Mechanical resonance suppression method based on improved active disturbance rejection control

Abstract

The invention discloses a mechanical resonance suppression method based on improved active-disturbance-rejection control, and the method comprises the steps: firstly building a mathematical model of the electrical and mechanical relation of a permanent magnet synchronous motor, constructing a motor-load dual-inertia system through the mechanical coupling analysis of a servo system at a motor end and a load end, and carrying out the control of the motor-load dual-inertia system; and the intrinsic resonant frequency of the double-inertia system is identified. Secondly, constructing an extended state observer to estimate a low-frequency component of total disturbance, designing a resonance observer to estimate a high-frequency resonance component of the disturbance based on the resonant frequency parameter, and superposing the high-frequency resonance component to the low-frequency component to obtain an estimator of the total disturbance; and finally, according to the estimation result of the total disturbance, constructing a linear error state feedback control law, performing compensation correction on an original rotating speed instruction, obtaining an actual rotating speed loop output instruction, and completing mechanical resonance suppression. According to the method, the disturbance component at the resonant frequency is effectively tracked and estimated, and the disturbance observation precision and the steady-state precision near a resonance point are remarkably improved.

Description

Technical Field

[0001] This invention belongs to the field of motor control algorithms, and in particular relates to an active suppression control method for mechanical resonance of permanent magnet synchronous motor. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in industrial transmission and other fields due to their advantages such as simple structure, high efficiency, and high power density. Servo systems typically connect a PMSM to a load via couplings, gearboxes, and other transmission mechanisms, forming a typical dual-inertia system. The transmission mechanism is a crucial component of the servo system, serving as the link for power transmission. However, because the transmission mechanism is not perfectly rigid, its elastic characteristics can lead to speed oscillations, i.e., mechanical resonance. As the dynamic performance of servo systems continues to improve, the impact of neglecting the elastic element becomes increasingly significant. For systems with mechanical resonance, this can lead to deteriorated control performance, longer settling times, reduced speed loop bandwidth, and may even cause damage to the system's mechanical structure, or even shaft breakage, posing a significant threat to system and personnel safety. Therefore, in elastic servo systems, it is usually necessary to implement measures to suppress mechanical resonance.

[0003] Traditional methods for suppressing mechanical resonance in dual-inertia elastic systems primarily involve altering the transmission mechanism, such as by adding dampers. This method increases system damping, reduces oscillation amplitude, and thus suppresses system resonance. However, adding dampers increases cost, complicates the mechanical structure, and reduces the system's dynamic performance, failing to meet the demands for high dynamic performance.

[0004] Currently, methods for addressing mechanical resonance in servo systems are mainly divided into two categories: passive and active. Passive methods primarily utilize notch filters to strongly attenuate signals at specific frequencies while having almost no impact on signals in other frequency bands, effectively suppressing mechanical resonance. The advantage of this method is its simplicity and ease of implementation. However, while suppressing the original system's resonant frequency, the addition of the filter may introduce new resonant points into the system, altering its resonance characteristics and increasing the difficulty of control.

[0005] Direct control methods primarily address high-frequency disturbances caused by mechanical resonance in servo systems by introducing active resonance suppression algorithms into the motor speed loop. To further improve the system's disturbance rejection performance, researchers have proposed various improved speed loop control strategies, such as sliding mode control, predictive control, and adaptive control. Among these, active disturbance rejection control (ADRC), a novel control structure developed based on classical PID control, is widely used in mechanical resonance suppression due to its excellent robustness and disturbance rejection capabilities. ADRC-based direct control methods estimate resonance disturbances using an observer and compensate for the speed loop, thereby actively suppressing the effects of mechanical resonance. However, in practical applications, the limited bandwidth of the observer and its insufficient amplitude response at the resonant frequency lead to reduced accuracy in resonance disturbance estimation, thus affecting the overall control performance. Therefore, improving controller performance has become a key research topic in this field. Summary of the Invention

