FTPPI sliding mode and GTO optimized permanent magnet synchronous motor rotating speed loop control method

Abstract

The invention belongs to the technical field of permanent magnet synchronous motors, and particularly relates to a permanent magnet synchronous motor rotating speed loop control method based on FTPPI sliding mode and GTO optimization, and the method comprises the steps: 1, building the mathematical modeling of a permanent magnet synchronous motor; 2, a sliding mode surface is designed according to the finite time adjustable boundary, so that the rotating speed error of the permanent magnet synchronous motor is converged within the boundary within the finite time; 3, designing an amplitude limiting function on the basis of the sliding mode surface to prevent the derivative of the rotating speed error from violently fluctuating so as to obtain an ideal torque instruction; 4, introducing a current circle equation and a voltage circle equation as boundary conditions, and iterating an optimal dq-axis current instruction by taking the minimum motor power loss as an objective function; and 5, through decoupling control, rotating speed and torque double-closed-loop control is completed. According to the invention, a method of combining finite time preset performance inversion and efficiency optimal gradient optimization is adopted, and double closed-loop control of a rotating speed loop and a torque current loop of the permanent magnet synchronous motor is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of permanent magnet synchronous motors, and in particular to a permanent magnet synchronous motor speed loop control method and system based on FTPPI sliding mode and GBO optimization. Background Art

[0002] Permanent Magnet Synchronous Motor (PMSM) is a three-phase AC motor known for its excellent efficiency, power density and control accuracy. This motor consists of three sets of stator windings with a phase difference of 120 degrees and a rotor equipped with permanent magnets. By sending PWM (pulse width modulation) signals to the three-phase inverter to control the switching state of IGBT (insulated gate bipolar transistor), voltage and three-phase current are generated in the stator winding, which in turn generates a stator magnetic field that interacts with the rotor magnetic field to drive the motor to rotate.

[0003] The existing technology has problems such as speed error convergence, speed error derivative fluctuation and optimal current command allocation under a given torque command in permanent magnet synchronous motor control.

[0004] To this end, the present invention proposes a permanent magnet synchronous motor speed loop control method based on FTPPI sliding mode and GBO optimization. Summary of the invention

[0005] In view of the problems existing in the prior art, the present invention provides a permanent magnet synchronous motor speed loop control method using FTPPI sliding mode and GBO optimization.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A permanent magnet synchronous motor speed loop control method based on FTPPI sliding mode and GBO optimization, the method comprising:

[0008] Step 1: Establish mathematical modeling of permanent magnet synchronous motor;

[0009] Step 2: Design a sliding surface based on a finite time adjustable boundary so that the speed error of the permanent magnet synchronous motor converges within the boundary within a finite time;

[0010] Step 3: Designing a limiting function based on the sliding surface to prevent the derivative of the speed error from fluctuating violently, thereby obtaining an ideal torque command;

[0011] Step 4: Use the stochastic gradient optimization algorithm, introduce the current circle and voltage circle equations as boundary conditions, take the minimum motor power loss as the objective function, and iterate to get the optimal dq axis current command;

[0012] Step 5: Through decoupling control, the response to the ideal torque is achieved, and the dual closed-loop control of speed and torque is completed.

[0013] Furthermore, in step 1, the mathematical model of the permanent magnet synchronous motor is:

[0014]

[0015] From formula (1), we can get:

[0016]

[0017] Among them, Trq is the torque, J is the moment of inertia, B is the friction coefficient, ωm is the mechanical speed, pn is the pole pair number, pn*ωm=ωe is the electrical angular velocity, ψf is the magnetic flux, id and iq are the dq-axis currents, ud and uq are the dq-axis voltages, Rs is the stator resistance, and Ld and Lq are the dq-axis inductances.

