Permanent magnet synchronous motor model-free adaptive fast terminal sliding mode control method and system

Abstract

The invention discloses a model-free self-adaptive discrete time fast terminal sliding mode control method and system based on a novel discrete approaching rate, and the method is compared with a conventional PI controller, a sliding mode controller and a model-free self-adaptive linear sliding mode controller. The response speed of the system is improved, and the method does not depend on a system model any more. Meanwhile, on the basis of input and output data of the permanent magnet synchronous motor system, a pseudo-partial derivative estimation algorithm is constructed according to a criterion function to obtain a time-varying parameter, a pseudo-partial derivative resetting mechanism is perfected, motor control based on data driving is achieved, and convergence of the pseudo-partial derivative estimation algorithm and stability of a control algorithm are analyzed; the control method is high in control precision and high in response speed, the robustness and the anti-interference performance of the system are improved, and then the control performance of the motor system under the complex working condition is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of permanent magnet synchronous motors, and more specifically, to a model-free adaptive fast terminal sliding mode control method and system for permanent magnet synchronous motors of rail transit, mining electric locomotives, and electric vehicles. Background Art

[0002] In recent years, permanent magnet synchronous motors have been widely used in defense equipment, electric vehicles, rail transportation, industrial production and other fields due to their simple structure, high efficiency and high reliability. As the main core component of the traction system, permanent magnet synchronous motors (PMSM) are responsible for the transmission and conversion of electrical energy to mechanical energy, and play a key role in safe and reliable operation.

[0003] However, in actual operation, permanent magnet synchronous motors will be affected by uncertainty factors such as parameter perturbations and external interference, which will affect the system control performance. There are still certain shortcomings in dealing with load changes and parameter uncertainties, making it difficult to meet the needs of high-performance control scenarios, which in turn affects safe and stable operation.

[0004] In addition, due to the uncertainty of parameter perturbations and external disturbances, the model-based control method depends on the motor parameters and cannot ensure that the system still has good control performance under parameter perturbations and severe external disturbances. Therefore, in order to ensure the stable operation of permanent magnet synchronous motors, it is necessary to seek new control methods to achieve efficient and reliable operation of motors under parameter perturbations and external disturbances. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method and system for model-free adaptive fast terminal sliding mode control of a permanent magnet synchronous motor in view of the deficiencies and defects of the prior art.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for model-free adaptive fast terminal sliding mode control of a permanent magnet synchronous motor, characterized in that it comprises the following steps:

[0008] Step 1: Establish a first-order model of the permanent magnet synchronous motor control system based on a compact dynamic linearization format, which is specifically expressed as

[0009] Δn(k+1)=φ(k)Δi q (k);

[0010] Among them, Δn(k+1)=n(k+1)-n(k), Δn(k+1) is the speed difference between the speed n(k+1) at time k+1 and the speed n(k) at time k; φ(k) is the pseudo partial derivative at time k; Δiq (k) = i q (k)-i q (k-1), Δi q (k) is the q-axis current i at time k q (k) and the q-axis current i at time k-1 q (k-1) current difference;

[0011] Step 2: Design an improved pseudo partial derivative estimation algorithm:

[0012] The specific process of designing the improved pseudo partial derivative estimation algorithm in step 2 is as follows:

[0013] Step 2.1, designing an estimation criterion function of pseudo partial derivatives for the permanent magnet synchronous motor speed control system;

[0014]

[0015] Among them, J(φ(k)) is the estimation criterion function of the pseudo partial derivative φ(k) at time k; n(k-1) is the speed at time k-1, is the estimated value of the pseudo partial derivative at time k-1; μ is the weight factor, μ>0;

[0016] By finding the extreme value of J(φ(k)), we can obtain the estimation algorithm of the traditional pseudo partial derivative:

[0017]

[0018] in, is the estimated value of the pseudo partial derivative at time k, is the estimated value of the pseudo partial derivative at time k-1; λ is the step size factor, 0<λ<0; Δn(k)=n(k)-n(k-1), Δn(k) is the speed difference between the speed n(k) at time k and the speed n(k-1) at time k-1;