[0006] To address the aforementioned problems, this invention proposes an improved active disturbance rejection controller based on a resonant observer, and applies it to the speed loop control algorithm of a permanent magnet synchronous motor to solve the control performance degradation problem caused by elastic factors in servo systems. Traditional linear active disturbance rejection controllers use an extended state observer to estimate external disturbances and model uncertainties, effectively suppressing low-frequency disturbances. However, their observation capability at the resonant frequency is insufficient when mechanical resonance exists. Therefore, this invention introduces a resonant observation term into the original structure to enhance the observer's disturbance tracking capability at the mechanical resonant frequency. Based on achieving effective observation of resonant disturbances, a linear state error feedback control law is combined to compensate for speed commands, thereby effectively suppressing speed harmonics caused by elastic elements and significantly improving the dynamic and steady-state performance of the system.

[0007] To achieve the above-mentioned objectives, the present invention comprises the following steps:

[0008] This invention provides a mechanical resonance suppression method based on improved active disturbance rejection control, comprising the following steps:

[0009] S1. Establish a mathematical model of the electrical and mechanical relationship of the permanent magnet synchronous motor, use spring damping element to characterize the elastic characteristics of the servo system, and construct a motor-load dual inertia system model by analyzing the mechanical coupling of the servo system at the motor end and the load end, and establish the corresponding motor-load dual inertia system.

[0010] The process of establishing the corresponding dual-inertia system is as follows: By establishing an electrical and mechanical coupling model of the permanent magnet synchronous motor and further analyzing the mechanical relationship between the servo system at the motor end and the load end, the actual structure can be abstracted into a system with two main rotational inertias, i.e., a dual-inertia system. Based on this, a mathematical model of the motor-load dual-inertia system is established.

[0011] S2. Use the sinusoidal sweep frequency method to identify the intrinsic resonant frequency of the motor-load dual inertia system proposed in S1.

[0012] By applying a sinusoidal sweep frequency signal to the current loop, the speed output curve and the actual q-axis current response curve of the motor-load dual inertia system are recorded. The obtained data are analyzed by fast Fourier transform to obtain the amplitude-frequency characteristic curve of the motor-load dual inertia system. The resonant frequency of the motor-load dual inertia system is determined based on the position of the amplitude peak in the amplitude-frequency characteristic curve.

[0013] S3. Treat all quantities in the servo system that can affect the output, other than the input, as the total disturbance, and construct an extended state observer to estimate the low-frequency components of the total disturbance.

[0014] S4. Based on the resonant frequency parameters obtained by the sinusoidal frequency sweep identification in S2, a resonant observer is designed to estimate the high-frequency resonant components of the disturbance, which are then superimposed on the low-frequency components obtained in S3 to obtain an estimate of the total disturbance.

[0015] S5. Based on the estimation results of the total disturbance, construct a linear error state feedback control law, compensate and correct the original speed command, obtain the actual speed loop output command, and complete the mechanical resonance suppression.

[0016] The disturbance estimation stage of the quasi-resonant enhanced extended state observer consists of two parts: an original integrator and a newly added quasi-resonant control stage. The integrator retains the characteristics of the original observer, effectively estimating low-frequency and constant-form disturbances within the bandwidth. In other applications, increasing the observer's bandwidth can broaden the disturbance estimation range to ensure good control performance. However, in servo systems, due to the presence of resonant characteristics, as the increased bandwidth parameter gradually approaches the resonant frequency, the system's steady-state performance deteriorates sharply, making it difficult to balance steady-state and dynamic performance.

[0017] The resonant control circuit can effectively estimate the speed oscillation disturbances caused by the mechanical characteristics of the servo system, thereby achieving high-precision tracking of periodic disturbances caused by the elastic element. The resonant observer overcomes the bandwidth limitation problem of the original extended state observer under mechanical resonance conditions. This design combines low-frequency disturbance observation capability with resonant band enhancement performance, representing a key innovation that distinguishes it from traditional active disturbance rejection control.

[0018] The beneficial effects of this invention are:

[0019] (1) By introducing a resonant observer on the basis of the traditional extended state observer and using the resonant frequency obtained by frequency sweep identification as a parameter, the effective tracking and estimation of the disturbance component at the resonant frequency is realized, which significantly improves the disturbance observation accuracy of the system near the resonant point.