[0018] Furthermore, in the step 2, a speed loop sliding mode control algorithm is designed based on finite time preset performance inversion (FTPPI):

[0019] Set the speed command to The speed error is:

[0020]

[0021] Then the derivative of the error is:

[0022]

[0023] FTPPI is defined as:

[0024]

[0025] Among them, λ0, λ ∞ is a positive number, and λ ∞ <e ω (0)<λ0,T f is the expected convergence time of the preset performance;

[0026] The speed ring sliding surface design based on FTPPI is:

[0027]

[0028] According to formula (6), when e ω =0, s = 0; when e ω When it approaches λ, s approaches +∞; when e ωWhen it approaches -λ, s approaches -∞; it can be seen that the adjustment target of the sliding surface is that the speed error is 0, and a boundary is set for the error; when the error approaches the boundary, the adjustment of the sliding mode control is larger, so as to ensure that the error is always within the boundary;

[0029] By taking the derivative of formula (6), we can get:

[0030]

[0031] Because the speed error e ω satisfy:

[0032] -λ <e ω <λ (8);

[0033] 0<λ-e ω <2λ (9);

[0034] 0 <e ω +λ<2λ (10);

[0035] Therefore, s and e ω Same number; and because In (λ-e ω ) 2 (e ω +λ) 2 >0, so and Same sign; according to the Lyapunov stability condition, let the Lyapunov function and its derivative be:

[0036]

[0037]

[0038] Therefore, the design reaching law is:

[0039]

[0040] Substituting formula (15) into formula (12), we can get:

[0041]

[0042] Furthermore, in the formula (16), when t→∞, e ω →0 o'clock, It will cause serious steady-state fluctuations in the speed loop regulation; therefore Design a clipping function:

[0043]

[0044] When e ω →∞, Does not affect the normal adjustment of the speed loop; when e ω →0, according to Taylor expansion:

[0045]

[0046] It can be seen from formula (18) that the limiting function can effectively limit the steady-state fluctuation of the speed loop; the change rate of the Lyapunov function at this time is:

[0047]

[0048]

[0049] According to formula (19), as long as You can Established, ensuring the stability of the speed loop; thus, the condition for the stability of the speed loop is:

[0050]

[0051] From formula (20), we can see that the denominator on the right side of the inequality sign is Therefore, the denominator cannot approach infinitesimal, and the value of the fraction cannot approach infinity, that is, it must be bounded; thus, there is always k that satisfies the condition of formula (20), and at the same time, it can be ensured that formula (19) is always less than 0, thereby ensuring the stability of the speed loop.

[0052] Furthermore, in step 4, the "efficiency optimal gradient optimization" current loop control algorithm is designed based on the constraint conditions:

[0053] Substituting formula (17) into formula (4), we can obtain:

[0054]

[0055] According to formula (1), the torque command Trq can be * Convert to the corresponding current command and Therefore, it is necessary to determine the optimal current command;

[0056] The current command is determined by the principle of "optimal motor efficiency"; the formula for the known three-phase AC power is:

[0057] P ac =3*U 相rms *I 相rms *cosθ (22);

[0058]

[0059]

[0060] Substituting equations (23)-(25) into equation (22), we can obtain:

[0061]

[0062] The mechanical power is:

[0063] P mot (i d ,i q )=Trq(i d ,i q )*ω m (27);

[0064] Considering that the motor efficiency of electric motor and generator is the inverse of each other, in order to unify the formula, "minimum loss" is used to express "optimal motor efficiency", that is:

[0065] e p (u d ,i d ,u q ,i q )=P ac (u d ,i d ,u q ,i q )-P mot (i d ,i q ) (28);

[0066] In order to simplify the parameters, when Trq is known * Under the condition of , substitute formula (1) into formula (28), use id to represent iq through the torque formula, and then use id and iq to represent ud and uq; at this time, id can be used to represent iq, ud, and uq at the same time, that is, iq=Iq(id), ud=Ud(id), uq=Uq(id), and we can get:

[0067] e p (i d )=P ac (i d )-P mot (i d ) (29);

[0068] Then the loss objective function of "optimal motor efficiency" is:

[0069]

[0070] Of course, the selection of id, iq, ud, and uq is not without range, and needs to be within the current circle and voltage circle; according to formula (1), it can be known that:

[0071]

[0072] Find the id with the best motor efficiency, that is, find the optimal id within the constraints of the current circle and the voltage circle, so that the motor loss represented by the objective function G(id) is minimized; therefore, the constraints are supplemented and a new objective function is constructed:

[0073]

[0074] Among them, a and b are the penalty factors of the constraints; the larger the penalty factor, the closer id and iq are to the constraints, the smaller the deviation from the constraints, and the larger the inverse of the deviation, which makes the objective function larger, thus ensuring that the optimization process is within the constraints;