[0019] Step 2.2: Add an adjustment term to the traditional pseudo-partial derivative estimation algorithm

[0020]

[0021] Where κ is a positive constant; e(k) = n d (k)-n(k), e(k) is the expected speed n at time k d The error between the speed at time k and n(k); e(k-1) = n d (k-1)-n(k-1), e(k-1) is the expected speed n at time k-1 d The error between the speed n(k-1) and the speed at time k-1;

[0022] Step 2.3, the specific expression of the pseudo partial derivative estimation algorithm can be obtained as follows:

[0023]

[0024] Among them, sgn(·) is the sign function;

[0025] Step 2.4, the algorithm reset mechanism is:

[0026]

[0027] Where φ(1) is The initial value of ε0 is a sufficiently small positive number, usually 10 to the power of -n, and its exponent is adjusted appropriately according to the complexity of the system; if any of the reset mechanisms is met, The value of is reset to make the algorithm more capable of tracking time-varying parameters;

[0028] The improved pseudo partial derivative parameter estimation algorithm only collects the input and output data of the permanent magnet synchronous motor to obtain the estimated value of the pseudo partial derivative at the current moment, and outputs it to the model-free adaptive fast terminal sliding mode control module;

[0029] Step 3: Design a model-free adaptive fast terminal sliding mode controller for the speed loop

[0030] The specific process of designing the speed loop model-free adaptive fast terminal sliding mode controller module in step 3 is as follows:

[0031] Step 3.1, define the state error as e(k)=n d (k)-n(k); where n d (k) is the expected speed at time k, n(k) is the speed at time k;

[0032] Step 3.2, select the discrete fast terminal sliding surface s(k)

[0033]

[0034] Where, ξ>0, ξ is the coefficient of the error exponential term; c0>0; p, q>0, and p, q are odd numbers; c>0;

[0035] The discrete fast terminal sliding surface is rewritten one step forward as

[0036]

[0037] Where ξ>0, ξ is the coefficient of the error exponential term; e(k+1)=n d(k+1)-n(k+1), e(k+1) is the error between the expected speed nd(k+1) at time k+1 and the speed n(k+1) at time k+1; c0>0; p, q>0, and p, q are odd numbers; c>0; γ1=c0 / T s , γ2=c-γ1;

[0038] Step 3.3, select a new type of fast power reaching law as

[0039] s(k+1)=s(k)-CT s |s(k) α sgn(s(k))-ε2T s |e(k) β s(k);

[0040] Where, T s is the sampling period, C≥0 is an adjustable coefficient; 0<α<1, 0<β<1, ε2>0;

[0041] In order to further reduce the chattering, the sign function sgn(s(k)) is improved to obtain a new sign function H(s), whose function expression is:

[0042]

[0043] Among them, k is a coefficient;

[0044] Step 3.4, the specific expression of the designed speed loop model-free adaptive fast terminal sliding mode controller module is:

[0045] In the formula, The control law of the speed loop model-free adaptive fast terminal sliding mode controller;

[0046] Step 3.5 When k ≥ 0, select the Lyapunov function as V = s(k) 2 / 2, the derivative yields:

[0047]

[0048] in, is the derivative of V; Therefore, it can be proved that the state error of the speed loop model-free adaptive fast terminal sliding mode controller module (8) is e(k) and will converge in a finite time, and the designed controller is stable;

[0049] Step 4: Output of the q-axis current from the model-free adaptive fast terminal sliding mode controller Input to the current loop based on PI control, and output the d-axis reference voltage Reference voltage of q axis Transmitted to the Park inverse transformation module (4) to obtain the α-axis reference voltage β-axis reference current Will The voltage is transmitted to the SVPWM control module (3), and the trigger pulse is transmitted to the three-phase inverter module (2), which outputs a three-phase voltage to drive the permanent magnet synchronous motor (1).

