CN116317752A - A speed smooth switching control method for permanent magnet in-wheel motors in a wide speed range - Google Patents

Abstract

The invention discloses a speed smooth switching control method of a permanent magnet hub motor within a wide speed range. Step 1 is to establish the first-order mechanical motion equation of the permanent magnet synchronous motor; step 2 is to establish the first-order mechanical motion equation of the permanent magnet synchronous motor. Establish the linear extended state observer LESO, in order 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, using the resonance integral extended state observer RI‑ ESO, so that it can simultaneously observe the sinusoidal disturbance and constant disturbance in the motor control process; step 4, use the method of switching RI-ESO input to ensure the stable operation of the system in a wide speed range, and also ensure that there are harmonic disturbances In step 5, when switching T _e as the observer input, the value of the resonance gain can be appropriately increased, and the harmonic suppression ability can be improved with the increase of the speed, which can be adjusted according to the actual situation.

Description

A speed smooth switching control method for permanent magnet in-wheel motors in a wide speed range

technical field

The invention relates to the technical field of control of permanent magnet hub motors, in particular to a speed smooth switching control strategy for permanent magnet hub motors within a wide speed range.

Background technique

In recent years, permanent magnet in-wheel motors (PMSHMs) have been widely used in direct drive fields, such as electric vehicles, electric propulsion, and robotics, due to their simple structure, high reliability, and high control precision.

However, in the actual use of permanent magnet hub motors, torque ripple still inevitably exists. There are many reasons for torque ripple, such as cogging torque and flux harmonics caused by the structure of the motor body, voltage and current harmonics caused by inverter dead zone effects and current measurement errors. Torque ripple will directly cause speed fluctuation, position fluctuation, especially for larger low-order torque ripple. In severe cases, it may even lead to unstable operation of the system. Therefore, in order to ensure the smooth regulation of the speed and the safe and reliable operation of the system, certain methods must be used to suppress the torque ripple.

For the suppression of electromagnetic torque ripple, the current technical solutions can be roughly divided into two categories: one is to reduce the electromagnetic torque ripple from the perspective of motor body structure design and optimization, and the other is to achieve torque ripple through control algorithm design. inhibition. The scheme of suppressing torque ripple from the design of the motor body will not only increase the design and manufacturing complexity of the motor, increase the manufacturing cost, but also affect the power density of the motor. In addition, the optimal design of the motor body cannot overcome the torque ripple caused by the harmonics of the drive controller. From the point of view of control, active torque ripple suppression has strong flexibility and applicability, although it is difficult to completely eliminate factors such as torque ripple information detection and control errors.

To sum up, in the practical application of PMSHM, it is necessary to propose a speed smoothing control strategy to meet the motor operation requirements due to the speed fluctuation caused by the torque ripple and even the unstable operation of the system.

Contents of the invention

Based on the above deficiencies in the prior art, the present invention proposes a smooth switching control strategy for the speed of permanent magnet in-wheel motors within a wide speed range. The technical solution of the present invention is:

A speed smooth switching control method for a permanent magnet hub motor within a wide speed range, comprising the following steps:

Step 1, establishing the first-order mechanical motion equation of the permanent magnet synchronous motor;

Step 2. Establish the linear extended state observer LESO according to the first-order mechanical motion equation of the permanent magnet synchronous motor. In order to realize the complete design of the linear active disturbance rejection controller LADRC, establish the tracking differentiator and the feedback control law;

Step 3, improve the structure of LESO, and adopt the resonance integral extended state observer RI-ESO (Resonance-integral Extended State Observer), so that it can observe the sinusoidal disturbance and constant value disturbance that appear in the motor control process at the same time;

Step 4, use the method of switching RI-ESO input to ensure the stable operation of the system in a wide speed range, and also ensure the ability to suppress harmonic disturbances;

Step 5, when switching T _e as the observer input, the value of the resonance gain k _r can be appropriately increased, and the ability to suppress harmonics can be improved with the increase of the rotational speed, which can be adjusted according to the actual situation.

