A dual-time-scale parallel dual-loop control method for high-speed permanent magnet motors

Abstract

The present invention discloses a dual-time-scale parallel dual-loop control method for high-speed permanent magnet motors. The method considers the speed tracking problem of high-speed motors during operation, collects the state parameters of high-speed permanent magnet motors, establishes a nonlinear singular perturbation model for high-speed permanent magnet motors, decouples the d-axis and q-axis currents and speeds of high-speed permanent magnet motors based on the nonlinear singular perturbation model, and obtains a linear current sub-model of a fast time scale and a nonlinear speed sub-model of a slow time scale. A sliding mode control law is designed based on the linear fast current sub-model to improve the response speed and robustness of the current loop, and a H is designed based on the nonlinear slow speed sub-model. ∞ The robust control law eliminates the chattering phenomenon and improves the anti-interference ability of the speed loop. The present invention adopts a dual-time scale parallel dual-loop control method to effectively reduce the coupling and interaction between the inner and outer loops.

Description

Technical Field

[0001] The present invention relates to the field of electric drive technology, and in particular to a dual-time-scale parallel dual-loop control method for a high-speed permanent magnet motor. Background Art

[0002] At present, the mainstream control methods in the field of motors are mostly dual-loop control strategies with a series structure. The input of the current loop is the output of the speed loop, and the two sub-controllers are in a series relationship. The cascade dual closed-loop control strategy alleviates the contradiction and conflict between control indicators and improves the control quality and control accuracy. In particular, if the response speed of the inner loop is significantly higher than that of the outer loop and the controller gain of the inner loop is greater than the gain of the outer loop, the resonance of the inner and outer loops can be effectively avoided. However, the cascade control strategy also has shortcomings: it requires that the variables of the inner and outer loops be measurable or observable, and adds additional auxiliary measurement units or computational complexity, which greatly increases the complexity of the system model and the controller design cost. Moreover, the inner and outer loops of the cascade dual closed-loop control are interactive, and the current dynamic characteristics of the inner loop will greatly affect the tracking performance of the outer loop speed, which makes the design process of the cascade inner and outer loop controllers with good control performance cumbersome and difficult.

[0003] In addition, in the high-speed motor drive system, the dynamic change rate of the current loop is in the millisecond level, and the dynamic change rate of the speed loop is in the second level, and the time scale difference between the two is very large. More specifically, the current response speed of the transient process of the high-speed permanent magnet synchronous motor is fast, which produces a huge current shock, threatening the reliability of the system, while the speed increases slowly. Due to the inherent characteristics of the dynamic performance of the electromechanical system, the electrical time constant is much smaller than the mechanical time constant. Especially for high-speed motors, the inductance parameter is very small (about 10-4 order of magnitude), and there is a time scale difference between the state variables. The system has a two time scale (Two Time Scale, TTS) characteristic. However, in the traditional motor series dual-loop control algorithm, the sampling, observation, control signal calculation and parameter correction of the electromagnetic state and mechanical state all use the same execution cycle. For the control problem of dual-time-scale system, if the time scale is based on the slow scale of mechanical dynamics, it is difficult to make an appropriate and timely response to the fast-time-scale electromagnetic dynamics; if the fast-time-scale of electromagnetic dynamics is used as the benchmark, the difference of the slow-time-scale dynamics is almost zero, resulting in serious loss of effective digits and huge errors; and if the intermediate time scale is used as the benchmark, due to the significant difference between the fast and slow time scales, the processing of fast and slow dynamics will encounter similar pathological characteristics, namely rigidity characteristics. When a single-time-scale control strategy is applied to a dual-time-scale high-speed motor system, it will inevitably lead to the loss of effective information of the system or numerical pathological problems in the digital control process. Summary of the invention

[0004] In response to the problems existing in the prior art, the present invention provides a dual-time-scale parallel dual-loop control method for high-speed permanent magnet motors, proposes a parallel dual-loop control strategy for motor systems, breaks through the control bottleneck of existing high-speed permanent magnet synchronous motors, realizes complete decoupling of the current loop and the speed loop, and improves the accuracy and robustness of high-speed permanent magnet motor control.