[0020] (2) The low-frequency disturbance estimation result is superimposed with the resonance disturbance estimation result to form a comprehensive estimate of the total disturbance. The speed command is compensated based on the linear error state feedback control law, thereby effectively offsetting the speed harmonics caused by the elastic connection and improving the dynamic response speed and steady-state accuracy of the system.

[0021] (3) The proposed control strategy improves upon the original linear active disturbance rejection control framework, enabling resonance disturbance observation without additional sensors. The algorithm has a simple structure and convenient parameter tuning, making it suitable for engineering applications in practical servo drive systems.

[0022] (4) This method has strong robustness to changes in model parameters and external load disturbances, and can maintain stable control performance under different elastic connection conditions and load inertia. Attached Figure Description

[0023] Figure 1 This is a control principle diagram of the present invention;

[0024] Figure 2 This is a force analysis diagram of the motor-load dual inertia system of the present invention;

[0025] Figure 3 This is a control block diagram of the extended state observer improved by using a resonant observer in this invention;

[0026] Figure 4 A comparison of the amplitude-frequency response curves of single-inertia and dual-inertia systems;

[0027] Figure 5 A comparison of the operating performance of traditional PI control and the algorithm proposed in this invention;

[0028] Figure 6 A comparison of the operating performance of traditional active disturbance rejection control and the algorithm proposed in this invention;

[0029] Figure descriptions: QRESO: Extended State Observer improved by a resonant observer; LSEF: Linear Error State Feedback; PMSM: Permanent Magnet Synchronous Motor. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0031] It should also be noted that, in order to avoid obscuring the present invention with unnecessary details, only the structures and / or processing steps closely related to the present invention are shown in the accompanying drawings, while other details that are not closely related to the present invention are omitted.

[0032] Figure 1 The control principle diagram of the present invention includes an improved active disturbance rejection controller module, a dual inertial system module, a current loop PI control module, an SVPWM module, an inverter module, and a coordinate transformation module.

[0033] This invention provides a mechanical resonance suppression method based on improved active disturbance rejection control. First, a motor-load dual-inertia system model is constructed. Then, by injecting a sinusoidal sweep frequency signal into the current loop input terminal, the resonant frequency of the system is obtained using the fast Fourier analysis results of the speed output and q-axis current. Next, based on the first step, all quantities in the dual-inertia model that can affect the output, besides the input, are considered as the total disturbance, and an extended state observer is constructed to estimate the low-frequency disturbance components. Then, using the resonant frequency parameters obtained from the second step of frequency sweep identification, a resonant observer is designed to estimate the high-frequency resonant components of the disturbance, which are then superimposed on the low-frequency disturbance obtained in the third step to obtain an estimate of the total disturbance. Finally, based on the disturbance estimation results, a linear error state feedback control law is constructed to compensate and correct the original speed command, obtaining the actual speed command.

[0034] The specific steps of this method are as follows:

[0035] S1, Establish and construct a model of a motor-load dual-inertia system:

[0036] First, the mechanical equations of the permanent magnet synchronous motor are:

[0037]

[0038] In equation (1), ω m This refers to the rotor's mechanical angular velocity; J is a differential operator; m P represents the motor's inertia and number of pole pairs, and ψ represents the motor's moment of inertia and number of pole pairs. f For permanent magnet flux linkage in motors; T e and T l B represents the electromagnetic torque and load torque of the motor; B is the frictional viscosity coefficient; i q and K t These are the input current command and torque coefficient of the servo system, respectively.

[0039] Figure 2 This paper demonstrates the force transmission process in a servo system, using a spring-damped element to simulate the mechanical properties of an elastic component. Based on the constructed dual-inertia model, force analyses are performed on the motor side and the load side separately, thus establishing a motor-load dual-inertia system model.

[0040]

[0041] The controller of the motor has a driving inertia of J. m The motor produces an electromagnetic torque of T. e The speed at which the motor shaft rotates is ω m The angle of rotation is θ m T s The torsional stiffness of the transmission link is K, which represents the interaction force between the motor and the load. s The damping coefficient is C s The resulting inertia is J l The load rotates, and the rotational speed and angle on the load side are ω. l and θ l .

