A speed smooth switching control method of a permanent magnet wheel hub motor in a wide speed range

Abstract

The application discloses a permanent magnet wheel hub motor speed smooth switching control method in a wide speed range, step 1, a first-order mechanical motion equation of a permanent magnet synchronous motor is established; step 2, a linear extended state observer LESO is established according to the first-order mechanical motion equation of the permanent magnet synchronous motor, a tracking differentiator and a feedback control law are established for realizing complete linear active disturbance rejection controller LADRC design; step 3, the structure of the LESO is improved, a resonant integral extended state observer RI-ESO is adopted, so that the RI-ESO can simultaneously observe the sinusoidal disturbance and the constant disturbance occurring in the motor control process; step 4, the method of switching the RI-ESO input is adopted to ensure the stable operation of the system in a wide speed range, and the suppression ability of the harmonic disturbance is also ensured; step 5, the T e The value of the resonant gain can be appropriately increased when the observer is inputted, the suppression ability of the harmonic is improved with the increase of the speed, and the actual situation can be adjusted.

Description

Technical Field

[0001] This invention relates to the field of control technology for permanent magnet hub motors, and specifically to a smooth speed switching control strategy for permanent magnet hub motors over a wide speed range. Background Technology

[0002] In recent years, permanent magnet hub motors (PMSHMs) have been widely used in direct drive fields such as electric vehicles, electric propulsion, and robots due to their advantages of simple structure, high reliability, and high control precision.

[0003] However, torque ripple is still unavoidable in the actual use of permanent magnet hub motors. There are many reasons for torque ripple, such as cogging torque and flux harmonics caused by the motor's structure, voltage and current harmonics caused by inverter dead-zone effects and current measurement errors. Torque ripple directly causes speed and position fluctuations, especially for larger low-order torque ripples. In severe cases, it can even lead to system instability. Therefore, to ensure smooth speed control and safe and reliable system operation, certain methods must be adopted to suppress torque ripple.

[0004] Current technical solutions for suppressing electromagnetic torque ripple can be broadly categorized into two types: one is to reduce electromagnetic torque ripple from the perspective of motor structure design and optimization; the other is to suppress torque ripple through control algorithm design. Suppressing torque ripple through motor design not only increases the complexity and cost of motor design and manufacturing but also affects the motor's power density. Furthermore, optimized motor design cannot overcome torque ripple caused by harmonics in the drive controller. While actively suppressing torque ripple from a control perspective is difficult to completely eliminate due to limitations in torque ripple detection and control errors, it offers greater flexibility and applicability.

[0005] In summary, given the speed fluctuations and even system instability caused by torque pulsation in practical applications of PMSHM, it is necessary to propose a speed smoothing control strategy to meet the motor operation requirements. Summary of the Invention

[0006] Based on the shortcomings of the existing technology, this invention proposes a smooth speed switching control strategy for permanent magnet hub motors over a wide speed range. The technical solution of this invention is as follows:

[0007] A method for smooth speed switching control of a permanent magnet hub motor over a wide speed range includes the following steps:

[0008] Step 1: Establish the first-order mechanical motion equations of the permanent magnet synchronous motor;

[0009] Step 2: Based on the first-order mechanical motion equation of the permanent magnet synchronous motor, establish the linear extended state observer (LESO). To realize the complete linear active disturbance rejection controller (LADRC) design, establish the tracking differentiator and feedback control law.

[0010] Step 3: Improve the structure of LESO by using the Resonance-integral Extended State Observer (RI-ESO) to enable it to simultaneously observe sinusoidal disturbances and constant disturbances that occur during motor control.

[0011] Step 4: The method of switching RI-ESO input is used to ensure the stable operation of the system over a wide speed range, while also ensuring the ability to suppress harmonic disturbances.

[0012] Step 5, switching T e When used as an observer input, the resonant gain k can be appropriately increased. r The value of increases with the rotational speed, enhancing the ability to suppress harmonics. It can be adjusted according to the actual situation.

[0013] Furthermore, the specific process of step 1 is as follows:

[0014] First, the first-order mechanical motion equations of the permanent magnet synchronous motor are established as follows:

[0015]

[0016] In the formula, ω is the mechanical angular velocity of the motor rotor, rad / s; T e T L These are electromagnetic torque and load torque, respectively, in N·m; T r The pulsating torque mainly includes cogging torque caused by the motor itself, and sixth harmonic torque caused by the inverter dead time, etc. e * The electromagnetic torque is given by B, the viscous friction coefficient is B, the moment of inertia is J, the control gain is b = 1 / J, and the total disturbance is... The total disturbance f without considering torque tracking error n =-(Bω+T) r +T L ) / J.