[0005] To achieve the above technical objectives, the present invention adopts the following technical solution: a dual-time-scale parallel dual-loop control method for a high-speed permanent magnet motor, specifically comprising the following steps:

[0006] Step 1: collect the state parameters of the high-speed permanent magnet motor, determine the singular perturbation parameter ε according to the order of magnitude of the d-axis winding equivalent inductance and the q-axis winding equivalent inductance in the state parameters, and establish a singular perturbation nonlinear mathematical model;

[0007] Step 2: Reduce the order and decouple the singular perturbation nonlinear mathematical model using singular perturbation theory to obtain a nonlinear slow time scale sub-model, and linearize the nonlinear slow time scale sub-model to obtain n linear slow time invariant sub-models;

[0008] Step 3: For n linear slow time-invariant sub-models, combine the threshold γ of the noise impact on the state and each operating point to obtain H ∞ Robust control law, computing the slow time scale control input u s (t k );

[0009] Step 4: Calculate the fast time scale parameter τ, change the time scale of the singular perturbation nonlinear mathematical model, obtain the fast time scale sub-model, select the diagonal matrix M to solve the first positive definite matrix O and the second positive definite matrix Q, and calculate the control input u of the fast time scale sub-model f (τ);

[0010] Step 5: Input the calculated slow time scale control u(t k ) and the control input u of the fast time scale sub-model f (τ) Input the ultra-high-speed permanent magnet motor and perform dual-time-scale parallel dual-loop control.

[0011] Furthermore, the collected state parameters of the high-speed permanent magnet motor include: d-axis winding equivalent inductance, q-axis winding equivalent inductance, winding equivalent resistance, permanent magnet flux, number of motor pole pairs, moment of inertia, and load torque.

[0012] Furthermore, the singular perturbation nonlinear mathematical model is:

[0013]

[0014]

[0015]

[0016] Among them, i d is the d-axis winding current, is the d-axis winding current derivative, r is the winding equivalent resistance, ω e is the angular velocity, L q is the equivalent inductance of the q-axis winding, u d is the d-axis winding voltage, i q is the q-axis winding current, is the q-axis winding current derivative, L d is the equivalent inductance of the d-axis winding, u q is the q-axis winding voltage, is the angular velocity derivative, P n is the number of pole pairs of the motor, J is the moment of inertia, ψ f is the permanent magnet flux, T l is the load torque.

[0017] Furthermore, the nonlinear slow time scale sub-model is:

[0018]

[0019] in, is the slow component of angular velocity, is the derivative of the slow component of angular velocity, u d is the d-axis winding voltage, u q is the q-axis winding voltage, T l is the load torque, P n is the number of pole pairs of the motor, J is the moment of inertia,

[0020] Furthermore, the process of linearizing the nonlinear slow time scale submodel in step 2 is specifically as follows: the angular velocities of the high-speed permanent magnet motor are arranged in sequence, and the angular velocity intervals are divided, and the division points are the operating points, and there are n operating points in total, and the nonlinear slow time scale submodel is linearized at the angular velocity interval division points to obtain n linear slow time-invariant submodels, each of which is:

[0021]

[0022] Among them, θ j is the operating point index, δω e is the error between the slow component measurement value of the current angular velocity and the operating point of the corresponding angular velocity interval, u s (θ j ) is the jThe slow sub control input at .

[0023] Furthermore, step three includes the following sub-steps:

[0024] Step 3.1: The threshold value of the influence of noise on the state γ>0, if there exists a positive definite matrix P>0 that satisfies the following inequality condition Find H ∞ Robust control law K(θ j );

[0025] Step 3.2: Measure t k Angular velocity ω at time e (t k ), and calculate the first weight coefficient α1(t k ) and the second weight coefficient α2(t k ):

[0026] ω e (t k )=α1(t k )θ m +α2(t k )θ m+1

[0027] α1(t k )+α2(t k )=1,

[0028] Among them, θ m is the mth operating point, θ m+1 is the m+1th operating point, ω e (t k )∈[θ m ,θ m+1 ];

[0029] Step 3.3: According to the first weight coefficient α1(t k ) and the second weight coefficient α2(t k ), and t k Time H ∞ Robust control law K(θ(t k )) can be described as: K(θ(t k ))=α1(t k )K m (θ m )+α2(t k )K m+1 (θ m+1 ), and then calculate the slow time scale control input u s (t k )=K(θ(t k ))δω e (t k).