Further, the specific process of step 1 is:

Firstly, the first-order mechanical motion equation of the permanent magnet synchronous motor is established as follows:

不考虑转矩跟踪误差的总扰动f_n＝-(Bω+T_r+T_L)/J。Where ω is the mechanical angular velocity of the motor rotor, rad/s; T _e , T _L are the electromagnetic torque and load torque, N m; T _r is the pulsating torque, which mainly includes the cogging caused by the motor body. torque, and the sixth-order harmonic torque caused by the dead time of the inverter, etc., T _e ^* is the electromagnetic torque given value, B is the viscous friction coefficient, J is the moment of inertia, and the control gain b=1/J , the total disturbance

The total disturbance f _n =-(Bω+T _r +T _L )/J without considering the torque tracking error.

Further, the specific process of step 2 is:

The linear extended state observer LESO is established as follows:

为测量速度与观测速度之间的误差，δ_n为测速噪声，b＝1/J为控制增益。带有^的变量为估计值，h₁，h₂为观测器的增益，根据带宽法整定策略，可以确定观测器参数为h₁＝2ω_o，/>

ω_o为观测器带宽；In the formula,

It is the error between the measured speed and the observed speed, δ _n is the speed measurement noise, and b=1/J is the control gain. The variable with ^ is the estimated value, h ₁ and h ₂ are the gain of the observer, according to the tuning strategy of the bandwidth method, the observer parameter can be determined as h ₁ =2ω _o ,/>

ω _o is the observer bandwidth;

In order to realize the design of a complete linear active disturbance rejection controller (LADRC), tracking differentiators and feedback control laws are also required. In order to simplify the controller design and make parameter tuning convenient, the linear tracking differentiator is ignored and the linear feedback control law is used. The linear feedback control law design for:

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

取自扩张状态观测器的观测速度，/>

取自扩张状态观测器的观测扰动，k_ps为控制器的比例增益；Where ω ^* is the speed loop reference input,

The observed velocity from the extended state observer, />

The observed disturbance from the extended state observer, k _ps is the proportional gain of the controller;

Considering that it is impossible for the actual system to produce infinite output, the output torque needs to be limited, and the limiting function adopted is

为最大转矩参考，/>

为饱和转矩参考。In the formula

is the maximum torque reference, />

is the saturation torque reference.

Further, in step 3, the resonance integral extended state observer RI-ESO adopted in the s domain is expressed as follows:

为测量速度与观测速度之间的误差，/>

为速度观测值，δ_n为测速噪声，k_r1，k_r2…k_rn为谐振增益，都大于0，b＝1/J为控制增益，ω_h1，ω_h2…ω_hn为谐振频率；式中/>

为对常值扰动或者低频扰动的观测值，/>

为对谐波扰动的观测值，k₁，k₂为观测器的增益，采用带宽整定策略，观测器参数k₁＝2ω_o，/>

ω_o为观测器带宽；In the formula

is the error between the measured velocity and the observed velocity, />

is the speed observation value, δ _n is the speed measurement noise, k _r1 , k _r2 ... k _rn are the resonance gains, all of which are greater than 0, b=1/J is the control gain, ω _h1 , ω _h2 ... ω _hn are the resonance frequencies; where />

is the observed value of constant disturbance or low frequency disturbance, />

is the observed value of the harmonic disturbance, k ₁ and k ₂ are the gain of the observer, adopt the bandwidth tuning strategy, the observer parameter k ₁ =2ω _o ,/>

ω _o is the observer bandwidth;

The observer adopts the form of an integrator for constant disturbances, and the form of a resonant controller for the observation of harmonic disturbances.

Further, the specific process of step 4 is:

When T _e is used as the input of the observer, there is

According to the analysis, the closed-loop transfer function _Δcl of the system is

In the formula, T _ci is the time constant of the torque loop, Δ ₂ =s ² +k ₁ s+k ₂ is the characteristic polynomial of LADRC, k _ps is the proportional gain of the controller, ω _h is the resonant frequency, k _r is the resonant gain

According to the Hurwitz stability criterion, when there is a delay in the torque loop, using T _e as the input of the observer, the system is constant stable, but compared with the case of using T _e ^* as the input of the observer, The strategy of switching input is used to ensure the stable operation of the system and also to ensure the ability to suppress harmonic disturbances, as shown in equation (16)