[0017] Furthermore, the specific process of step 2 is as follows:

[0018] The linear extended state observer LESO is established as follows:

[0019]

[0020] In the formula, δ represents the error between the measured velocity and the observed velocity. n Let b = 1 / J be the speed measurement noise, and b = 1 / J be the control gain. Variables marked with ^ are estimated values, and h1 and h2 are the observer gains. Based on the bandwidth method tuning strategy, the observer parameters can be determined as h1 = 2ω. o , ω o For observer bandwidth;

[0021] To achieve a complete linear active disturbance rejection controller (LADRC) design, a tracking differentiator and a feedback control law are also required. To simplify the controller design and facilitate parameter tuning, the linear tracking differentiator is ignored, and a linear feedback control law is adopted. The linear feedback control law is designed as follows:

[0022]

[0023] In the formula, the mechanical angular velocity ω and the total disturbance f to These are usually unknown and can generally be replaced by their observed values. Therefore, the linear control law shown in the equation can be further expressed as:

[0024]

[0025] In the formula ω * For speed loop reference input, The observation rate is taken from the extended state observer. The observation perturbation, k, is taken from the extended state observer. ps The proportional gain of the controller;

[0026] Considering that a real system cannot produce infinite output, the output torque needs to be limited. The limiting function used is...

[0027]

[0028] In the formula For maximum torque reference, This serves as a reference for saturated torque.

[0029] Furthermore, in step 3, the resonant integral extended state observer RI-ESO is expressed in the s-domain as follows:

[0030]

[0031] In the formula To account for the error between the measured speed and the observed speed, For velocity observations, δ n For speed measurement noise, k r1 k r2 …k rnThe resonant gain is greater than 0, b = 1 / J is the control gain, and ω h1 ω h2 …ω hn Where is the resonant frequency; For observations of constant or low-frequency disturbances, For the observation of harmonic disturbances, k1 and k2 are the gain of the observer, and a bandwidth tuning strategy is adopted. The observer parameter k1 = 2ω o , ω o For observer bandwidth;

[0032] The observer uses an integrator for constant disturbances and a resonant controller for harmonic disturbances.

[0033] Furthermore, the specific process of step 4 is as follows:

[0034] Using T e When used as input to the observer, there is

[0035]

[0036] Based on the analysis, the closed-loop transfer function Δ of the system can be obtained. cl for

[0037]

[0038] In the formula T ci Let Δ2 be the torque loop time constant. 2 +k1s+k2 is the characteristic polynomial of LADRC, k ps ω is the proportional gain of the controller. h k is the resonant frequency. r For resonant gain

[0039] According to the Herwitz stability criterion, when there is a delay in the torque loop, T is used. e As input to the observer, the system is constant, but compared to using T... e * As an observer input, a strategy of switching inputs is adopted to ensure stable operation of the system while also ensuring the ability to suppress harmonic disturbances, as shown in equation (16).

[0040]

[0041] In the formula, u represents the observer input, ω hmax ω is the maximum resonant frequency. h_lim The resonant frequency limit can be obtained offline by calculating the stability condition.

[0042]

[0043] In the formula, C1, B1, and A1 are parameters set to simplify the expression. The specific expression is shown in equation (11).

[0044]

[0045] In equation (11), x, y, A, B, C, K, a 21 a 31 b, c, and d are also parameters established to simplify expressions, specifically...

[0046]

[0047] in

[0048]

[0049] In the formula k ps T is the proportional gain of the controller. ci Let k be the torque loop time constant, k1 and k2 be the observer gains, and k r This is the resonant gain;

[0050] In the formula ω h_lim The resonant frequency limit can be obtained offline by calculating the stability condition, ω hmax The maximum resonant frequency is achieved when simultaneously suppressing 1st, 2nd, and 6th order torque ripples:

[0051] ω hmax =6p n ω (29)

[0052] In the formula p n It is an extreme logarithm.