[0030] Furthermore, step 4 includes the following sub-steps:

[0031] Step 4.1. Calculate fast time scale parameters The time scale of the singular perturbation nonlinear mathematical model is changed to obtain a fast time scale sub-model:

[0032]

[0033] in, is the fast component of the d-axis current variable, is the fast component of the q-axis current variable, is the fast component of the d-axis voltage variable, is the fast component of the q-axis voltage variable, t is the time variable, t0 is the initial moment, is the slow variable ω e The value of .

[0034] Step 4.2, select the diagonal matrix M = diag{λ1λ2}>0 to solve the first positive definite matrix O and the second positive definite matrix Q, and calculate the control input of the fast time scale sub-model in, is the nominal input ignoring the uncertain input in the control input of the fast time scale sub-model, s(τ) is the sliding mode function, ||s(τ)||2 is the second norm of the sliding mode function, and h is a small positive number.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] (1) In the traditional series dual-loop control strategy, the control effect of the outer loop greatly affects the performance of the inner loop, the controller design is complex, and the parameter adjustment process is cumbersome; while the dual-time-scale parallel dual-loop control method of the present invention fully considers the dual-time-scale characteristics of the high-speed permanent magnet motor, adopts the singular perturbation method, and proposes a parallel dual-loop control method, which completely decouples the electromagnetic dynamic part and the mechanical dynamic part, reduces the model order, and weakens the interaction between the inner and outer loops;

[0037] (2) The present invention designs a sliding mode function in the fast time scale sub-model to meet the demand for fast response in the fast time scale sub-model, and designs H in the linear slow time-invariant sub-model. ∞ Robust control law to eliminate the "jittering" side effect caused by sliding mode control, improve the anti-interference ability of high-speed permanent magnet motors, and ensure safe operation performance;

[0038] (3) The dual-time-scale parallel dual-loop control method of the present invention is not limited to the control problem of high-speed permanent magnet motors, but can be extended to other mechatronic systems with obvious dual-time-scale characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a flow chart of a dual-time-scale parallel dual-loop control method for a high-speed permanent magnet motor according to the present invention;

[0040] Figure 2 The embodiment is a simulation principle diagram of a dual-time-scale parallel dual-loop control method for a high-speed permanent magnet motor;

[0041] Figure 3 This is a control input effect diagram of the fast time scale sub-model in the embodiment, Figure 3 (a) is the input diagram of the d-axis winding tachyon controller. Figure 3 (b) is the input diagram of the q-axis winding tachyon controller;

[0042] Figure 4 This is a diagram showing the effect of slow time scale control input in the embodiment. Figure 4 (a) Input diagram of the d-axis winding slow sub-controller, Figure 4 (b) is the input diagram of the q-axis winding slow sub-controller;

[0043] Figure 5 It is the phase current diagram of phase A;

[0044] Figure 6 It is the waveform of motor speed;

[0045] Figure 7 is the q-axis winding current diagram;

[0046] Figure 8 This is the d-axis winding current diagram. DETAILED DESCRIPTION

[0047] The technical solution of the present invention is further explained below in conjunction with the accompanying drawings.

[0048] like Figure 1 The present invention is a flow chart of a dual-time-scale parallel dual-loop control method for a high-speed permanent magnet motor. The dual-time-scale parallel dual-loop control method specifically includes the following steps:

[0049] Step 1: Collect the state parameters of the high-speed permanent magnet motor, including: d-axis winding equivalent inductance, q-axis winding equivalent inductance, winding equivalent resistance, permanent magnet flux, motor pole pair number, moment of inertia, and load torque; and determine the singular perturbation parameter ε according to the order of magnitude of the d-axis winding equivalent inductance and the q-axis winding equivalent inductance in the state parameters, and establish a singular perturbation nonlinear mathematical model. The singular perturbation model nonlinear mathematical model can effectively characterize the dual time scale characteristics of the engineering system. The main idea of ​​the singular perturbation method is: decoupling-separate design-combination. By utilizing the time scale difference of the high-speed permanent magnet motor dynamics, forced decoupling is implemented on different time scales, fast and slow decomposition is achieved, and the high-speed permanent magnet motor is reduced in order. The fast and slow subsystem controllers are designed separately, and the controller of the high-speed permanent magnet motor is combined. The establishment of the singular perturbation nonlinear mathematical model fully considers the time scale difference of the mechanical dynamics and electromagnetic dynamics inside the high-speed motor, which can effectively improve the dynamic response performance. The singular perturbation nonlinear mathematical model in the present invention is:

