control machine tools, robotics, precision manufacturing, and aerospace. Magnetic screw motors can achieve high transmission efficiency without traditional mechanical couplings, so they have become a key driving force for the next-generation drive systems.

[0003] In the field of control technology, active disturbance rejection control (ADRC) has become a research hotspot attracting much attention due to its excellent performance. To further improve the performance of ADRC, a series of optimization strategies have been continuously explored and proposed in the industry.

[0004] For example, a quasi-resonant control method has been introduced. This method focuses on compensating for periodic disturbances, thus significantly enhancing the disturbance rejection ability of ADRC. Through precise algorithm design, it can effectively cope with periodically occurring disturbances and ensure the stability of the system in the face of such disturbances. However, there is still room for improvement in dealing with non-periodic disturbances and multi-frequency disturbances.

[0005] In addition, an active disturbance rejection control strategy integrating neural networks and improved differentiation has been proposed to optimize the parameter tuning process. This strategy cleverly combines the self-learning ability of neural networks and the fast response characteristics of improved differentiation to achieve fast and precise tuning of control parameters, greatly improving the adaptability and control accuracy of the system. However, in practical applications, this method requires a large amount of data to train neural networks, and the computational complexity is relatively high, which to a certain extent limits its wide application.

[0006] Enhancing the ability to observe disturbance signals is crucial for precisely compensating for disturbances during motor operation. Some research has optimized the parameter adjustment process of the linear auto-disturbance rejection controller through bandwidth design and significantly enhanced the system's anti-disturbance analysis ability. This design can respond more quickly to disturbance signals and improve the system's anti-interference performance. However, there are still certain bandwidth limitations when dealing with high-frequency disturbances. Other research has proposed an improved disturbance observer that innovatively separates disturbance estimation from state reconstruction and introduces new parameters to adjust the disturbance suppression performance, thereby independently enhancing the system's flexibility. This separated design enables the system to observe and compensate for disturbances more accurately, but the introduction of new parameters also increases the difficulty of system design and debugging. Another study has conducted an in-depth error theory analysis of the extended state observer and optimized the system control performance with the help of an improved nonlinear function. Through error theory analysis, the performance of the observer can be evaluated more accurately, and the improved nonlinear function further enhances the control effect of the system. However, there are still problems such as phase lag and small observer gain in existing methods, which limit the response speed and compensation accuracy of the system to rapidly changing disturbances and affect the further expansion of auto-disturbance rejection control in high-precision and high-performance application scenarios. Summary of the Invention

[0007] In view of the related problems existing in traditional auto-disturbance rejection control strategies, the present invention proposes a linear speed control strategy for a magnetic force ball screw motor using an improved auto-disturbance rejection controller. This method is universal, simple to calculate, and easy to implement.

[0008] To achieve the technical objectives, the present invention adopts the following technical solutions:

[0009] The linear speed control strategy for a magnetic force ball screw motor based on an improved auto-disturbance rejection controller includes the following steps:

[0010] Step 1: Analyze the internal structure and working principle of the magnetic force ball screw motor and establish a corresponding mathematical model;

[0011] Step 2: In view of the flexible structure of the magnetic force ball screw motor, select an auto-disturbance rejection controller (ADRC) to control the linear speed of the motor, and establish the basic mathematical model of the second-order ADRC according to the motor voltage equation and motion equation;

[0012] Step 3: Design the second-order nonlinear tracking differentiator (TD) part to extract the speed signal and other required mutation signals;

[0013] Step 4: Design the nonlinear state error feedback (NLSEF) part to dynamically compensate for the disturbance error to obtain the final control quantity;

[0014] Step 5: Design an extended state observer (ESO) to observe the linear speed error and disturbance signal;

[0015] Step 6: To improve the error observation ability of the extended state observer and thus enhance the disturbance rejection ability of the linear drive system, the ESO is made higher-order and the acceleration error signal is introduced at a reasonable position in the state equation. Through parameter tuning, a higher-order double-error extended state observer (HSESO) with better observation performance is designed.