[0042] This model can describe the mechanical resonance characteristics caused by the elastic transmission link, providing a theoretical basis for subsequent disturbance observation and control strategy design.

[0043] S2, the resonant frequency of the motor-load dual-inertia system is obtained by the sinusoidal frequency sweep method:

[0044] Based on the established dual-inertia model, the sinusoidal sweep frequency method is used to verify and test the resonance characteristics of the servo system.

[0045] The specific method is as follows: A sinusoidal sweep signal with a frequency gradually increasing from 1 Hz to 100 Hz is applied to the input terminal of the current loop. By acquiring the motor speed response and q-axis current response signals, a Fast Fourier Transform (FFT) analysis is performed to obtain the amplitude-frequency characteristic curve of the motor-load dual-inertia system. In systems containing resonant characteristics, a peak and a dip frequency can be obtained from the curve. The resonant frequency and anti-resonant frequency of the motor-load dual-inertia system can be intuitively obtained from the curve. This frequency parameter will be used as a key input in the subsequent design of the resonant observer to improve the estimation capability of mechanical resonance disturbances.

[0046] S3 treats quantities other than the input that can affect the output (such as load disturbance, parameter change, friction, etc.) as the total disturbance and constructs an extended state observer to estimate the low-frequency disturbance component of the total disturbance.

[0047] Combining equations (1) and (2), and considering all quantities other than the input that can affect the output as disturbances, we can obtain:

[0048]

[0049] The total disturbance referred to the load side can be expressed as: The design state variable is [ω] m f] T The corresponding estimator is The input is i q Construct the extended state observer ESO equation set:

[0050]

[0051] β1 and β2 are the observer gains, designed to have the following values:

[0052]

[0053] Where ω0 is the observer bandwidth, the magnitude of which directly determines how quickly the observer estimates the disturbance response. The bandwidth of this ESO enables the observer to track and acquire low-frequency components. The poles of the observer are determined by specifying the observer bandwidth. The optimal value of this bandwidth allows the observer to quickly track low-frequency disturbances and is significantly lower than the resonant frequency to avoid degrading the system response.

[0054] S4. Based on the resonant frequency parameters obtained by the sinusoidal frequency sweep identification in S2, a resonant observer is designed to estimate the high-frequency resonant components of the disturbance, which are then superimposed on the low-frequency components obtained in S3 to obtain an estimate of the total disturbance.

[0055] Ideal resonant observers have certain problems in practical engineering applications. Therefore, this patent's improvement strategy employs a quasi-resonant observer, whose transfer function expression is as follows:

[0056]

[0057] In the formula K r ω is the quasi-resonant gain coefficient. c ω is the cutoff frequency of the quasi-resonant controller. r The resonant frequency is selected from the resonant point identified offline via S2.

[0058] By superimposing a quasi-resonant observer on the original extended state observer expression, we can obtain the improved state-space expression:

[0059]

[0060] The resonant frequency in the servo system is estimated by improving the state-space expression, and then superimposed with the original gain to obtain the total disturbance estimate after reinforcement at the resonant point. The block diagram of the proposed controller can be obtained according to equation (7). Figure 3As shown in the figure, compared with the original observer, the disturbance estimation stage of the quasi-resonant enhanced extended state observer consists of two parts: an original integrator and a newly added quasi-resonant control stage. The integrator retains the characteristics of the original observer, effectively estimating low-frequency and constant-form disturbances within the bandwidth; while the resonant control stage can effectively estimate disturbances caused by speed oscillations due to the mechanical characteristics of the servo system, thus achieving high-precision tracking of periodic disturbances caused by the elastic element. This design combines low-frequency disturbance observation capability with resonant band enhancement performance, which is a key innovation distinguishing it from traditional active disturbance rejection control.

[0061] S5. Based on the total disturbance estimation result, a linear error state feedback control law is constructed to compensate and correct the original speed command, thereby obtaining the actual speed loop output command and completing the mechanical resonance suppression.