In the formula, u represents the observer input, ω _hmax is the maximum value of the resonance frequency, and ω _{h_lim} is the limit value of the resonance frequency, which can be obtained offline by calculating the stability condition

In the formula, C ₁ , B ₁ , and A ₁ are parameters set to simplify the expression, and the specific expression is shown in formula (11)

In formula (11), x, y, A, B, C, K, a ₂₁ , a ₃₁ , b, c, d are also parameters set up to simplify the expression, specifically

in

where k _ps is the proportional gain of the controller, T _ci is the time constant of the torque loop, k ₁ and k ₂ are the gain of the observer, and k _r is the resonance gain;

In the formula, ω _{h_lim} is the limit value of resonance frequency, which can be obtained offline by calculating the stability condition, and ω _hmax is the maximum value of resonance frequency. For example, when suppressing the 1st order, 2nd order and 6th order torque ripple at the same time:

ω _hmax = 6p _n ω (29)

In the formula, p _n is the pole logarithm.

Further, in step 5, the adaptive gain k _r set is

k _r1 =k _r (1+aω _e )=k _r (1+ap _n πn/30) (30)

ω _e is the electrical angular velocity, n is the mechanical rotor angular velocity, rpm; a is a constant greater than 0 for the adaptive gain.

Beneficial effects: Compared with the traditional linear active disturbance rejection control (LADRC), the RI-ESO-based ADRC can well suppress the sinusoidal pulsating torque, and the speed fluctuation is reduced from 17.5rpm to 4.5rpm. When switching T _e as the input of the observer, the value of the resonance gain k _r can be appropriately increased, and the ability to suppress harmonics can be improved with the increase of the rotational speed, which can be adjusted according to the actual situation. In this step, the method based on MRI-ESO ( The active disturbance rejection control of the improved resonance integral extended state observer) switches control at high speed, which can achieve better ripple torque suppression effect and ensure the stability of the system in a wide speed range.

Description of drawings

In order to illustrate the embodiments of the present invention or the technical solutions in the prior art more clearly, the following will briefly introduce the drawings required in the embodiments. Apparently, the drawings in the following description are some embodiments of the present invention, and those skilled in the art can also obtain other drawings according to these drawings without any creative work.

1 is a block diagram of the overall control structure of the system based on MRI-ESO ADRC according to an embodiment of the present invention;

Fig. 2 is the control structure block diagram of the traditional LADRC based on LESO according to the embodiment of the present invention;

Fig. 3 is the Bode diagram of the anti-interference performance of the traditional LADRC based on LESO according to the embodiment of the present invention

Figure 4 is a Bode diagram of the anti-interference performance of RI-ADRC based on RI-ESO according to the embodiment of the present invention

Fig. 5 is the three-dimensional curve that the resonant frequency ω _h changes with the proportional gain k _ps and the bandwidth ω _o of the embodiment of the present invention

FIG. 6 is a structural block diagram of RI-ADRC based on RI-ESO according to an embodiment of the present invention;

Fig. 7 is the structural diagram of MRI-ESO of the embodiment of the present invention

Fig. 8 is the simulated torque ripple simulation waveform of the embodiment of the present invention

Fig. 9 is the comparison waveform of ADRC simulation based on LESO and RI-ESO according to the embodiment of the present invention

Fig. 10 is a simulation waveform diagram of active disturbance rejection control based on RI-ESO at a given step of 100-400rpm according to the embodiment of the present invention

Fig. 11 is a simulation waveform diagram of active disturbance rejection control based on MRI-ESO under a given step of 100-500rpm according to the embodiment of the present invention

Detailed ways

In order to make the purpose of the present invention, technical solutions and advantages clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only Some, but not all, embodiments of the invention.