[0016] Step 7: Build a closed-loop control system consisting of a speed loop and a current loop. The magnetic grating ruler detects the actual speed of the magnetic force lead screw motor and inputs it into the extended state observer for extended calculation of the disturbance quantity. The observed speed obtained by the observer is used as the feedback speed v of the motor. The speed error of the motor is obtained by comparing the given speed with the observed value. Using the improved ADRC, according to the linear speed error and the disturbance observation value, the desired current iq* of the magnetic force lead screw motor is calculated. The desired q-axis voltage uq of the motor is obtained by comparing the given current with the feedback current iq of the current sensor. According to the vector control algorithm, the given d-axis current id* = 0, and combined with the feedback current, the d-axis voltage ud is calculated through a PI controller.

[0017] Step 8: The obtained reference voltages ud and uq are input into the SVPWM module after coordinate transformation to obtain the switching signals of each phase. Subsequently, the obtained switching signals are input into the inverter to control the motor, realizing the high tracking performance control of the magnetic force lead screw motor.

[0018] The present invention has the following beneficial effects: 1. Establish a magnetic force lead screw motor model, design an active disturbance rejection controller according to the motor motion characteristics, which effectively improves the disturbance rejection ability of the motor linear speed control compared with the traditional PI control, and fills the gap in the active disturbance rejection control of the magnetic force lead screw motor linear speed control. 2. The extended state observer in the higher-order controller is made higher-order and the acceleration error is introduced at a reasonable position in the state equation to obtain an improved active disturbance rejection controller. Compared with the existing technology, the improved method proposed by the present invention improves the observation ability of the extended state observer for disturbance errors, thus improving the disturbance rejection performance of the control system, and has a certain generality. The simulation and experimental results show that the use of this improved active disturbance rejection control strategy can achieve high-quality operation of the magnetic force lead screw motor linear drive system. Description of the Drawings

[0019] Figure 1 : Block diagram of the active disturbance rejection linear speed control of the magnetic force lead screw motor;

[0020] Figure 2 : Structure diagram of the magnetic force lead screw motor;

[0021] Figure 3 : Structure diagram of the ADRC controller;

[0022] Figure 4 : Bode diagram of the disturbance signal observation by different extended state observers;

[0023] Figure 5 : Simulation result diagram of the magnetic screw motor at a given speed of 15 mm / s; (a) speed waveform; (b) speed error waveform; (c) speed observation error waveform;

[0024] Figure 6 : Experimental diagram of speed mutation of the magnetic screw motor; (a) speed waveform; (b) speed observation error waveform Specific implementation manners

[0025] The technical solutions in the embodiments of the present invention will be described in detail and completely below with reference to the accompanying drawings in the embodiments of the present invention.

[0026] Step 1: Establish a mathematical model of the magnetic screw motor. The motor design combines a magnetic screw and a rotor, and the rotor is located between the stator and the actuator. Radial permanent magnets are arranged between the rotor and the stator, and the magnetic flux is transmitted to the spiral permanent magnet through the rotor core. The permanent magnet synchronous motor part in the magnetic screw motor is a surface-mounted motor, and its voltage and torque equations can be expressed as follows:

[0027]

[0028] Wherein, u d and u q are the dq-axis voltages respectively, L d and L q are the dq-axis inductance values respectively, P n is the number of pole pairs, ψ f is the magnetic flux of the permanent magnet.

[0029] The motion equation of the magnetic screw motor is:

[0030]

[0031]

[0032] Where J is the moment of inertia; B is the damping coefficient; T e is the electromagnetic torque; T l is the load torque of the rotor, where h = λ / 2π, which is the ratio of the motor pole pitch to the radian of one cycle, that is, the transmission ratio between the rotational motion of the motor rotor and the linear motion of the magnetic screw.