[0050] Furthermore, the pseudo partial derivative parameter estimation module (11) and the model-free adaptive fast terminal sliding mode control module (8) include:

[0051] The pseudo partial derivative parameter estimation module (11) is connected to the PMSM module (1) and the model-free adaptive fast terminal sliding mode controller module (8) respectively, and according to the speed n(k-1) at the k-1 moment output by the PMSM module (1), n(k-1) and the expected speed n at the k-1 moment d The error e(k-1) of (k-1) and the q-axis current i at time k-1 output by the model-free adaptive fast terminal sliding mode controller module (8) q (k-1), online estimation of pseudo partial derivatives and will Input into the model-free adaptive fast terminal sliding mode controller module (8);

[0052] The speed loop model-free adaptive fast terminal sliding mode controller module (8) is connected to the PMSM module (1), the pseudo partial derivative parameter estimation module (11) and the current loop module (9) based on PI control, and the speed n(k) at the time k output by the PMSM module (1) is calculated according to the desired speed n at the time k. d (k) and the online estimated pseudo partial derivative output by the pseudo partial derivative parameter estimation module (11) Output d-axis reference voltage Q-axis reference voltage

[0053] Furthermore, the speed loop model-free fast terminal sliding mode controller module (8) outputs a q-axis current Input into the current loop based on PI control, and obtain the reference voltage of the d-axis Reference voltage of q axis Transmitted to the Park inverse transformation module (4) to obtain the α-axis reference voltage β-axis reference current Will The voltage is transmitted to the SVPWM control module (3), and the trigger pulse is transmitted to the inverter module (2), which outputs a three-phase voltage to drive the permanent magnet synchronous motor (1).

[0054] Furthermore, the permanent magnet synchronous motor model-free adaptive fast terminal sliding mode control system does not require any PMSM model information and is only based on the expected speed n at time k. d (k), the motor speed n(k) at time k, and the output i of the model-free adaptive fast terminal sliding mode control system at time k-1 q (k-1), the estimated value of the online pseudo partial derivative at time k And input into the speed loop model-free fast terminal sliding mode controller module (8), and finally obtain the q-axis current at time k

[0055] The present invention adopts the Model-free Adaptive Fast Terminal Sliding Mode Control (MFAFTSMC) method of the speed loop, which can achieve a fast dynamic response of the permanent magnet traction system compared with the traditional PI controller and the traditional sliding mode controller (Sliding Mode Control, SMC). This method only uses the input and output data of the motor at the previous moment, improves the pseudo partial derivative (PPD) estimation algorithm, and combines the terminal sliding mode control based on the fast power approach rate with the tight format model-free adaptive control. This design no longer relies on the model information of the motor, but is directly based on the estimated pseudo partial derivative, which improves the motor convergence speed, shortens the time to reach the sliding surface, enhances the system robustness and anti-interference performance, improves the dynamic and steady-state performance, and ensures the high-performance control of the permanent magnet synchronous motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 This is a system structure block diagram of an embodiment of the present invention;

[0057] In the figure, 1 is a permanent magnet synchronous motor, 2 is a three-phase inverter, 3 is a SVPWM module (i.e., space vector pulse width modulation), 4 is an inverse Park transform, 5 is a current transformer, 6 is a Clark transform, 7 is a Park transform, 8 is a speed loop model-free adaptive fast terminal sliding mode controller, 9, 10 is a current loop PI controller, and 11 is a pseudo-partial derivative parameter estimation.

[0058] Figure 2 This is a structural block diagram of the speed loop model-free adaptive fast terminal sliding mode controller of the present invention;

[0059] Figure 3 This is an embodiment of the present invention: a comparison diagram of the speed response of MFAFTSMC and PI control, SMC and MFASMC at a constant motor speed of 1000r / min;

[0060] Figure 4This is an embodiment of the present invention: a comparison diagram of the speed errors of MFAFTSMC and PI control, SMC and MFASMC at a constant motor speed of 1000r / min;

[0061] Figure 5 This is an embodiment of the present invention: a comparison diagram of the output torque of MFAFTSMC and PI control, SMC and MFASMC at a constant motor speed of 1000r / min;