[0075] The stochastic gradient based optimization algorithm (GBO) is used to iterate the optimization of id;

[0076] First, the initial vector of GBO is randomly generated in the D-dimensional search space and can be defined as:

[0077] X n =X min +rand(1,0)*(X max -X min ) (34)

[0078] Among them, X max and X min are the upper and lower limits of the variable respectively; the optimal solution is a one-dimensional vector id, so D = 1; set X min is the value of the "maximum torque voltage ratio" MTPV at this speed, X max is the id current value at zero torque at this speed;

[0079] The gradient search rule includes the rule itself GSR, which is used to improve the algorithm's exploration ability and avoid falling into the global optimum; it also includes the moving direction DM, which is used to generate a suitable search direction and improve the convergence speed; based on GSR and DM, the current vector is updated location;

[0080]

[0081] ρ1=2*rand*α-α (36);

[0082] ρ2=2*rand*α-α (37);

[0083]

[0084] β=β min +(β max -β min)*(1-(m / M) 3 ) 2 (39);

[0085] Δx=rand(1:N)*|step| (40);

[0086]

[0087] Among them, β min and β max are 0.2 and 1.2 respectively, m is the current iteration number, M is the maximum iteration number, randn represents a standard normal distribution random number, ε is a very small positive number between [0,0.1], rand(1:N) is an N-dimensional random vector between [0,1], r1, r2, r3, r4 (r1≠r2≠r3≠r4) are randomly selected from [1,N], and unequal integers, step is determined by X best and Determine the step size, X best and X worst Calculated by the objective function G(id);

[0088] By using the current vector in formula (35) Replace the best vector X best The position of can generate the following new vector

[0089]

[0090] based on and The new position generated by the next iteration for:

[0091]

[0092] Where ra and rb are random numbers between [0,1];

[0093] In order to help the algorithm escape from the local optimum, a local escape operator mechanism is added to the GBO algorithm. The algorithm is as follows:

[0094]

[0095] Among them, f1 is a random number in [-1,1], f2 is a standard normal distribution random number, pr is a probability value, and u1, u2, and u3 are three random integers;

[0096] Through the above stochastic gradient optimization algorithm, the id with the smallest corresponding objective function G(id) in the solution space is taken as the d-axis current command id*, and the q-axis current command iq* is:

[0097]

[0098] Based on the known current command, the current error is defined as:

[0099]

[0100] Furthermore, in step 5, by substituting equation (51) into equation (1), the decoupled current loop control voltage can be obtained as:

[0101]

[0102] The torque loop can be controlled according to formula (52).

[0103] The above technical solution of the present invention has the following beneficial technical effects:

[0104] The present invention adopts a method combining finite-time preset performance inversion and efficiency optimal gradient optimization to realize the dual closed-loop control of the permanent magnet synchronous motor speed loop and torque current loop. First, the sliding surface is designed according to the finite-time adjustable boundary to ensure that the speed error converges within the boundary within a finite time. In order to prevent the derivative of the speed error from fluctuating violently, a limiting function is designed on this basis to obtain an ideal torque command. In order to allocate the optimal dq-axis current command under the condition of determining the torque command, the present invention adopts a stochastic gradient optimization algorithm, introduces the current circle and voltage circle equations as boundary conditions, takes the minimum motor power loss as the objective function, and iterates the optimal dq-axis current command. Finally, through decoupling control, the response to the ideal torque is achieved, and the dual closed-loop control of speed and torque is completed. BRIEF DESCRIPTION OF THE DRAWINGS

[0105] Figure 1 This is a speed-torque dual closed-loop structure block diagram proposed by the present invention. DETAILED DESCRIPTION

[0106] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention is further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings. It should be understood that these descriptions are only exemplary and are not intended to limit the scope of the present invention. In addition, in the following description, the description of well-known structures and technologies is omitted to avoid unnecessary confusion of the concept of the present invention.