[0033] Step 2: Considering the linear motion characteristics of the motor and the displacement between the moving rotor and the stator, design a second-order active disturbance rejection controller for the speed outer loop:

[0034]

[0035] It can be further rewritten as:

[0036]

[0037] where is a time-varying disturbance term; As the theoretical error gain coefficient, it is adjustable; K t = 1.5P n F f .

[0038] Step 3: Design a second-order nonlinear tracking differentiator (TD) to extract the velocity signal and other required mutation signals. A reasonable transition process can obtain the desired velocity signal, and the desired acceleration signal can be extracted after noise suppression. Its discrete second-order nonlinear expression is as follows:

[0039]

[0040] In the formula, the state variables v1 and v2 represent the expected linear velocity v and the expected acceleration respectively; r is the velocity factor, which can be adjusted. The larger the r value, the faster the expected command tracking speed; h is the filtering factor, and the larger the h, the better the filtering effect; T is the differential interval, and the smaller the T, the better the filtering effect. Generally, T is slightly smaller than h.

[0041] The fhan function in the formula is as follows:

[0042]

[0043] where u(k) is the input expected linear velocity signal, and sign is the sign function. It outputs 1, -1, or 0 according to whether the input value is positive, negative, or equal to zero respectively.

[0044] Step 4: Subtract the v tracking signal of the TD from the v observed signal in the observer, and then perform nonlinear combination into a series controller form, and the corresponding NLSEF form can be obtained as:

[0045]

[0046] In the formula, i q ’ is the preset torque control amount; i q * is the final control amount after adding the feedforward disturbance.

[0047] Step 5: Use the active disturbance rejection control law in Step 2 to expand a disturbance variable from the second-order nonlinear system of the motor control, and then construct an extended state observer as:

[0048]

[0049] Among them, z1 is the observed value of v; z2 is the observed value of ; e1 is the observation error of v; z3 is the observed value of the total disturbance f(x2, w, t); u is the control quantity output by the ADRC controller; β1 and β2 are the output correction factors of the observation error of v; β3 is the output correction factor of the disturbance observation error.

[0050] Step 6: High-order the traditional ESO, then the state equation of the system is:

[0051]

[0052] The state equation after introducing the acceleration error is:

[0053]

[0054] Write out the error transfer function G(s):

[0055]

[0056] Because its disturbance error transfer function has one more parameter, that is, there is one more degree of freedom in the parameter tuning process. Let β3 = aβ4, and select an appropriate a to obtain an ideal observer. Compared with the traditional linear extended state observer (LESO) and the high-order extended observer (HESO) after high-ordering, the improved double-error extended state observer has a larger disturbance rejection gain and a smaller phase delay.

[0057] Step 7: Build a closed-loop control system composed of a speed loop and a current loop, and embed the designed ADRC into the speed loop.

[0058] Step 8: Input the obtained reference voltages u d 、u q After coordinate transformation, input them into the SVPWM module to obtain the switching signals of each phase; then input the obtained switching signals into the inverter to control the motor, realizing the high tracking performance control of the magnetic force screw motor.

[0059] Figure 1 The block diagram of the active disturbance rejection linear speed control of the magnetic force screw motor is given. Figure 4 The Bode diagrams of the disturbance signal observation by different extended state observers under the same bandwidth are given. Figure 5 The simulation result diagram of the magnetic force screw motor at a given speed of 15 mm / s is given. Figure 5 (b) It can be seen from the speed error waveform that the linear speed response of the motor is smoother and the system has strong disturbance rejection ability under the observer proposed in the present invention. Figure 5 (c) The speed observation error waveform also verifies that the proposed observer has stronger disturbance observation ability. Figure 6 (a) and Figure 6(b) shows the speed response curve of the motor when the given linear speed increases suddenly from 10 mm / s to 20 mm / s at 6 s and the observer error estimation curve. The observation error of the proposed HSESO is significantly smaller at the peak in the constant speed section, and the corresponding steady-state error of the linear speed is within 2.4%. In the variable speed stage, the convergence time of HSESO is 1.14 s, which is much lower than 3.93 s and 1.45 s of the other two observers, reflecting that under the disturbance estimation of the proposed observer, the forward variable speed system has good dynamic and steady-state performance.