[0062] Figure 6 This is an embodiment of the present invention: a comparison diagram of the speed response of MFAFTSMC and PI control, SMC and MFASMC under zero load of the motor;

[0063] Figure 7 An embodiment of the present invention is as follows: a comparison diagram of the speed errors of MFAFTSMC and PI control, SMC and MFASMC under zero load of the motor;

[0064] Figure 8 This is an embodiment of the present invention: a comparison diagram of the output torque of MFAFTSMC and PI control, SMC and MFASMC under zero load of the motor;

[0065] Fig. 9 An embodiment of the present invention is as follows: a comparison diagram of the speed response of MFAFTSMC and PI control, SMC and MFASMC under a given motor speed and load change;

[0066] Fig.10 An embodiment of the present invention is as follows: a comparison diagram of the speed errors of MFAFTSMC and PI control, SMC and MFASMC under a given motor speed and load change;

[0067] Fig.11 An embodiment of the present invention is as follows: a comparison diagram of the output torque of MFAFTSMC and PI control, SMC and MFASMC under a given motor speed and load change;

[0068] Fig.12 An embodiment of the present invention is as follows: PPD estimated value waveform diagrams at a constant motor speed of 1000 r / min, at zero motor load, and at a given motor speed and load change;

[0069] Fig.13 This is an embodiment of the present invention: a comparison diagram of the speed response of MFAFTSMC and PI control, SMC and MFASMC under the condition that the load motor is zero load in the motor drag experiment;

[0070] Fig.14This is an embodiment of the present invention: a comparison diagram of the output torque of MFAFTSMC and PI control, SMC and MFASMC under the condition that the load motor is zero load in the motor drag experiment;

[0071] Fig.15 This is an embodiment of the present invention; in the motor towing experiment, the load motor is under load conditions, and the speed response comparison diagram of MFAFTSMC and PI control, SMC and MFASMC;

[0072] Fig.16 This is an embodiment of the present invention: a comparison diagram of the output torque of MFAFTSMC and PI control, SMC and MFASMC under the condition that the load motor is under load in the motor drag experiment;

[0073] Fig.17 This is an embodiment of the present invention: a comparison diagram of the speed errors of MFAFTSMC and PI control, SMC and MFASMC under the load condition of the load motor in the motor drag experiment. DETAILED DESCRIPTION

[0074] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0075] Figure 1 The present invention is a block diagram of a model-free adaptive fast terminal sliding mode control method and system implementation for a permanent magnet synchronous motor. Figure 1 In the example, the current sensor (5) detects the stator current information i of the permanent magnet synchronous motor (PMSM) a and i b Transmitted to the Clarke transformation module (6), the α-axis current i is obtained α , β-axis current i β ; Position and speed detection to obtain the permanent magnet synchronous motor electrical position angle θ e and electrical angular velocity ω e ; Then the electrical position angle θ e 、α-axis current i α , β-axis current i β Transmitted to the Park transformation module (7), the d-axis current i is obtained d , q-axis current i q ; The error e(k) between the expected speed nd(k) at time k and the speed n(k) at time k, and the q-axis current at time k-1 The pseudo partial derivative at time k is obtained by the pseudo partial derivative (PPD) estimation algorithm module (11). Will Input to the speed loop MFAFTSMC controller module (8) to obtain the q-axis current The d-axis reference voltage is obtained by the current loop PI controller (9) and (10) and q-axis reference voltage The d-axis reference voltage and q-axis reference voltage Transmitted to the Park inverse transformation module (4) to obtain the α-axis reference voltage β-axis reference voltage Will The signal is transmitted to the SVPWM (i.e., space vector pulse width modulation) module (3), and the obtained trigger pulse is transmitted to the three-phase inverter module (2), which outputs a three-phase voltage to drive the permanent magnet synchronous motor (1).