Step 1: The present invention is based on the traditional linear active disturbance rejection controller (LADRC) based on the linear extended state observer (LESO), improves the structure of the LESO and optimizes the setting parameters, and improves the anti-harmonic disturbance performance of the traditional LADRC And system stability performance, specifically:

Firstly, the first-order mechanical motion equation of the permanent magnet synchronous motor is established as follows:

不考虑转矩跟踪误差的总扰动f_n＝-(BQ+T_r+T_L)/J。Where ω is the mechanical angular velocity of the motor rotor, rad/s; T _e , T _L are the electromagnetic torque and load torque, N m; T _r is the pulsating torque, which mainly includes the cogging caused by the motor body. torque, and the sixth-order harmonic torque caused by the dead time of the inverter, etc., T _e ^* is the electromagnetic torque given value, B is the viscous friction coefficient, J is the moment of inertia, and the control gain b=1/J , the total disturbance

The total disturbance f _n =-(BQ+T _r +T _L )/J without considering the torque tracking error.

Step 2: According to formula (1), the traditional LESO is established as follows:

为测量速度与观测速度之间的误差，带有^的变量为估计值，h₁，h₂为观测器的增益。根据带宽法整定策略，可以确定观测器参数为h₁＝2ω_o，/>

ω_o为观测器带宽。In the formula,

For the error between the measured speed and the observed speed, the variable with ^ is the estimated value, h ₁ and h ₂ are the gain of the observer. According to the tuning strategy of the bandwidth method, the observer parameters can be determined as h ₁ =2ω _o ,/>

ω _o is the observer bandwidth.

In order to realize a complete linear active disturbance rejection controller (LADRC) design, a tracking differentiator and a feedback control law are required. In order to simplify the controller design and facilitate parameter tuning, the linear tracking differentiator is ignored and the linear feedback control law is used

The linear feedback control law is designed as:

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

取自扩张状态观测器的观测速度，/>

取自扩张状态观测器的观测扰动，k_ps为控制器的比例增益Where ω ^* is the speed loop reference input,

The observed velocity from the extended state observer, />

The observed perturbation from the extended state observer, k _ps is the proportional gain of the controller

Considering that it is impossible for the actual system to produce infinite output, the output torque needs to be limited, and the limiting function adopted is

为最大转矩参考，/>

为饱和转矩参考。In the formula

is the maximum torque reference, />

is the saturation torque reference.

The traditional LADRC control block diagram based on LESO is shown in Figure 2

The Bode diagram analysis shows that the traditional LESO-based LADRC controller has a good ability to suppress constant disturbances and low-frequency disturbances, but it has poor or even no ability to suppress harmonic disturbances of a specific order. This is because the traditional LESO adopts the principle of DC internal model, which can completely observe constant value disturbance and basically observe low frequency disturbance, and at the same time, feedback and compensate the observed value to the control rate.

Step 3: In order to achieve common suppression of constant disturbances and harmonic disturbances, it is necessary to improve the structure of the traditional LESO. The traditional LESO does not distinguish the disturbance and regard it as a whole. In the actual motor control application , there are sinusoidal disturbances such as torque ripple, so it is necessary to improve the structure of LESO so that it can observe sinusoidal disturbances and constant disturbances at the same time. The RI-ESO expression that the present invention adopts is as follows

In the formula, k _r1 , k _r2 ... are the resonance gain, ω _h1 , ω _h2 ... are the resonance frequency.

The control block diagram of LADRC based on RI-ESO is shown in Figure 6

为对常值扰动或者低频扰动的观测，/>

为对谐波扰动的观测，观测器对常值扰动采用积分器形式，而对谐波扰动的观测采用谐振控制器形式。In the formula

For the observation of constant disturbance or low frequency disturbance, />

For the observation of harmonic disturbances, the observer adopts the form of an integrator for constant disturbances, and the form of a resonant controller for the observation of harmonic disturbances.

同时设定谐振增益k_r＝λk₂，λ＞0。According to the bandwidth method, the system parameters can be determined as: k ₁ =2ω _o ,

At the same time, set the resonance gain k _r =λk ₂ , where λ>0.

By analyzing the Bode diagram, it can be found that the system has a good ability to suppress harmonic disturbances of specific frequencies, and the suppression performance for constant value disturbances and low-frequency disturbances is similar to that of traditional LESO, as shown in Figure 3.