[0053] Furthermore, in step 5, the adaptive gain k is set. r for

[0054] k r1 =k r (1+aω e )=k r (1+ap n πn / 30) (30)

[0055] ω e denoted as ω0, where ωn is the mechanical rotor angular velocity in rpm; and α is a constant with an adaptive gain greater than 0.

[0056] Beneficial effects: Compared to traditional linear active disturbance rejection control (LADRC), the RI-ESO-based active disturbance rejection effectively suppresses sinusoidal pulsating torque, reducing speed fluctuation from 17.5 rpm to 4.5 rpm. (The last sentence appears to be incomplete and unrelated to the preceding text. It likely refers to a specific technical feature or function, but without further context, it's impossible to translate accurately.) eWhen used as an observer input, the resonant gain k can be appropriately increased. r The value of increases with the speed, enhancing the ability to suppress harmonics. It can be adjusted according to the actual situation. In this step, active disturbance rejection control based on MRI-ESO (improved resonant integral extended state observer) is used for switching control at high speed, which can achieve a good pulsating torque suppression effect and ensure the stability of the system over a wide speed range. Attached Figure Description

[0057] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly described below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0058] Figure 1 This is a block diagram of the overall control structure of the system based on MRI-ESO active disturbance rejection control according to an embodiment of the present invention;

[0059] Figure 2 This is a block diagram of the control structure of a traditional LADRC based on LESO, according to an embodiment of the present invention.

[0060] Figure 3 Bode plot of the disturbance rejection performance of traditional LADRC based on LESO in an embodiment of the present invention.

[0061] Figure 4 Bode plot of the disturbance rejection performance of RI-ADRC based on RI-ESO in an embodiment of the present invention.

[0062] Figure 5 The resonant frequency ω in this embodiment of the invention h With proportional gain k ps and bandwidth ω o Changing three-dimensional curves

[0063] Figure 6 This is a block diagram of the RI-ADRC structure based on RI-ESO according to an embodiment of the present invention;

[0064] Figure 7 This is a structural diagram of the MRI-ESO according to an embodiment of the present invention.

[0065] Figure 8 The simulated torque ripple waveform for an embodiment of the present invention

[0066] Figure 9 The following are simulation comparison waveforms of active disturbance rejection control based on LESO and RI-ESO in embodiments of the present invention.

[0067] Figure 10The above is a simulation waveform diagram of active disturbance rejection control based on RI-ESO under a given step speed of 100-400 rpm according to Embodiment 1 of the present invention.

[0068] Figure 11 The above is a simulation waveform diagram of MRI-ESO active disturbance rejection control under a given step jump of 100-500 rpm according to an embodiment of the present invention. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions in the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments.

[0070] Step 1: This invention is based on the traditional Linear Active Disturbance Rejection Controller (LADRC) based on the Linear Extended State Observer (LESO). The structure of LESO is improved and the tuning parameters are optimized to enhance the harmonic disturbance rejection performance and system stability of the traditional LADRC. Specifically:

[0071] First, the first-order mechanical motion equations of the permanent magnet synchronous motor are established as follows:

[0072]

[0073] In the formula, ω is the mechanical angular velocity of the motor rotor, rad / s; T e ,T L These are electromagnetic torque and load torque, respectively, in N·m; T r The pulsating torque mainly includes cogging torque caused by the motor itself, and sixth harmonic torque caused by the inverter dead time, etc. e * The electromagnetic torque is given by B, the viscous friction coefficient is B, the moment of inertia is J, the control gain is b = 1 / J, and the total disturbance is... The total disturbance f without considering torque tracking error n =-(BQ+T) r +T L ) / J.

[0074] Step 2: Based on equation (1), establish the traditional LESO as follows:

[0075]

[0076] In the formula, The error between the measured velocity and the observed velocity is represented by the variable marked with ^, which is the estimated value. h1 and h2 are the observer gains. Based on the bandwidth method tuning strategy, the observer parameters can be determined as h1 = 2ω. o , ωo This represents the observer bandwidth.

[0077] To achieve a complete Linear Active Disturbance Rejection Controller (LADRC) design, a tracking differentiator and a feedback control law are also required. To simplify the controller design and facilitate parameter tuning, the linear tracking differentiator is ignored, and a linear feedback control law is adopted.