[0107] like Figure 1 As shown, the present invention provides a permanent magnet synchronous motor speed loop control method based on FTPPI sliding mode and GBO optimization, the method comprising:

[0108] Step 1: Establish mathematical modeling of permanent magnet synchronous motor;

[0109] Step 2: Design a sliding surface based on a finite time adjustable boundary so that the speed error of the permanent magnet synchronous motor converges within the boundary within a finite time;

[0110] Step 3: Designing a limiting function based on the sliding surface to prevent the derivative of the speed error from fluctuating violently, thereby obtaining an ideal torque command;

[0111] Step 4: Use the stochastic gradient optimization algorithm, introduce the current circle and voltage circle equations as boundary conditions, take the minimum motor power loss as the objective function, and iterate to get the optimal dq axis current command;

[0112] Step 5: Through decoupling control, the response to the ideal torque is achieved, and the dual closed-loop control of speed and torque is completed.

[0113] Specifically:

[0114] 1. Mathematical modeling of permanent magnet synchronous motor:

[0115] The mathematical model of the known permanent magnet synchronous motor is:

[0116]

[0117] From formula (1), we can get:

[0118]

[0119] Among them, Trq is the torque, J is the moment of inertia, B is the friction coefficient, ωm is the mechanical speed, pn is the pole pair number, pn*ωm=ωe is the electrical angular velocity, ψf is the magnetic flux, id and iq are the dq-axis currents, ud and uq are the dq-axis voltages, Rs is the stator resistance, and Ld and Lq are the dq-axis inductances.

[0120] 2. Design of speed loop sliding mode control algorithm based on finite time preset performance inversion

[0121] Set the speed command to The speed error is:

[0122]

[0123] Then the derivative of the error is:

[0124]

[0125] Finite Time Preset Performance Inversion (FTPPI) refers to converging the speed error to a preset adjustable boundary range within a finite time. FTPPI can be defined as:

[0126]

[0127] Among them, λ0, λ ∞ is a positive number, and λ ∞ <e ω (0)<λ0,T f It is the expected convergence time of the preset performance.

[0128] FTPPI can constrain the speed error in transient and steady-state performance to meet the preset performance. Therefore, the speed loop sliding surface based on FTPPI can be designed as:

[0129]

[0130] According to formula (6), when e ω =0, s = 0. When e ω When it approaches λ, s approaches +∞. ω When it approaches -λ, s approaches -∞. It can be seen that the adjustment target of the sliding surface is that the speed error is 0, and a boundary is set for the error. When the error approaches the boundary, the adjustment of the sliding mode control is larger, so as to ensure that the error is always within the boundary. This is more accurate than the sliding mode control without boundary.

[0131] By taking the derivative of formula (6), we can get:

[0132]

[0133] Because the speed error e ω satisfy:

[0134] -λ <e ω <λ (8);

[0135] 0<λ-e ω <2λ (9);

[0136] 0 <e ω +λ<2λ (10);

[0137] Therefore, s and e ω The same sign. And because in s, (λ-e ω ) 2 (e ω +λ) 2 >0, so and According to the Lyapunov stability condition, the Lyapunov function and its derivative are:

[0138]

[0139] Therefore, the design reaching law is:

[0140]

[0141] Substituting formula (15) into formula (12), we can get:

[0142]

[0143] However, when t→∞, e ω →0 o'clock, It will cause serious steady-state fluctuations in the speed loop regulation. Design a clipping function:

[0144]

[0145] When e ω →∞, It does not affect the normal adjustment of the speed loop. ω →0, according to Taylor expansion:

[0146]

[0147] From formula (18), we can see that the limit function can effectively limit the steady-state fluctuation of the speed loop. The change rate of the Lyapunov function at this time is:

[0148]

[0149] According to formula (19), as long as You can It is established to ensure the stability of the speed loop. Therefore, the condition for the stability of the speed loop is:

[0150]

[0151] From formula (20), we can see that the denominator on the right side of the inequality sign is Therefore, the denominator cannot approach infinitesimal, and the value of the fraction cannot approach infinity, that is, it must be bounded. Therefore, there is always k that satisfies the condition of formula (20), and at the same time, it can be ensured that formula (19) is always less than 0, thereby ensuring the stability of the speed loop.

[0152] 3. Design of “Efficiency Optimal Gradient Optimization” Current Loop Control Algorithm Based on Constraints

[0153] Substituting formula (17) into formula (4), we can obtain:

[0154]

[0155] According to formula (1), the torque command Trq can be * Convert to the corresponding current command and Therefore, it is necessary to determine the optimal current command.