[0060] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the claims and their equivalents.

Claims

1. A linear speed control method for a magnetic screw motor based on an improved anti-disturbance controller, characterized in that: The steps include: Step 1: Analyze the internal structure and working principle of the magnetic screw motor and establish the corresponding mathematical model; Step 2: In view of the structural flexibility of the magnetic screw motor, the ADRC is selected to control the linear speed of the motor. The basic mathematical model of the second-order ADRC of the speed outer loop is established according to the motor voltage equation and the motion equation. Step 3: Design the second-order nonlinear tracking differentiator TD part to extract the speed signal and other required mutation signals; Step 4: Design the nonlinear state error feedback NLSEF part to dynamically compensate the disturbance error to obtain the final control quantity; Step 5: Design the extended state observer ESO to observe the linear velocity error and disturbance signal; Step 6: In order to improve the error observation capability of the extended state observer and thus improve the anti-disturbance capability of the linear drive system, the ESO is made higher-order and the acceleration error signal is introduced at a reasonable position in the state equation. By setting parameters, a higher-order dual-error extended state observer HSESO with better observation performance is designed. Step 7: Build a closed-loop control system consisting of a speed loop and a current loop. The magnetic scale detects the actual speed of the magnetic screw motor and inputs it into the extended state observer to expand the disturbance. The observed speed obtained by the observer is used as the feedback speed v of the motor. The given speed is compared with the observed value to obtain the speed error of the motor. The improved ADRC is used to calculate the expected current iq of the magnetic screw motor based on the linear speed error and the disturbance observation value. * , compare the given current with the current sensor feedback current iq to get the expected q-axis voltage u of the motor q , according to the vector control algorithm, given the d-axis current i d * =0, combined with the feedback current, the d-axis voltage u is calculated by the PI controller d ; Step 8: The obtained reference voltage u d 、u q After coordinate transformation, it is input into the SVPWM module to obtain the switching signal of each phase; The obtained switching signal is then input into the inverter to control the motor, thereby achieving high tracking performance control of the magnetic screw motor.

2. A method according to claim 1, characterized in that In step 1, the motor design combines a magnetic screw and a rotor, where the rotor is located between the stator and the actuator; radial permanent magnets are arranged between the rotor and the stator, and the magnetic flux is transferred to the helical permanent magnets through the rotor core; the permanent magnet synchronous motor part in the magnetic screw motor is a surface-mounted motor, and its voltage and torque equations can be expressed as follows: Among them, u d and u q are the dq axis voltage, i d and i q are dq axis current, L d and L q are the dq axis inductance, P n is the number of magnetic pole pairs, ψ f is the permanent magnet flux, R is the motor resistance, ω e is the electrical angular velocity, T e is the electromagnetic torque. The motion equation of the magnetic screw motor is: Where J is the moment of inertia; B is the damping coefficient; T e is the electromagnetic torque; T l is the load torque of the rotor; f t is the motor axial thrust, f l is the load thrust; v and w are the motor linear velocity and mechanical angular velocity respectively; where h = λ / 2π, is the ratio of the motor pole pitch to one cycle radian, that is, the transmission ratio between the motor rotor rotational motion and the magnetic screw linear motion, Δh is the transmission ratio error, x and θ are the linear displacement and rotor angle respectively.