[0078] The linear feedback control law is designed as follows:

[0079]

[0080] In the formula, the mechanical angular velocity ω and the total disturbance f to These are usually unknown and can generally be replaced by their observed values. Therefore, the linear control law shown in the equation can be further expressed as:

[0081]

[0082] In the formula ω * For speed loop reference input, The observation rate is taken from the extended state observer. The observation perturbation, k, is taken from the extended state observer. ps The proportional gain of the controller

[0083] Considering that a real system cannot produce infinite output, the output torque needs to be limited. The limiting function used is...

[0084]

[0085] In the formula For maximum torque reference, This serves as a reference for saturated torque.

[0086] The traditional LADRC control block diagram based on LESO is as follows: Figure 2 As shown

[0087] Bode plot analysis reveals that the LADRC controller based on traditional LESO has good suppression capabilities for constant disturbances and low-frequency disturbances, but poor or no suppression capability for harmonic disturbances of specific orders. This is because traditional LESO uses the DC internal model principle, which can completely observe constant disturbances and basically observe low-frequency disturbances, while feeding back the observed values ​​to compensate the control law.

[0088] Step 3: To achieve simultaneous suppression of both constant and harmonic disturbances, the structure of the traditional LESO needs to be improved. The traditional LESO does not differentiate between disturbances, treating them as a whole. However, in practical motor control applications, sinusoidal disturbances such as torque ripple exist. Therefore, the LESO structure needs to be improved to simultaneously observe both sinusoidal and constant disturbances. The RI-ESO expression used in this invention is as follows:

[0089]

[0090] In the formula k r1 k r2 …, where ω is the resonant gain. h1 ω h2 …is the resonant frequency.

[0091] The LADRC control block diagram based on RI-ESO is as follows: Figure 6 As shown

[0092] In the formula For the observation of constant or low-frequency disturbances, To observe harmonic disturbances, the observer uses an integrator for constant disturbances and a resonant controller for harmonic disturbances.

[0093] According to the bandwidth method, the system parameters can be determined as: k1 = 2ω o , Simultaneously set the resonant gain k r =λk2, λ>0.

[0094] Bode plot analysis reveals that the system exhibits good suppression capability for harmonic disturbances at specific frequencies, while its suppression performance for constant and low-frequency disturbances is similar to that of traditional LESO. Figure 3 .

[0095] Since the above analysis is based on not considering torque loop delay, and torque loop inevitably has a delay during system control, even if the torque loop uses deadbeat control with fast response, it will still cause a two-step delay in the control system. Typically, the torque loop can be modeled as a first-order inertial element.

[0096]

[0097] When considering the torque loop bandwidth, the relationship between torque setpoint and disturbance becomes:

[0098]

[0099] like Figure 4 According to the derivation, considering the torque loop bandwidth, the closed-loop transfer function of the RI-ESO-based active disturbance rejection control is:

[0100]

[0101] Take k ps =300, ω o =500rad / s, λ=1, the current loop uses deadbeat control, and the sampling period is 0.1ms, then T ci =2T s =0.2ms. Taking a 10-pole permanent magnet hub motor as an example, when the 6th order torque harmonic is suppressed (with electrical angle as the fundamental frequency), the system speed stability limit is 338 r / min, and the resonant frequency limit ω iim =338Hz, therefore, when using RI-ADRC based on RI-ESO for harmonic suppression, system instability will occur.

[0102] Step 4: To this end, the present invention employs a method of switching the RI-ESO input to ensure stable operation of the system over a wide speed range, using T... e When used as input to the observer, there is

[0103]

[0104] Based on the analysis, the closed-loop transfer function of the system is:

[0105]

[0106] According to the Herwitz stability criterion, when there is a delay in the torque loop, T is used. e As input to the observer, the system is constant, but compared to using T... e * As an observer input, T is used e As the observer input, due to the lack of... The observation results for this part of the disturbance are somewhat poor. Therefore, a strategy of switching inputs can be adopted to ensure the stable operation of the system while also ensuring the ability to suppress harmonic disturbances, as shown in Equation (16).