[0050]

[0051]

[0052]

[0053] Among them, i d is the d-axis winding current, is the d-axis winding current derivative, r is the winding equivalent resistance, ω e is the angular velocity, L q is the equivalent inductance of the q-axis winding, u d is the d-axis winding voltage, i q is the q-axis winding current, is the q-axis winding current derivative, L d is the equivalent inductance of the d-axis winding, u q is the q-axis winding voltage, is the angular velocity derivative, P n is the number of pole pairs of the motor, J is the moment of inertia, ψ f is the permanent magnet flux, T l is the load torque.

[0054] Step 2: Use singular perturbation theory to reduce the order and decouple the singular perturbation nonlinear mathematical model to obtain a nonlinear slow time scale sub-model, thereby achieving the decoupling of the slow state and the fast state. In order to deal with the nonlinear characteristics of the slow time scale sub-model, the linear variable parameter theory is used to linearize the nonlinear slow time scale sub-model to obtain n linear slow time-invariant sub-models, which greatly reduces the difficulty of controller design for the slow sub-system;

[0055] Specifically, let ε=0 in formulas (1)-(2), and inversely solve for the slow component i of the d-axis winding current d s , q-axis winding current slow component i q s ,

[0056]

[0057]

[0058] Substituting into formula (3), we get:

[0059]

[0060] remember Then the nonlinear slow time scale sub-model in the present invention is:

[0061]

[0062] in, is the slow component of angular velocity, is the derivative of the slow component of angular velocity, u d is the d-axis winding voltage, u q is the q-axis winding voltage, T l is the load torque, P n is the number of pole pairs of the motor, and J is the moment of inertia.

[0063] The process of linearizing the nonlinear slow time scale submodel in the present invention is specifically as follows: the angular velocities of the high-speed permanent magnet motor are arranged in sequence, and the angular velocity intervals are divided, and the division points are the operating points, and there are n operating points in total, and the nonlinear slow time scale submodel is linearized at the angular velocity interval divisions to obtain n linear slow time-invariant submodels, each of which is:

[0064]

[0065] Further assume that there is an interference signal δv in the model, c is the coefficient of the interference signal, and consider that the output of the slow subsystem is the speed itself, then we have

[0066]

[0067] y=δω e (10)

[0068] Among them, θ j is the operating point index, δω e is the error between the slow component measurement value of the current angular velocity and the operating point of the corresponding angular velocity interval, u s (θ j) is the j The slow sub control input at .

[0069] The present invention uses the linear variable parameter theory to simplify the nonlinear characteristics of the slow time scale sub-model. On the one hand, it reduces the difficulty of controller design and saves the calculation space of the controller design algorithm. On the other hand, it avoids linearization at a single operating point and preserves the nonlinear dynamic characteristics of high-speed motors. Step 3: Considering that there must be external interference in the system, the present invention designs H for the speed loop ∞ Robust control law is used to overcome the influence of external disturbance on the speed, so that the speed can stably follow the ideal speed. Therefore, for n linear slow time-invariant sub-models, combined with the threshold value γ of the influence of noise on the state and each operating point, H is obtained. ∞ Robust control law makes the operating point θ j The closed-loop linear slow submodel at is robust and stable, and the slow time scale control input u is calculated. s (t k ); comprising the following sub-steps:

[0070] Step 3.1, design state feedback controller: u s (t) = K(θ j )δω e , substituting into formulas (9)-(10), we get:

[0071]

[0072] For the threshold value γ>0 of the influence of noise on the state, if there exists a positive definite matrix P>0 that satisfies the following inequality condition

[0073]

[0074] Find H ∞ Robust control law K(θ j ); then formula (11) at the operating point θ j is asymptotically stable, and the transfer function T from the disturbance δv to the output y(t) δvy (s) Satisfy robust performance indicators

[0075] Next, in order to verify the rationality and effectiveness of the proposed control scheme, a robust stability proof is performed.