Since the above analysis is based on the fact that the torque loop delay is not considered, there will inevitably be a delay in the torque loop during the system control process, even if the torque loop adopts deadbeat control with fast response It will still cause a 2-step delay in the control system, and usually the torque loop can be modeled as a first-order inertial link, namely

When considering the torque loop bandwidth, the relationship between torque reference and disturbance becomes

As shown in Figure 4. According to the derivation, when considering the bandwidth of the torque loop, the closed-loop transfer function of ADRC based on RI-ESO is

Take k _ps = 300, ω _o = 500rad/s, λ = 1, the current loop adopts dead-beat control, and the sampling period is 0.1ms, then T _ci = 2T _s = 0.2ms, and the permanent magnet wheel hub motor with 10 pairs of poles is used as For example, when suppressing the sixth-order torque harmonic (with the electrical angle as the fundamental frequency), the system speed stability limit is 338r/min, and the resonance frequency limit ω _iim =338hz, so the RI-ADRC based on RI-ESO is used for harmonic System instability occurs when suppressed.

Step 4: For this reason, the present invention adopts the method of switching RI-ESO input to ensure the stable operation of the system in a wide speed range. When T _e is used as the input of the observer, there is

According to the analysis, the closed-loop transfer function of the system is

这部分扰动的观测，观测效果要差一些，为此可以采用切换输入的策略来保证系统的稳定运行同时也保证具有谐波扰动的抑制能力，如式(16)所示According to the Hurwitz stability criterion, when there is a delay in the torque loop, using T _e as the input of the observer, the system is constant stable, but compared with the case of using T _e ^* as the input of the observer, Using T _e as the observer input due to the lack of

The observation effect of this part of the disturbance is poorer. Therefore, the strategy of switching input can be adopted to ensure the stable operation of the system and also ensure the ability to suppress harmonic disturbances, as shown in formula (16)

In the formula, ω _{h_lim} is the limit value of resonance frequency, which can be obtained offline by calculating the stability condition, and ω _hmax is the maximum value of resonance frequency. For example, when suppressing the 1st order, 2nd order and 6th order torque ripple at the same time:

ω _hmax = 6p _n ω (45)

where p _n is the number of pole pairs

Step 5: At the same time, in order to improve the ability to suppress harmonics, the value of resonance gain k _r can be appropriately increased when switching T _e as the input of the observer, that is, the value of k _r is proportionally increased when the speed exceeds the specified speed, and the set The adaptive gain k _r is

k _r1 =k _r (1+aω _e )=k _r (1+ap _n πn/30) (46)

ω _e is the electrical angular velocity, n is the mechanical rotor angular velocity, rpm; a is a constant whose adaptive gain is greater than 0, and the ability to suppress harmonics is improved with the increase of the rotational speed, which can be adjusted according to the actual situation

According to the stability criterion, the switching conditions are set offline, and the MRI-ADRC based on MRI-ESO is constructed. When the motor is running at high speed and the harmonic suppression frequency reaches the limit value, switching T _e as the observer input is the premise to ensure the ability of harmonic suppression. , while ensuring the stability of the system, the structural block diagram of MRI-ESO is shown in Figure 7.

转矩环采用无差拍控制器，输出为交直轴的电压u_d和u_q。电压经过坐标变换后，采用空间矢量脉宽调制(SVPWM)技术来控制三相逆变器功率器件的通断，由此来控制逆变器输出电压的幅值与相位；电流传感器采集得到三相电流经坐标变换后得到电流反馈量和；坐标变换所需的转子位置角由位置传感器采集得到；转速反馈由采集得到的位置信号计算得到。The overall control flow chart of the proposed inventive method is shown in Figure 1. The speed loop adopts an active disturbance rejection controller based on MRI-ESO, and the current loop adopts a dead-beat controller with fast response characteristics. First, the given motor speed ω ^* Make a difference with the actual speed ω _m of the motor to obtain the electromagnetic torque given value through MRI-ADRC control

The torque loop adopts the deadbeat controller, and the output is the voltage u _d and u _q of the direct axis. After the coordinate transformation of the voltage, the space vector pulse width modulation (SVPWM) technology is used to control the on-off of the three-phase inverter power device, thereby controlling the amplitude and phase of the inverter output voltage; the current sensor collects the three-phase The current feedback amount is obtained after the coordinate transformation; the rotor position angle required by the coordinate transformation is collected by the position sensor; the speed feedback is calculated by the collected position signal.