[0062] After estimating the total disturbance Then, linear error state feedback is introduced as the control law. Design After substituting into equation (3), we get Then when When the estimation error approaches 0, the new input i q0 With output ω m This can be represented as a first-order linear system, and finally proportional feedback control i is used. q0 =K l (ω m * -ω m ), ω m * By setting the desired angular velocity, the system control can be completed, and finally the actual rotational speed loop output command i is calculated. q The expression is:

[0063]

[0064] By introducing a disturbance compensation term into the control law, speed fluctuations caused by resonance disturbances can be effectively eliminated, thus achieving active suppression of mechanical resonance.

[0065] To verify the feasibility of this invention, a physical experiment was conducted on the proposed method. The parameters of the permanent magnet synchronous motor used in the experiment were: stator resistance R = 0.33Ω, dq-axis inductance L... d =L q =0.196mH, number of pole pairs p=5, permanent magnet flux linkage ψ s =0.0069Wb, motor inertia J m =2.8e-5kg·m 2 Load inertia J m =2.12e-4kg·m 2 DC bus voltage udc =24V.

[0066] To verify the existence of mechanical resonance in the dual-inertia elastic system, a sinusoidal sweep frequency signal was applied to the current loop, and a fast Fourier analysis was performed on the velocity output curve and the actual q-axis current curve to obtain the system's amplitude-frequency response curve, as shown below. Figure 4 As shown, a single-inertial system refers to a single-motor system, while a dual-inertial system refers to a motor-load elastic system. It can be observed that compared to a single-inertial system, the curve of a dual-inertial system clearly shows a dip and a peak, from which the corresponding resonant frequencies ω can be found. NTF and the anti-resonant frequency ω ARF The frequencies identified offline are incorporated into an improved active disturbance rejection (ADRR) resonant observer for control. The experimental condition involves applying a sudden applied rated load with a set speed command of 500 rpm. The control performance differences between PI control, traditional ADRR, and the improved ADRR algorithm proposed in this patent are compared. Figure 5 and Figure 6 The data analysis curves for the traditional algorithm and the proposed algorithm are shown under the same working conditions.

[0067] As shown by the curve: From Figure 5 The results show that when the speed loop uses PI control, after a sudden application of the rated load while the speed is stable, the speed drops by 100 r / min. Due to the elasticity, the speed fluctuates by 37 r / min in steady state. The frequency of the most prevalent harmonic component is the anti-resonant frequency, with an amplitude of 1.35% of the DC speed component. From... Figure 5 The results show that when the speed loop uses a traditional active disturbance rejection control strategy, after a sudden increase in rated load when the speed is stable, the speed drops by 63 r / min, the steady-state speed fluctuation is 35 r / min, and the amplitude of the highest-proportion harmonic component is 1.29% of the DC speed component. From... Figure 5 The results show that when the speed loop uses the method proposed in this paper, after a sudden application of the rated load when the speed is stable, the speed drops by 63 r / min, the steady-state fluctuation of the speed is 22 r / min, and the frequency amplitude of the highest harmonic component is 0.45% of the DC speed component.

[0068] The experimental results show that PI control in a dual-inertia system is limited by the anti-resonance frequency, resulting in slow response and steady-state fluctuations. While traditional active disturbance rejection control can improve the dynamic response under low- and medium-frequency disturbances, its effect on suppressing steady-state resonance is limited. The method proposed in this paper, while maintaining the fast response characteristics of active disturbance rejection control, significantly enhances the ability to suppress specific resonant disturbances by introducing a resonance observation term, effectively improving the overall control performance of the system.

[0069] In summary, this invention provides an improved active disturbance rejection control (ADRC) method for permanent magnet synchronous motors based on a resonant observer. This method addresses the mechanical resonance problem caused by elastic connections in servo systems by introducing a resonant observer into the traditional ADRC framework. By modeling the resonant frequency parameters identified through frequency sweep experiments, it achieves joint observation and compensation for low-frequency disturbances and resonant disturbances. This method not only retains the fast response characteristics of ADRC to step disturbances but also significantly improves the system's disturbance suppression capability at the resonant frequency, thereby effectively reducing speed fluctuations and improving the overall control performance and stability of the permanent magnet synchronous motor servo system.