[0076] The mathematical model of the permanent magnet synchronous traction motor in the dq coordinate system is:

[0077]

[0078] Among them, u d 、u q : stator voltage component on dq axis (V);

[0079] i d 、i q : stator current component on dq axis (A);

[0080] L d , L q : stator winding dq axis inductance (mH); P n : number of pole pairs;

[0081] R: stator resistance (Ω); J: moment of inertia (kg·m 2 );

[0082] B: Friction coefficient (N·m·s); T e : electromagnetic torque (N·m);

[0083] T L : load torque (N·m); ψ r : Permanent magnet flux (Wb);

[0084] ω e : electrical angular velocity (rad / s); ω m : Mechanical angular velocity (rad / s).

[0085] use When the vector control strategy is adopted, the PMSM electromagnetic torque equation can be rewritten according to formula (1) as follows:

[0086]

[0087] Combining equations (1) and (2), the first-order forward Euler method is used to discretize the motor motion equations, and we can get

[0088]

[0089] Where, T s is the sampling period, iq(k) is the q-axis current of the system at time k.

[0090] Since n(k)=30ω m (k) / π, so we can get:

[0091]

[0092] Among them, n(k) is the speed of the system at time k.

[0093]

[0094] Further arrangement of formula (4) yields:

[0095] n(k+1)=ν1n(k)+ν2i q (k)+T M (5)

[0096] in:

[0097] S1: Establish a model-free adaptive model of the speed loop of the permanent magnet synchronous motor control system based on tight-form linear dynamics

[0098] Note 1: From equation (5), it can be seen that the speed loop control of the permanent magnet synchronous motor is a single-input single-output (SISO) discrete nonlinear system, which satisfies the condition that the system input and output are observable and controllable.

[0099] Note 2: When using feedback control algorithm to control the speed of permanent magnet synchronous motor, there is a bounded control input signal, which can make the actual output of the system close to the expected output, the system state is controllable, the system output is observable, and the system satisfies the generalized Lipschitz condition. That is, for any time k and Δi q ≠0, the system satisfies:

[0100] Δn(k+1)|≤b|Δi q (k)| (6)

[0101] Among them, Δn(k+1)=n(k+1)-n(k), b>0 is a positive constant, Δi q (k) = i q (k)-i q (k-1).

[0102] Note 3: A finite change in the control input will not cause the system output to increase or decrease infinitely, and the following assumption 1 is satisfied.

[0103] Assumption 1: The system is about the control input i q The partial derivative of (k) is continuous, and the input and output of the system satisfy the generalized Lipschitz condition.

[0104] Theorem 1: For a permanent magnet synchronous motor speed drive system that satisfies Assumption 1, when |Δi q When (k)|≠0, there must be a bounded pseudo partial derivative φ(k), and the model based on compact format dynamic linearization is obtained as follows:

[0105] Δn(k+1)=φ(k)Δi q (k) (7)

[0106] Among them, Δn(k+1)=n(k+1)-n(k), Δn(k+1) is the speed difference between the speed n(k+1) at time k+1 and the speed n(k) at time k; φ(k) is the pseudo partial derivative at time k; Δi q (k) = i q (k)-i q (k-1), Δi q (k) is the q-axis current i at time k q (k) and the q-axis current i at time k-1 q (k-1) current difference;

[0107] The speed controller and current controller of the traditional permanent magnet synchronous motor control system are both PI controllers or model-free controllers (Sliding Mode Control, SMC), which cannot adapt well to the application occasions where the permanent magnet synchronous motor control system faces complex working conditions, especially parameter perturbations, load disturbances, etc. This embodiment proposes a model-free adaptive fast terminal sliding mode control (MFAFTSMC) method for the speed loop of a permanent magnet synchronous motor.

[0108] S2: Design of Model-Free Adaptive Fast Terminal Sliding Mode Control (MFAFTSMC) for PMSM Speed ​​Loop

[0109] Define the MFAFTSMC controller state error as:

[0110] e(k)=n d (k)-n(k) (8)

[0111] Where n d (k) is the expected speed at time k, n(k) is the speed at time k;

[0112] The discrete fast terminal sliding mode function is designed as:

[0113]

[0114] Where ξ is the coefficient of the error exponential term, ξ>0; e(k+1)=n d (k+1)-n(k+1), e(k+1) is the state error at time k+1; c>0, c0>0; p, q>0, and p, q are odd numbers.