The system _block diagram of MRI-ESO is shown in Fig. 2. _The input of the observer is T _e ^{* or} T _e , and the output is the observed value of the rotational speed and disturbance. Observe the rotational speed, as well as the constant value disturbance and harmonic disturbance, output and feed back to the linear control rate, and obtain the reference torque T _e ^* through the linear feedback control rate.

In order to verify the correctness and validity of the theory, a simulation platform of the improved ADRC based on the permanent magnet in-wheel motor is established. As shown in Figure 8, the actual torque ripple is simulated by imposing periodic load disturbances of different frequencies on the load end (Torque). The expression of the applied load torque is T _L =2sin(Ω _e t)+1sin (2Ω _e t)+0.5sin(6Ω _e t). Figure 9 shows the ADRC based on RI-ESO at t=0.5s for a given 100rpm step. Compared with the traditional linear ADRC (LADRC), the ADRC based on RI-ESO can The sinusoidal pulsating torque is well suppressed, and the speed fluctuation is reduced from 17.5rpm to 4.5rpm. Figure 10 shows that when the speed is 100rpm-400rpm, the ADRC based on RI-ESO will produce instability, which is caused by the bandwidth of the torque loop. Figure 11 shows that when the speed is 100rpm-500rpm , using MRI-ESO-based active disturbance rejection control to switch control at high speeds can achieve a better ripple torque suppression effect and ensure system stability in a wide range of speeds.

The above is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto, any person familiar with the technical field within the technical scope disclosed in the present invention, according to the technical solution of the present invention Any equivalent replacement or change of the inventive concepts thereof shall fall within the protection scope of the present invention.

Claims (6)

1. The method for controlling the smooth speed switching of the permanent magnet hub motor within a wide rotating speed range is characterized by comprising the following steps of:

step 1, establishing a first-order mechanical motion equation of a permanent magnet synchronous motor;

step 2, a linear expansion state observer LESO is established according to a first-order mechanical motion equation of the permanent magnet synchronous motor, and a tracking differentiator and a feedback control law are established for realizing complete linear active disturbance rejection controller LADRC design;

step 3, improving the structure of the LESO, and adopting a resonance integral extended state observer RI-ESO to enable the resonance integral extended state observer RI-ESO to observe sinusoidal disturbance and constant disturbance in the motor control process at the same time;

step 4, a method of switching RI-ESO input is adopted to ensure stable operation of the system in a wide rotating speed range, and meanwhile, the suppression capability of harmonic disturbance is ensured;

step 5, at the time of switching T _e The resonance gain k can be increased appropriately when input as an observer _r The value of the harmonic suppression capacity is improved along with the rising of the rotating speed, and the harmonic suppression capacity can be adjusted according to actual conditions.

2. The method for smoothly switching and controlling the speed of a permanent magnet hub motor within a wide rotating speed range according to claim 1, wherein the specific process of step 1 is as follows:

firstly, a first-order mechanical motion equation of the permanent magnet synchronous motor is established as follows:

wherein omega is the mechanical angular speed of the motor rotor and rad/s; t (T) _e ,T _L Electromagnetic torque, load torque, N.m. respectively; t (T) _r The torque ripple mainly comprises cogging torque caused by the motor body, sixth-order harmonic torque caused by the dead time of an inverter and the like, and T is _e ^* For a given electromagnetic torque, B is the coefficient of viscous friction, J is the moment of inertia, the control gain b=1/J, the total disturbance

Total disturbance f irrespective of torque tracking error _n ＝-(Bω+T _r +T _L )/J。

3. The method for smoothly switching and controlling the speed of a permanent magnet hub motor within a wide rotating speed range according to claim 1, wherein the specific process of the step 2 is as follows:

the linear extended state observer LESO is established as follows:

in the method, in the process of the invention,

delta for error between measured and observed speed _n For the noise measurement, b=1/J is the control gain. The variables with a are estimated values, h ₁ ，h ₂ For the gain of the observer, according to the bandwidth method setting strategy, the observer parameter can be determined to be h ₁ ＝2ω _o ，/>