[0156] This article adopts the principle of "optimal motor efficiency" to determine the current command. The formula for three-phase AC power is known to be:

[0157] P ac =3*U 相rms *I 相rms *cosθ (22);

[0158]

[0159] Substituting equations (23)-(25) into equation (22), we can obtain:

[0160]

[0161] The mechanical power is:

[0162] P mot (i d ,i q )=Trq(i d ,i q )*ω m (27);

[0163] Considering that the motor efficiency of electric motor and generator is the inverse of each other, in order to unify the formula, "minimum loss" is used to express "optimal motor efficiency", that is:

[0164] e p (u d ,i d ,u q ,i q )=P ac (u d ,i d ,u q ,i q )-P mot (i d ,i q ) (28);

[0165] In order to simplify the parameters, when Trq is known * Under the condition of , substitute formula (1) into formula (28), use id to represent iq through the torque formula, and then use id and iq to represent ud and uq. At this time, id can be used to represent iq, ud, and uq at the same time, that is, iq = Iq (id), ud = Ud (id), uq = Uq (id), and we can get:

[0166] e p (i d )=P ac (i d )-P mot(i d ) (29);

[0167] Then the loss objective function of "optimal motor efficiency" is:

[0168]

[0169] Of course, the selection of id, iq, ud, and uq is not without range, and they need to be within the current circle and voltage circle. According to formula (1), we can know that:

[0170]

[0171] In summary, we need to find the id with the best motor efficiency, that is, to find the optimal id within the constraints of the current circle and the voltage circle, so that the motor loss represented by the objective function G(id) is minimized. Therefore, we add constraints and construct a new objective function:

[0172]

[0173] Among them, a and b are the penalty factors of the constraints. The larger the penalty factor, the closer id and iq are to the constraints, the smaller the deviation from the constraints, and the larger the inverse of the deviation, which makes the objective function larger, thus ensuring that the optimization process is within the constraints.

[0174] This patent uses a gradient-based optimizer (GBO) to iterate the optimization of the ID.

[0175] First, the initial vector of GBO is randomly generated in the D-dimensional search space and can be defined as:

[0176] X n =X min +rand(1,0)*(X max -X min ) (34);

[0177] Among them, X max and X min are the upper and lower limits of the variable respectively. The optimal solution of this patent is a one-dimensional vector id, so D = 1. Considering the working range of id at each speed, X is set min is the value of the "maximum torque voltage ratio" MTPV at this speed, X max It is the id current value at zero torque at this speed.

[0178] The gradient search rule includes the rule itself GSR, which is used to improve the algorithm's exploration ability and avoid falling into the global optimum. It also includes the moving direction DM, which is used to generate a suitable search direction and improve the convergence speed. Based on GSR and DM, update the current vector location.

[0179]

[0180] ρ1=2*rand*α-α (36);

[0181] ρ2=2*rand*α-α (37);

[0182]

[0183] β=β min +(β max -β min )*(1-(m / M) 3 ) 2 (39);

[0184] Δx=rand(1:N)*|step| (40);

[0185]

[0186] Among them, β min and β max are 0.2 and 1.2 respectively, m is the current iteration number, M is the maximum iteration number, randn represents a standard normal distribution random number, ε is a very small positive number between [0,0.1], rand(1:N) is an N-dimensional random vector between [0,1], r1, r2, r3, r4 (r1≠r2≠r3≠r4) are randomly selected from [1,N], and unequal integers, step is determined by X best and Determine the step size, X best and X worst Calculated by the objective function G(id).

[0187] By using the current vector in formula (35) Replace the best vector X best The position of can generate the following new vector

[0188]

[0189]

[0190] based on and The new position generated by the next iteration for:

[0191]

[0192] Where ra and rb are random numbers between [0,1].

[0193] In order to help the algorithm escape from the local optimum, a local escaping operator (LEO) mechanism is added to the GBO algorithm. The algorithm is as follows:

[0194]

[0195] Among them, f1 is a random number in [-1,1], f2 is a standard normal distribution random number, pr is a probability value, and u1, u2, and u3 are three random integers.