[0115] When s(k)=0, the speed error change rate is:

[0116]

[0117] That is, when the system state error moves toward the sliding surface, the convergence speed is exponential It is determined jointly by the coefficient term ce(k-1).

[0118] The sliding mode function (9) is rewritten one step forward as:

[0119]

[0120] Where ξ>0, ξ is the coefficient of the error exponential term; e(k+1)=n d (k+1)-n(k+1), e(k+1) is the error between the expected speed nd(k+1) at time k+1 and the speed n(k+1) at time k+1; c0>0; p, q>0, and p, q are odd numbers; c>0; γ1=c0 / T s , γ2=c-γ1;

[0121] Design a new type of fast power reaching law:

[0122] s(k+1)=s(k)-CT s |s(k) α sgn(s(k))-ε2T s |e(k) β s(k) (12)

[0123] In the formula, C≥0 is an adjustable coefficient, 0<α<1, 0<β<1, ε2>0.

[0124] Note 4: The first term in equation (12) is the power reaching law, and the second term is the exponential term ε2s(k) and the state variable power function |e(k)| β The product of |e(k)| and this combination is called the variable gain reaching law. By introducing the state variable |e(k)|, the oscillation problem caused by the exponential term can be alleviated.

[0125] Note 5: When the system is far away from the sliding surface, the power term and the variable exponential term work together to accelerate the approach rate and shorten the arrival time; when the system approaches the sliding surface, |e(k)| β The value of is close to 0, and the system motion state is mainly determined by the power term, which ensures the global convergence speed. The fast power reaching law (12) not only retains the advantages of the traditional power reaching law, but also accelerates the global convergence speed and effectively suppresses chattering.

[0126] In order to further reduce the chattering, the sign function sgn(s(k)) is improved to obtain a new sign function H(s), and its function expression is:

[0127]

[0128] Combining equations (11), (12) and (13), we can obtain:

[0129]

[0130] Combining equation (8) and equation (7), we can get

[0131]

[0132] Substituting equation (14) into equation (15), the designed MFAFTSMC control law is:

[0133]

[0134] S3: Improved Pseudo Partial Derivative (PPD) Estimation

[0135] Pseudo partial derivative (PPD) is a time-varying parameter, and its exact true value is difficult to obtain. In order to make the estimated value of PPD follow the changes of the motor drive system more quickly, this paper improves the estimation algorithm of pseudo partial derivative (PPD) by adding an adjustment term between the current moment φ(k) and the previous moment φ(k-1) to make the pseudo partial derivative reset mechanism more perfect.

[0136] First, design the estimation criterion function of PPD:

[0137]

[0138] Among them, J(φ(k)) is the estimation criterion function of the pseudo partial derivative φ(k) at time k; n(k-1) is the speed at time k-1, is the estimated value of the pseudo partial derivative at time k-1; μ is the weight factor, μ>0;

[0139] By finding the extreme value of formula (17), we can obtain the traditional PPD estimation algorithm:

[0140]

[0141] in, is the estimated value of the pseudo partial derivative at time k, is the estimated value of the pseudo partial derivative at time k-1; Δn(k)=n(k)-n(k-1), Δn(k) is the speed difference between the speed n(k) at time k and the speed n(k-1) at time k-1; λ is the step size factor, 0<λ<1, which makes the algorithm more flexible and general.