[0107]

[0108]

[0109]

[0110] In the formula ω h_lim The resonant frequency limit can be obtained offline by calculating the stability condition, ω hmax The maximum resonant frequency is achieved when simultaneously suppressing 1st, 2nd, and 6th order torque ripples:

[0111] ωhmax =6p n ω (45)

[0112] In the formula p n Extreme logarithm

[0113] Step 5: Simultaneously, to improve the ability to suppress harmonics, when switching T... e When used as an observer input, the resonant gain k can be appropriately increased. r The value of k is determined by the proportional increase of k when the rotational speed exceeds the specified speed. r The value is the set adaptive gain k. r for

[0114] k r1 =k r (1+aω e )=k r (1+ap n πn / 30) (46)

[0115] ω e Here, is the electrical angular velocity, n is the mechanical rotor angular velocity (rpm); a is a constant with an adaptive gain greater than 0, which increases the ability to suppress harmonics as the rotational speed increases, and can be adjusted according to actual conditions.

[0116] Based on stability criteria, offline switching conditions were set, and an MRI-ADRC based on MRI-ESO was constructed. Switching was performed when the motor was running at high speed and the harmonic suppression frequency reached its limit. e To ensure both harmonic suppression and system stability, the structural block diagram of the MRI-ESO is shown below. Figure 7 As shown.

[0117] The overall control flow diagram of the proposed invention method is as follows: Figure 1 As shown, the speed loop uses an MRI-ESO-based active disturbance rejection controller, and the current loop uses a deadbeat-free controller with fast response characteristics. First, the motor's given speed ω is... * With the actual speed ω of the motor m The electromagnetic torque setpoint is obtained by subtraction and MRI-ADRC control. The torque loop employs a deadbeat controller, with the output being a voltage u on both the direct and quadrature axes. d and u q After coordinate transformation, the voltage is controlled by space vector pulse width modulation (SVPWM) technology to control the switching of the power devices in the three-phase inverter, thereby controlling the amplitude and phase of the inverter output voltage; the current sensor collects the three-phase current and obtains the current feedback quantity after coordinate transformation; the rotor position angle required for coordinate transformation is collected by the position sensor; the speed feedback is calculated from the collected position signal.

[0118] The system block diagram of MRI-ESO is as follows: Figure 2 As shown, the input to the observer is T. e * or T e The output is the observed rotational speed and disturbance values. First, the input of the observer is determined to be T based on the switching conditions. e * Or T e Next, the rotational speed, constant disturbance, and harmonic disturbance are observed, output, and fed back to the linear control law. The reference torque T is obtained through the linear feedback control law. e * .

[0119] To verify the correctness and effectiveness of the theory, a simulation platform for an improved active disturbance rejection controller based on a permanent magnet hub motor was established. For example... Figure 8 As shown, periodic load disturbances of different frequencies are applied at the load end (Torque) to simulate actual torque pulsation. The expression for the applied load torque is T. L =2sin(Ω) e t)+1sin(2Ω e t)+0.5sin(6Ω e t). Figure 9 The demonstration shows that, given a 100 rpm step change, at t = 0.5 s, the RI-ESO-based active disturbance rejection control can effectively suppress sinusoidal pulsating torque compared to the traditional linear active disturbance rejection control (LADRC), reducing the speed fluctuation from 17.5 rpm to 4.5 rpm. Figure 10 The study demonstrates that instability occurs in RI-ESO-based active disturbance rejection control at speeds between 100 rpm and 400 rpm, due to torque loop bandwidth limitations. Figure 11 The study demonstrated that, with an MRI-ESO-based active disturbance rejection control system switching control at high speeds, the system can achieve good pulsating torque suppression and ensure stable performance over a wide speed range, from 100 rpm to 500 rpm.

[0120] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for smooth speed switching control of a permanent magnet hub motor over a wide speed range, characterized in that, Includes the following steps: Step 1: Establish the first-order mechanical motion equations of the permanent magnet synchronous motor; Step 2: Based on the first-order mechanical motion equation of the permanent magnet synchronous motor, establish the linear extended state observer (LESO). To realize the complete linear active disturbance rejection controller (LADRC) design, establish the tracking differentiator and feedback control law. Step 3: Improve the structure of LESO by using the Resonant Integral Extended State Observer RI-ESO, which enables it to simultaneously observe sinusoidal disturbances and constant disturbances that occur during motor control. Step 4: The method of switching RI-ESO input is used to ensure the stable operation of the system over a wide speed range, while also ensuring the ability to suppress harmonic disturbances. Step 5, switching T e Increase resonant gain when used as observer input The value of is adjusted according to the actual situation, as the rotational speed increases to improve the ability to suppress harmonics.