[0076] (1) First, it is proved that the closed-loop system is asymptotically stable under zero disturbance.

[0077] Assuming δv = 0, construct the Lyapunov function V(δω e ,t)=δω e T (t)Pδω e(t), for the function V(δω e ,t) Taking the derivative of formula (11) with respect to time t, we can get

[0078]

[0079] According to Schur's complement lemma, inequality (12) can be transformed into

[0080]

[0081] According to formula (14), it is obvious that Then according to formula (13), it is clear that It can be concluded that when the disturbance δv = 0, the equilibrium point of formula (11) is asymptotically stable.

[0082] (2) Next, we prove that when δv≠0, under the condition of matrix inequality (12), the system is robust.

[0083] For the function V(δω e ,t) Taking the derivative of formula (11) with respect to time t, we can get

[0084]

[0085] According to inequalities (14) and (15), we can rewrite it as

[0086]

[0087] That is to say

[0088] Further,

[0089]

[0090] Based on the proof of asymptotic stability in part (1), we know that δω e (∞)=0, now assume δω e (0) = 0, integrating both sides of inequality (16), we can obtain:

[0091]

[0092] Right now From this it is obvious that:

[0093] That is

[0094] Step 3.2: Measure t k Angular velocity ω at time e (t k ), and calculate the first weight coefficient α1(tk ) and the second weight coefficient α2(t k ):

[0095] ω e (t k )=α1(t k )θ m +α2(t k )θ m+1

[0096] α1(t k )+α2(t k )=1,

[0097] Among them, θ m is the mth operating point, θ m+1 is the m+1th operating point, ω e (t k )∈[θ m ,θ m+1 ];

[0098] Step 3.3: According to the first weight coefficient α1(t k ) and the second weight coefficient α2(t k ), and t k Time H ∞ Robust control law K(θ(t k )) can be described as: K(θ(t k ))=α1(t k )K m (θ m )+α2(t k )K m+1 (θ m+1 ), and then calculate the slow time scale control input u s (t k )=K(θ(t k ))δω e (t k ).

[0099] Step 4: Considering the rapidity of the current loop, the present invention selects a sliding mode control with good rapidity and robustness as the control method of the current loop, calculates the fast time scale parameter τ, changes the time scale of the singular perturbation nonlinear mathematical model, obtains the fast time scale sub-model, selects the diagonal matrix M to solve the first positive definite matrix O and the second positive definite matrix Q, and calculates the control input u of the fast time scale sub-model f (τ); comprising the following sub-steps:

[0100] Step 4.1. Calculate fast time scale parameters By changing the time scale of the singular perturbation nonlinear mathematical model, that is, transforming formulas (1)-(2), we obtain:

[0101]

[0102]

[0103] Where d(τ) is the noise, and the noise is bounded ||d(τ)||2<δ,δ>0, take and As a pseudo input, formulas (9)-(10) are organized into a fast time scale sub-model, which can effectively describe the dynamic characteristics of the decoupled fast state; the fast time scale sub-model in the present invention is:

[0104]

[0105] in, is the fast component of the d-axis current variable, is the fast component of the q-axis current variable, is the fast component of the d-axis voltage variable, is the fast component of the q-axis voltage variable, t is the time variable, t0 is the initial moment, is the slow variable ω e The value of .

[0106] Step 4.2, select the diagonal matrix M = diag{λ1 λ2}>0 to solve the first positive definite matrix O and the second positive definite matrix Q, and calculate the control input of the fast time scale sub-model:

[0107]

[0108] in, is the nominal input ignoring the uncertain input in the control input of the fast time scale sub-model, s(τ) is the sliding mode function, ||s(τ)||2 is the second norm of the sliding mode function, and h is a small positive number.