[0142] Secondly, an adjustment term is added to the traditional pseudo-partial derivative estimation algorithm:

[0143]

[0144] Where κ is a positive constant; e(k) = n d (k)-n(k), e(k) is the expected speed n at time k d The error between the speed at time k and n(k); e(k-1) = n d (k-1)-n(k-1), e(k-1) is the expected speed n at time k-1 d The error between the speed n(k-1) and the speed at time k-1;

[0145] Finally, the specific expression of the pseudo partial derivative estimation algorithm is:

[0146]

[0147] The algorithm reset mechanism is:

[0148]

[0149] Where φ(1) is The initial value of ε0 is a sufficiently small positive number, usually 10 to the power of -n, and its exponent is adjusted appropriately according to the complexity of the system; any one of the reset mechanisms that satisfies formula (21) will The value of is reset to make the algorithm more capable of tracking time-varying parameters;

[0150] Assumption 2: For a given PMSM, the expected output n is bounded d (k+1)=const, there is always a bounded input iq(k) such that the output of the system is equal to the constant when driven by this control input signal.

[0151] Assumption 3: For any time k and Δi q ≠0, the sign of the pseudo partial derivative remains unchanged, that is, the change in the output is always consistent with the behavior of the input change.

[0152] For the PMSM speed drive system, it can be seen from equations (5), (6), (8) and (16) that the system has satisfied assumptions 1-3.

[0153] Theorem 2: Assuming that conditions 1-3 are satisfied, when n d (k+1)=n d =const, when the MFAFTSMC control method (16) is adopted, the tracking error of the motor in the speed loop control system is monotonically convergent, and the input and output are bounded.

[0154] Define the pseudo partial derivative estimate error:

[0155]

[0156] Subtracting φ(k) from both ends of equation (18) and taking the absolute value yields:

[0157]

[0158] In the first term of formula (23), since λ∈(0,1], It decreases monotonically, and its maximum value is At this point there must be a constant m1 that satisfies:

[0159]

[0160] According to equations (6) and (7), we have:

[0161]

[0162] in, is a normal number, so

[0163] Similarly:

[0164]

[0165] In the formula, m2 is a constant.

[0166] Through formula (23) and formula (24), we can get:

[0167]

[0168] Since φ(k) is bounded, we can prove that Bounded.

[0169] The following is a proof of the boundedness of the system tracking error. First, choose the Lyapunov function as V = s(k) 2 / 2, so:

[0170]

[0171] Substituting into equation (12) and equation (13), we can obtain:

[0172]

[0173] When k ≥ 0, Therefore, under the control algorithm (16), |e(k)| converges to the neighborhood of zero. Therefore, the speed loop model-free adaptive fast terminal sliding mode controller module (8) will converge within a finite time, and the designed controller is stable;

[0174] Next, the permanent magnet synchronous motor vector control system was modeled and simulated. The system model is as follows: Figure 1 As shown, the simulation parameters of the permanent magnet synchronous motor are shown in Table 1:

[0175] Table 1 Parameters of permanent magnet drive system for electric vehicles

[0176]

[0177] Case 1: Simulation comparison results of PMSM with no load

[0178] Set the initial reference speed n d =800r / min, load torque T L =0. When t=0.5s, the reference speed increases to 1500r / min, and the simulation time is 1.4s. The simulation comparison results of PI control, SMC, MFASMC and MFAFTSMC are recorded.

[0179] Figure 3 The speed response comparison diagram of MFAFTSMC, PI control, SMC and MFASMC is given when the motor has a constant speed of 1000r / min.

[0180] Figure 4 The speed error comparison diagram of MFAFTSMC, PI control, SMC and MFASMC is given when the motor has a constant speed of 1000r / min.

[0181] Figure 5 The output torque comparison diagram of MFAFTSMC, PI control, SMC and MFASMC is given at a constant motor speed of 1000r / min;

[0182] from Figure 3It can be seen that when no-load, the four methods all reach the given speed within 0.01s. PI, SMC, and MFASMC all have overshoot, but the MFAFTSMC method responds to the speed faster, has a smaller overshoot, and a shorter convergence time. At t=0.5s, the reference speed is changed to 1500r / min. Under the control of PI, SMC, and MFASMC, the system can converge to the given speed within t=0.54s; under the control of MFAFTSMC, the system reaches the given speed at t=0.51s, and the overshoot is smaller. From Figure 4 It can be seen that the average speed error of PI control is 1.6r / min, the average speed error of SMC is 0.8r / min, the average speed error of MFASMC is 0.9r / min, and the average speed error of MFAFTSMC is smaller, always maintained within the range of 0.4r / min. Figure 5 It can be seen that compared with the other three methods, the MFAFTSMC algorithm has a more stable output torque and a better steady state.