3. A method according to claim 1, characterized in that In step 2, the speed outer loop second-order active disturbance rejection controller ADRC: Where M is the motor mass; J is the moment of inertia; B is the damping coefficient; T e is the electromagnetic torque; T l is the load torque of the rotor; v and Δv are the linear speed and speed error of the motor, and h = λ / 2π is the ratio of the motor pole pitch to one cycle of radians, that is, the transmission ratio between the rotational motion of the motor rotor and the linear motion of the magnetic screw; It can be further rewritten as: in is a time-varying disturbance term; As the theoretical error gain coefficient, it can be adjusted; K t =1.5P n F f .

4. A method according to claim 1, characterized in that In step 3, the second-order nonlinear TD is used to extract the velocity signal and other required mutation signals; a properly designed transition process can obtain the desired velocity signal and extract the desired acceleration signal after noise suppression; the expression of the second-order nonlinear tracking differentiator is: In the formula, fhan is the fastest function, fh is its abbreviation, state variables v1 and v2 represent the expected linear velocity v and expected acceleration respectively; r is the speed factor, which can be adjusted. The larger the r value, the faster the expected instruction tracking speed; h is the filter factor. The larger h is, the better the filtering effect; T is the differential interval. The smaller T is, the better the filtering effect. In general, T is slightly smaller than h. The fhan function is as follows: Among them, d, d0, y, a0 are all intermediate variables, u(k) is the input expected linear velocity signal, and sign is the sign function, which outputs 1, -1 or 0 according to whether the input value is positive, negative or equal to zero.

5. A method according to claim 1, characterized in that: In step 4, the v tracking signal of TD is subtracted from the v observation signal in the observer, and then nonlinearly combined into a series controller form, and the corresponding nonlinear state error feedback NLSEF form is obtained as: Where, e1 is the difference between the reference velocity v1 and the estimated velocity z1, e2 is the difference between the reference acceleration v2 and the estimated acceleration z2; z3 is the estimation error; β1 and β2 are the error gain coefficients of e1 and e2 respectively; fal is a nonlinear function that plays a role in smooth transition, α1 and α2 are two nonlinear coefficients of the nonlinear function; δ is the nonlinear system accuracy coefficient; b is the disturbance compensation gain coefficient; i q ' is the preset torque control amount; i q * is the final control quantity after adding the feedforward disturbance.

6. A method according to claim 1, characterized in that: In step 5, the extended state observer ESO is: Among them, x1 is the actual speed of the motor; b is the disturbance error gain coefficient; z1 is the observed value of v; z2 is the observed value of; e1 is the observed error of v; z3 is the observed value of the total disturbance f(x2,w,t); u is the control quantity output by the ADRC controller; β1 and β2 are the output correction factors of the v observation error; β3 is the output correction factor of the disturbance observation error.

7. A method according to claim 1, characterized in that In step 6, the high-order double-error extended state observer HSESO is used, and the state equation of the system is: Among them, e1 is the difference between the actual motor speed x1 and its observed value z1; z2 is the difference between the actual motor acceleration x2 and its observed value z2; z3 is the disturbance observation value; z4 is the observation value of the differential of the disturbance; β1, β2, β3, β4 are the error gain coefficients; The state equation after the acceleration error is introduced is: Among them, e1 is the difference between the actual motor speed x1 and its observed value z1; z2 is the difference between the actual motor acceleration x2 and its observed value z2; z3 is the disturbance observation value; z4 is the observation value of the differential of the disturbance; β1, β2, β3, β4, β5 are the error gain coefficients; Write the error transfer function G(s): Its disturbance error transfer function has one more parameter, that is, there is one more degree of freedom in the parameter tuning process. Let β3 = aβ4, and choose a suitable a to get the ideal observer. Compared with the traditional linear extended state observer (LESO) and the higher-order HESO, the higher-order dual-error extended state observer has a larger anti-disturbance gain and smaller phase delay.

8. The method according to claim 1, characterized in that The step 7 builds a closed-loop control system consisting of a speed loop and a current loop, and embeds the designed ADRC into the speed loop.

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