[0196] Through the above stochastic gradient optimization algorithm, the id with the smallest corresponding objective function G(id) in the solution space is taken as the d-axis current command id*, and the q-axis current command iq* is:

[0197]

[0198] Based on the known current command, the current error is defined as:

[0199]

[0200] Substituting equation (51) into equation (1), the decoupled current loop control voltage can be obtained as:

[0201]

[0202] The torque loop can be controlled according to formula (52).

[0203] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention is described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. FTPPI sliding mode and GBO optimized permanent magnet synchronous motor speed loop control method, characterized in that: The method comprises: Step 1: Establish mathematical modeling of permanent magnet synchronous motor; Step 2: Design a sliding surface based on a finite time adjustable boundary so that the speed error of the permanent magnet synchronous motor converges within the boundary within a finite time; Step 3: Designing a limiting function based on the sliding surface to prevent the derivative of the speed error from fluctuating violently, thereby obtaining an ideal torque command; Step 4: Use the stochastic gradient optimization algorithm, introduce the current circle and voltage circle equations as boundary conditions, take the minimum motor power loss as the objective function, and iterate to get the optimal dq axis current command; Step 5: Through decoupling control, the response to the ideal torque is achieved, and the dual closed-loop control of speed and torque is completed.

2. The FTPPI sliding mode and GBO optimized permanent magnet synchronous motor speed loop control method according to claim 1 is characterized in that: In the step 1, the mathematical model of the permanent magnet synchronous motor is: From formula (1), we can get: Among them, Trq is the torque, J is the moment of inertia, B is the friction coefficient, ωm is the mechanical speed, pn is the pole pair number, pn*ωm=ωe is the electrical angular velocity, ψf is the magnetic flux, id and iq are the dq-axis currents, ud and uq are the dq-axis voltages, Rs is the stator resistance, and Ld and Lq are the dq-axis inductances.

3. The FTPPI sliding mode and GBO optimized permanent magnet synchronous motor speed loop control method according to claim 2 is characterized in that: In the step 2, the speed loop sliding mode control algorithm is designed based on the finite time preset performance inversion (FTPPI): Set the speed command to The speed error is: Then the derivative of the error is: FTPPI is defined as: Among them, λ0, λ ∞ is a positive number, and λ ∞ <e ω (0)<λ0,T f is the expected convergence time of the preset performance; The speed ring sliding surface design based on FTPPI is: According to formula (6), when e ω =0, s = 0; when e ω When it approaches λ, s approaches +∞; when e ω When it approaches -λ, s approaches -∞; it can be seen that the adjustment target of the sliding surface is that the speed error is 0, and a boundary is set for the error; when the error approaches the boundary, the adjustment of the sliding mode control is larger, so as to ensure that the error is always within the boundary; By taking the derivative of formula (6), we can get: Because the speed error e ω satisfy: -l <e ω <λ (8); 0<λ-e ω <2min (9); 0 <e ω +λ<2λ (10); Therefore, s and e ω Same number; and because In (λ-e ω ) 2 (e ω +λ) 2 >0, so and Same sign; according to the Lyapunov stability condition, let the Lyapunov function and its derivative be: Therefore, the design reaching law is: Substituting formula (15) into formula (12), we can get:

4. The FTPPI sliding mode and GBO optimized permanent magnet synchronous motor speed loop control method according to claim 3 is characterized in that: In the above formula (16), when t→∞, e ω →0 o'clock, It will cause serious steady-state fluctuations in the speed loop regulation; therefore Design a clipping function: When e ω →∞, Does not affect the normal adjustment of the speed loop; when e ω →0, according to Taylor expansion: It can be seen from formula (18) that the limiting function can effectively limit the steady-state fluctuation of the speed loop; the change rate of the Lyapunov function at this time is: According to formula (19), as long as You can Established, ensuring the stability of the speed loop; thus, the condition for the stability of the speed loop is: From formula (20), we can see that the denominator on the right side of the inequality sign is Therefore, the denominator cannot approach infinitesimal, and the value of the fraction cannot approach infinity, that is, it must be bounded; thus, there is always k that satisfies the condition of formula (20), and at the same time, it can be ensured that formula (19) is always less than 0, thereby ensuring the stability of the speed loop.