ω _o Bandwidth for observer;

in order to realize the complete linear active disturbance rejection controller LADRC design, a tracking differentiator and a feedback control rule are also needed, and in order to simplify the controller design and facilitate parameter setting, the linear tracking differentiator is ignored and a linear feedback control rule is adopted, and the linear feedback control rule is designed as follows:

mechanical angular velocity ω and total disturbance f _to Are generally unknown and can be replaced by their observations, so the linear control law shown by the formula can be further expressed as:

omega in ^* For the speed loop reference input,

observation speed taken from the extended state observer, < >>

Observation perturbation, k, taken from an extended state observer _ps Proportional gain for the controller;

considering that an actual system cannot generate infinite output, the output torque also needs to be subjected to amplitude limiting treatment, and the adopted amplitude limiting function is that

In the middle of

For maximum torque reference, < >>

Is the saturated torque reference.

4. The method for smoothly switching and controlling the speed of a permanent magnet hub motor within a wide rotation speed range according to claim 1, wherein in the step 3, the adopted resonance integral extended state observer RI-ESO has the following expression in s domain:

in the middle of

For the error between the measured speed and the observed speed, < >>

Delta as a speed observation _n For measuring the speed noise k _r1 ，k _r2 …k _rn Is resonance gain, all are greater than 0, b=1/J is control gain, ω _h1 ，ω _h2 …ω _hn Is the resonant frequency; in->

For observations of constant disturbances or low frequency disturbances, +.>

K is the observed value of harmonic disturbance ₁ ，k ₂ For the gain of the observer, a bandwidth setting strategy is adopted, and the observer parameter k is ₁ ＝2ω _o ，/>

ω _o Bandwidth for observer;

the observer takes the form of an integrator for constant disturbances and a resonant controller for harmonic disturbances.

5. The method for smoothly switching and controlling the speed of a permanent magnet hub motor within a wide rotating speed range according to claim 1, wherein the specific process of the step 4 is as follows:

by T _e As input to the observer, there are

From the analysis, the closed loop transfer function delta of the system is available _cl Is that

T in _ci Delta as torque loop time constant ₂ ＝s ² +k ₁ s+k ₂ Is a characteristic polynomial, k, of LADRC _ps Omega is the proportional gain of the controller _h Is the resonant frequency, k _r Is the resonance gain

According to the Helvetz criterion, under the condition that the torque ring has delay, T is adopted _e As input to the observer, the system is constant, but compared to using T _e ^* As the condition of observer input, a strategy of switching input is adopted to ensure the stable operation of the system and simultaneously ensure the suppression capability of harmonic disturbance, as shown in a formula (16)

Where u represents observer input, ω _hmax For maximum resonant frequency omega _{h_lim} The limit value of the resonant frequency can be obtained off-line by calculating the stability condition

C in the formula ₁ ，B ₁ ，A ₁ Is a parameter set for simplifying the expression, the specific expression is shown in the formula (11)

In the formula (11), x, y, A, B, C, K, a ₂₁ ，a ₃₁ B, c, d are likewise parameters established for simplifying the expression, in particular

Wherein the method comprises the steps of

K in _ps T is the proportional gain of the controller _ci Is the torque loop time constant, k ₁ ，k ₂ To gain of observer, k _r Is the resonance gain;

omega in _{h_lim} The limit value of the resonant frequency can be obtained off-line by calculating the stability condition omega _hmax For maximum resonance frequency, such as when simultaneously suppressing 1 st, 2 nd and 6 th order torque ripple:

ω _hmax ＝6p _n ω (14)

in p _n Is polar logarithmic.

6. The method for smoothly switching speed of permanent magnet hub motor over a wide rotation speed range according to claim 1, wherein in step 5, the adaptive gain k is set _r Is that

k _r1 ＝k _r (1+aω _e )＝k _r (1+ap _n πn/30) (15)

ω _e The electrical angular velocity, n is the mechanical rotor angular velocity, rpm; a is the constant of the adaptive gain being greater than 0.

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