[0109] The first positive definite matrix O and the second positive definite matrix Q satisfy:

[0110]

[0111] Next, we prove the validity of formula (21):

[0112] If the parameters h>0, l>0 and the upper bound of the interference δ are known, under the action of formula (21), the tracking error e(τ) of formula (20) tends to 0,

[0113] Constructing Lyapunov functions

[0114] Taking the derivative of V(τ) with respect to τ, we get

[0115]

[0116] Where V eq (τ)=-s T (τ)Qs(τ),V N (τ)=-s T (τ)Osgn(s(τ)), where O and Q satisfy:

[0117] or

[0118] The derivative of s(τ) can be expressed as:

[0119]

[0120] Substituting formula (25) into formula (24) yields:

[0121]

[0122] From the above formula, we can inversely calculate u f :

[0123]

[0124] In fact, eq (τ) includes the nominal part and the uncertain part

[0125]

[0126] in

[0127] Based on the assumption ||d(t)||2<δ, u can be ignored eq The uncertainty component in (τ) Get the controller of the fast subsystem

[0128]

[0129] In order to make the system converge within a finite time, it is necessary It is known that l is a small positive number. Substituting formula (25) into formulas (27)-(28) yields:

[0130]

[0131] According to Schwarz inequality, the sufficient condition for inequality (29) is as follows:

[0132]

[0133] Furthermore, the above formula is equivalent to

[0134] In addition, in order to avoid the chattering caused by the sign function, the following approximate function is introduced

[0135] Step 5: Input the calculated slow time scale control u(t k ) and the control input u of the fast time scale sub-model f (τ) Input high-speed permanent magnet motor to perform dual-time scale parallel dual-loop control.

[0136] The dual-time-scale parallel dual-loop control method for high-speed permanent magnet motors of the present invention fully considers the dual-time-scale characteristics of high-speed motors, avoids the drawbacks of single-time-scale series dual-loop control, effectively reduces the dimension of high-speed motors, simplifies the complexity of controller design, and can significantly improve dynamic response performance.

[0137] Example

[0138] This embodiment uses a high-speed rare earth permanent magnet motor as an experimental object. The specific parameters of the high-speed rare earth permanent magnet motor are shown in Table 1:

[0139] Table 1 18000rmp / 110W high-speed permanent magnet motor parameters

[0140] Equivalent resistance 0.22Ω Pole pairs 1 Equivalent inductance 0.0001H Bus voltage 36V Permanent magnet flux amplitude 0.0004 Rated Power 200W Rated speed 18000rpm Sampling frequency 20kHz

[0141] like Figure 2 This is a simulation schematic diagram of a dual-time-scale parallel dual-loop control method based on a high-speed permanent magnet motor. The function of the PI controller is to provide an ideal signal for the tachyon model. The fast time scale sub-model adopts the sliding mode control method, and the slow time scale sub-model adopts the H-based linear variable parameter theory. ∞ Control method. Figure 3 The control input effect diagram of the fast time scale sub-model is shown. Figure 3 (a) is the input diagram of the d-axis winding tachyon controller. Figure 3 (b) is the input diagram of the q-axis winding tachyon controller. It can be seen that the tachyon controller changes quickly and responds quickly. Figure 4 This is a diagram showing the effect of slow time scale control input in the embodiment. Figure 4 (a) Input diagram of the d-axis winding slow sub-controller, Figure 4 (b) is the input diagram of the q-axis winding slow sub-controller. The slow sub-controller is relatively stable. The experimental results are consistent with the design expectations of the dual-time scale parallel dual-loop control method of the present invention. Figure 5 The A phase current diagram is shown. Figure 5 It can be seen that after the load is added, the current converges to a sinusoidal waveform very quickly; Figure 6This is the motor speed waveform. After the load changes suddenly, the speed returns to a stable state in a very short time. Figure 7 The waveform of the q-axis winding current is shown, and it can be seen that the q-axis current can quickly track the ideal value with good tracking effect; Figure 8 The d-axis winding current waveform is shown, with small ripple and good static performance.