5. The FTPPI sliding mode and GBO optimized permanent magnet synchronous motor speed loop control method according to claim 4 is characterized in that: In step 4, the "efficiency optimal gradient optimization" current loop control algorithm is designed based on the constraint conditions: Substituting formula (17) into formula (4), we can obtain: According to formula (1), the torque command Trq can be * Convert to the corresponding current command and Therefore, it is necessary to determine the optimal current command; The "motor efficiency optimization" principle is used to determine the current command; the formula for the known three-phase AC power is: P ac =3*U 相rms *I 相rms *cosθ (22); Substituting equations (23)-(25) into equation (22), we can obtain: The mechanical power is: P mot (i d ,i q )=Trq(i d ,i q )*ω m (27); Considering that the motor efficiency of electric motor and generator is the inverse of each other, in order to unify the formula, "minimum loss" is used to express "optimal motor efficiency", that is: yes p (in d ,and d ,in q ,and q )=P ac (in d ,and d ,in q ,and q )-P mot (and d ,and q )(28); In order to simplify the parameters, when Trq is known * Under the condition of , substitute formula (1) into formula (28), use id to represent iq through the torque formula, and then use id and iq to represent ud and uq; at this time, id can be used to represent iq, ud, and uq at the same time, that is, iq=Iq(id), ud=Ud(id), uq=Uq(id), and we can get: e p (i d )=P ac (i d )-P mot (i d )(29); Then the loss objective function of "optimal motor efficiency" is: Of course, the selection of id, iq, ud, and uq is not without range, and needs to be within the current circle and voltage circle; according to formula (1), it can be known that: Find the id with the best motor efficiency, that is, find the optimal id within the constraints of the current circle and the voltage circle, so that the motor loss represented by the objective function G(id) is minimized; therefore, the constraints are supplemented and a new objective function is constructed: Among them, a and b are the penalty factors of the constraints; the larger the penalty factor, the closer id and iq are to the constraints, the smaller the deviation from the constraints, and the larger the inverse of the deviation, which makes the objective function larger, thus ensuring that the optimization process is within the constraints; The stochastic gradient based optimization algorithm (GBO) is used to iterate the optimization of id; First, the initial vector of GBO is randomly generated in the D-dimensional search space and can be defined as: X n =X min +rand(1,0)*(X max -X min )(34) Among them, X max and X min are the upper and lower limits of the variable respectively; the optimal solution is a one-dimensional vector id, so D = 1; set X min is the value of the "maximum torque voltage ratio" MTPV at this speed, X max is the id current value at zero torque at this speed; The gradient search rule includes the rule itself GSR, which is used to improve the algorithm's exploration ability and avoid falling into the global optimum; it also includes the moving direction DM, which is used to generate a suitable search direction and improve the convergence speed; based on GSR and DM, the current vector is updated location; ρ1=2*rand*α-α (36); ρ2=2*rand*α-α (37); β=β min +(β max -b min )*(1-(m / M) 3 ) 2 (39); Δx=rand(1:N)*|step| (40); Among them, β min and β max are 0.2 and 1.2 respectively, m is the current iteration number, M is the maximum iteration number, randn represents a standard normal distribution random number, ε is a very small positive number between [0,0.1], rand(1:N) is an N-dimensional random vector between [0,1], r1, r2, r3, r4 (r1≠r2≠r3≠r4) are randomly selected from [1,N], and unequal integers, step is determined by X best and Determine the step size, X best and X worst Calculated by the objective function G(id); By using the current vector in formula (35) Replace the best vector X best The position of can generate the following new vector based on and The new position generated by the next iteration for: Where ra and rb are random numbers between [0,1]; In order to help the algorithm escape from the local optimum, a local escape operator mechanism is added to the GBO algorithm. The algorithm is as follows: Among them, f1 is a random number in [-1,1], f2 is a standard normal distribution random number, pr is a probability value, and u1, u2, and u3 are three random integers; Through the above stochastic gradient optimization algorithm, the id with the smallest corresponding objective function G(id) in the solution space is taken as the d-axis current command id*, and the q-axis current command iq* is: Based on the known current command, the current error is defined as:

6. The FTPPI sliding mode and GBO optimized permanent magnet synchronous motor speed loop control method according to claim 5 is characterized in that: In step 5, by substituting equation (51) into equation (1), the decoupling current loop control voltage can be obtained as: The torque loop can be controlled according to formula (52).

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