2. The method for smooth speed switching control of a permanent magnet hub motor over a wide speed range according to claim 1, characterized in that, Step 1 is as follows: First, the first-order mechanical motion equations of the permanent magnet synchronous motor are established as follows: （1）； In the formula, ω is the mechanical angular velocity of the motor rotor, rad / s; T e ,T L These are electromagnetic torque and load torque, respectively, in N·m; T r The pulsating torque includes cogging torque caused by the motor itself, and sixth harmonic torque caused by the inverter dead time. e * The electromagnetic torque is given by B, the viscous friction coefficient is B, the moment of inertia is J, the control gain is b = 1 / J, and the total disturbance is... The total disturbance without considering torque tracking error .

3. The method for smooth speed switching control of a permanent magnet hub motor over a wide speed range according to claim 1, characterized in that, Step 2 is as follows: The linear extended state observer LESO is established as follows: （1）； In the formula, δ represents the error between the measured velocity and the observed velocity. n For speed measurement noise, b = 1 / J is the control gain; variables marked with ^ are estimated values, h 1， h2 is the observer gain. Based on the bandwidth method tuning strategy, the observer parameters are determined as follows: , , For observer bandwidth; To achieve a complete linear active disturbance rejection controller (LADRC) design, a tracking differentiator and a feedback control law are also required. To simplify the controller design and facilitate parameter tuning, the linear tracking differentiator is ignored, and a linear feedback control law is adopted. The linear feedback control law is designed as follows: （3）； In the formula, the mechanical angular velocity Total disturbance By substituting their observed values, the linear control law shown in equation (3) is expressed as: （4）； In the formula For speed loop reference input, The observation rate is taken from the extended state observer. Observational perturbations taken from the extended state observer, The proportional gain of the controller; Considering that a real system cannot produce infinite output, the output torque needs to be limited. The limiting function used is: （5）； In the formula For maximum torque reference, This serves as a reference for saturated torque.

4. The method for smooth speed switching control of a permanent magnet hub motor over a wide speed range according to claim 1, characterized in that, In step 3, the resonant integral extended state observer RI-ESO is expressed in the s-domain as follows: （6）； In the formula To account for the error between the measured speed and the observed speed, For velocity observations, δ n For speed measurement noise, The resonant gain is greater than 0, and b = 1 / J is the control gain. Where is the resonant frequency; For observations of constant or low-frequency disturbances, For the observed values ​​of harmonic disturbances, k 1， k2 is the observer gain, using a bandwidth tuning strategy, and the observer parameters... , , For observer bandwidth; The observer uses an integrator for constant disturbances and a resonant controller for harmonic disturbances.

5. The method for smooth speed switching control of a permanent magnet hub motor over a wide speed range according to claim 1, characterized in that, The specific process of step 4 is as follows: Using T e When used as input to the observer, we have: （7）； Based on the analysis, the closed-loop transfer function Δ of the system can be obtained. cl for: （8）； In the formula T ci The torque loop time constant is... This is the characteristic polynomial of LADRC. ω is the proportional gain of the controller. h k is the resonant frequency. r This is the resonant gain; According to the Herwitz stability criterion, when there is a delay in the torque loop, T is used. e As input to the observer, the system is constant, but compared to using T... e * When used as the observer input, a strategy of switching inputs is employed to ensure stable system operation while also guaranteeing the ability to suppress harmonic disturbances, as shown in the following equation: (9); In the formula, u represents the observer input. The maximum resonant frequency. The resonant frequency limit can be obtained offline by calculating the stability condition: （10）； In the formula, C1, B1, and A1 are parameters set to simplify the expression; see the formula for the specific expression. : 0 (11); Mode Given x, y, A, B, C, K, a 21 a 31 b, c, and d are also parameters set up to simplify the expression, specifically: （12）； in: (13); In the formula T is the proportional gain of the controller. ci Let k be the torque loop time constant. 1， k2 is the gain of the observer, k r This is the resonant gain; In the formula The resonant frequency limit can be obtained offline by calculating the stability condition. When the resonant frequency is at its maximum value, and 1st, 2nd, and 6th order torque ripples are suppressed simultaneously: （14）； In the formula It is an extreme logarithm.

6. The method for smooth speed switching control of a permanent magnet hub motor over a wide speed range according to claim 1, characterized in that, In step 5, the adaptive gain is set. for: （15）； denoted as ω0, where ωn is the mechanical rotor angular velocity in rpm; and α is a constant with an adaptive gain greater than 0.

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