[0142] The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A dual-time-scale parallel dual-loop control method for high-speed permanent magnet motors. It is characterized in that The specific steps include: Step 1: Collect the state parameters of the high-speed permanent magnet motor, and determine the singular perturbation parameter ε according to the order of magnitude of the d-axis winding equivalent inductance and the q-axis winding equivalent inductance in the state parameters, and establish a singular perturbation nonlinear mathematical model: Among them, i d is the d-axis winding current, is the d-axis winding current derivative, r is the winding equivalent resistance, ω e is the angular velocity, L q is the equivalent inductance of the q-axis winding, u d is the d-axis winding voltage, i q is the q-axis winding current, is the q-axis winding current derivative, L d is the equivalent inductance of the d-axis winding, u q is the q-axis winding voltage, is the angular velocity derivative, P n is the number of pole pairs of the motor, J is the moment of inertia, ψ f is the permanent magnet flux, T l is the load torque; Step 2: Reduce the order and decouple the singular perturbation nonlinear mathematical model using singular perturbation theory to obtain a nonlinear slow time scale sub-model, and linearize the nonlinear slow time scale sub-model to obtain n linear slow time-invariant sub-models: Arrange the angular velocity of the high-speed permanent magnet motor in sequence and divide the angular velocity interval. The division point is the operating point. There are n operating points in total. Linearize the nonlinear slow time scale sub-model at the angular velocity interval division to obtain n linear slow time-invariant sub-models. Each linear slow time-invariant sub-model is: Among them, θ j is the operating point index, δω e is the error between the slow component measurement value of the current angular velocity and the operating point of the corresponding angular velocity interval, u s (θ j ) is the j The slow sub-control input at Step 3: For n linear slow time-invariant sub-models, combine the threshold γ of the noise impact on the state and each operating point to obtain H ∞ Robust control law, computing the slow time scale control input u s (t k ), including the following sub-steps: Step 3.1: The threshold value of the influence of noise on the state γ>0, if there exists a positive definite matrix P>0 that satisfies the following inequality condition Find H γ Robust control law K(θ j ); Step 3.2: Measure t k Angular velocity ω at time e (t k ), and calculate the first weight coefficient α according to the divided interval of angular velocity 1 (t k ) and the second weight coefficient α 2 (t k ): oh e (t k )=a 1 (t k )i m +a 2 (t k )i m+1 a 1 (t k )+a 2 (t k )=1, Among them, θ m is the mth operating point, θ m+1 is the m+1th operating point, ω e (t k )∈[θ m ,θ m+1 ]; Step 3.3: According to the first weight coefficient α 1 (t k ) and the second weight coefficient α 2 (t k ), and t k Time H ∞ Robust control law K(θ(t k )) can be described as: K(θ(t k ))=α 1 (t k )K m (θ m )+α 2 (t k )K m+1 (θ m+1 ), and then calculate the slow time scale control input u s (t k )=K(θ(t k ))δω e (t k ); Step 4: Calculate the fast time scale parameter τ, change the time scale of the singular perturbation nonlinear mathematical model, obtain the fast time scale sub-model, select the diagonal matrix M to solve the first positive definite matrix O and the second positive definite matrix Q, and calculate the control input u of the fast time scale sub-model f (τ); comprising the following sub-steps: Step 4.

1. Calculate fast time scale parameters The time scale of the singular perturbation nonlinear mathematical model is changed to obtain a fast time scale sub-model: in, is the fast component of the d-axis current variable, is the fast component of the q-axis current variable, is the fast component of the d-axis voltage variable, is the fast component of the q-axis voltage variable, t is the time variable, t 0 Initial moment, is the slow variable ω e The value of Step 4.2, select the diagonal matrix M = diag{λ 1 λ 2 }>0 Solve the first positive definite matrix O and the second positive definite matrix Q to calculate the control input of the fast time scale sub-model in, is the nominal input ignoring the uncertain input in the control input of the fast time scale submodel, s(τ) is the sliding mode function, ||s(τ)|| 2 is the second norm of the sliding mode function, h is a small positive number; Step 5: Input the calculated slow time scale control u(t k ) and the control input u of the fast time scale sub-model f (τ) Input high-speed permanent magnet motor to perform dual-time scale parallel dual-loop control.

2. According to the dual-time-scale parallel dual-loop control method for high-speed permanent magnet motors according to claim 1, It is characterized in that The collected state parameters of the high-speed permanent magnet motor include: d-axis winding equivalent inductance, q-axis winding equivalent inductance, winding equivalent resistance, permanent magnet flux linkage, motor pole pair number, moment of inertia, and load torque.

3. According to the dual-time-scale parallel dual-loop control method for high-speed permanent magnet motors according to claim 1, It is characterized in that The nonlinear slow time scale submodel is: in, is the slow component of angular velocity, is the derivative of the slow component of angular velocity, u d is the d-axis winding voltage, u q is the q-axis winding voltage, T l is the load torque, P n is the number of pole pairs of the motor, J is the moment of inertia,

Images