Claims

1. A method for mechanical resonance suppression based on improved active disturbance rejection control, characterized in that, Comprise the following steps: S1, the mathematical model of the electrical and mechanical relationship of permanent magnet synchronous motor is established, the mechanical coupling analysis of the servo system at the motor end and the load end is carried out, the motor-load double inertia system model is constructed, and the corresponding motor-load double inertia system is established; S2, the internal resonance frequency of the motor-load double inertia system is identified by using the sine sweep method; S3, the extended state observer is constructed to estimate the low frequency component of the total disturbance; S4, based on the resonance frequency parameters obtained by the sine sweep identification, the resonance observer is designed to estimate the high frequency resonance component of the disturbance, which is superimposed on the low frequency component to obtain the estimation of the total disturbance; S5, according to the estimation result of the total disturbance, the linear error state feedback control law is constructed to compensate and correct the original speed command, and the actual speed loop output command is obtained, and the mechanical resonance suppression is completed.

2. The method according to claim 1, wherein The step S1 is specifically implemented as: The mechanical equation of permanent magnet synchronous motor is: In formula (1), ω m is the rotor mechanical angular velocity; is the differential operator; J m and P are the motor inertia and the number of pole pairs, ψ f is the motor permanent magnet flux linkage; T e and T l are the motor electromagnetic torque and the load torque; B is the friction viscous coefficient; i q and K t are the input current command and the torque coefficient of the servo system, respectively; Through the force analysis of the double inertia of the motor end and the load end of the servo system, the motor-load double inertia system model is established: The angle of the motor rotation is θ m ; T s is the interaction force of the motor and the load, the torsional stiffness of the transmission link is K s , the damping coefficient is C s , the driving inertia is J l , the load rotates, the rotational speed and the angle of the load side are ω l and θ l , respectively.

3. The method according to claim 2, wherein The step S2 is specifically implemented as: by applying a sine sweep signal at the current loop given end, recording the speed output curve and the actual q-axis current response curve of the motor-load double inertia system, performing fast Fourier transform analysis on the obtained data, obtaining the amplitude-frequency characteristic curve of the motor-load double inertia system model, and determining the resonance frequency of the motor-load double inertia system model according to the peak position of the amplitude-frequency characteristic curve.

4. The method according to claim 3, wherein The step S3 is specifically implemented as follows: According to formula (1) and formula (2), the quantity that can affect the output in the servo system except the input quantity is regarded as the total disturbance, and the following formula can be obtained: The total disturbance is converted to the load side and expressed as The design state variable is [ω m f] T The corresponding estimator is The input is i q The extended state observer equation group is constructed: β1 and β2 are the observer gains, and the design value is: Wherein ω0 is the bandwidth of the extended state observer ESO, and the low frequency component is obtained by the bandwidth of the ESO.

5. The method according to claim 4, wherein The step S4 is specifically implemented as follows: The quasi-resonance observer is adopted, and its transfer function expression is: where K r is the quasi-resonant gain coefficient, ω c is the cutoff frequency of the quasi-resonant controller, ω r is the resonant frequency; On the basis of the original ESO expression, the quasi-resonance observer is superimposed, and the improved state space expression is: The resonance frequency existing in the servo system is estimated by the improved state space expression, and the total disturbance estimation quantity reinforced at the resonance point is obtained by superimposing the original gain.

6. The method according to claim 5, wherein The step S5 is specifically implemented as follows: After estimating the total disturbance Then, linear error state feedback is introduced as the control law; design After substituting into equation (3), we get Then when When the estimation error approaches 0, the new input i q0 With output ω m Represented as a first-order linear system, i is ultimately controlled by proportional feedback. q0 =K l (ω m * -ω m ), ω m * To determine the desired angular velocity, the final calculated actual rotational speed is obtained by outputting the loop command i. q The expression is:

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