[0183] Case 2: Simulation comparison results of PMSM with constant speed and sudden load change

[0184] Set reference speed n d =1000r / min, initial load torque T L =0.1N·m, load torque T when t=0.5s L Increase to 0.15N·m. Record the simulation comparison results of PI control, SMC, MFASMC and MFAFTSMC.

[0185] Figure 6 A comparison chart of the speed response of MFAFTSMC, PI control, SMC and MFASMC under zero load of the motor is given;

[0186] Figure 7 A comparison chart of the speed errors between MFAFTSMC and PI control, SMC and MFASMC under zero load of the motor is given;

[0187] Figure 8 The output torque comparison diagram of MFAFTSMC with PI control, SMC and MFASMC under zero load of the motor is given;

[0188] from Figure 6 It can be seen that PI control, SMC at t = 0.04s, MFASMC at t = 0.02s, and MFAFTSMC at t = 0.01s reach the target speed and remain stable; MFAFTSMC is significantly better than the other three control methods in terms of convergence speed and overshoot suppression. At t = 0.5s, the motor load suddenly increases, and the MFAFTSMC speed decreases the least, and the recovery time is also the shortest. Figure 7It can be seen that among the speed errors of the four methods, the speed error of MFAFTSMC is the smallest, and the average speed error is only 0.5r / min. Figure 8 From the output torque waveform, it can be seen that the torque pulsation suppression effect of MFAFTSMC is the best. Therefore, under the condition of constant speed and load disturbance, the MFAFTSMC proposed in this paper has the strongest anti-interference ability and the best robustness.

[0189] Case 3: Simulation comparison results of PMSM with sudden changes in speed and load

[0190] Set the initial reference speed n d =1000r / min, t=0.5s, the given speed increases to 1500r / min, t=1.0s the given speed drops to 1300r / min. Set the initial load torque T L =0.1N·m, load torque T when t=0.5s L When it increases to 0.15N·m and t=0.9s, the load torque T L Increased to 0.18N·m. The simulation comparison results of PI control, SMC, MFASMC and MFAFTSMC are given.

[0191] Fig. 9 A comparison chart of the speed response of MFAFTSMC, PI control, SMC and MFASMC is given under the given motor speed and load changes;

[0192] Fig.10 A comparison chart of the speed errors of MFAFTSMC, PI control, SMC and MFASMC is given under the given motor speed and load changes;

[0193] Fig.11 The output torque comparison diagram of MFAFTSMC, PI control, SMC and MFASMC under given motor speed and load changes is given.

[0194] Fig. 9 The table shows the speed response waveforms under the four control modes. It can be seen that MFAFTSMC and MFASMC reach a stable state at t=0.01s and t=0.025s respectively, while the other two methods reach stability after 0.04s. When the speed increases at t=0.5s, MFAFTSMC responds quickly, converges within 0.005s, and has minimal overshoot. When the load increases at t=0.9s and the speed decreases at t=1.0s, MFAFTSMC still shows stronger anti-interference ability and shorter recovery time compared with the other three methods. Fig.10 and Fig.11It can be seen that compared with the other three control algorithms, the MFAFTSMC algorithm has the smallest average speed error, the smallest torque ripple, and the fastest response speed. Therefore, in the case of sudden changes in speed and load, the proposed MFAFTSMC method has strong robustness and good control performance.

[0195] Case 4: Comparison results of the motor-to-motor drag experiment when the load motor is under zero load conditions

[0196] The reference speed is set to 1000r / min, and the motor starts running 3.5s after the platform is started. The motor speed increases from 0r / min to 1000r / min within 0.2s. Experimental results based on PI control, sliding mode control, MFASMC and MFAFTSMC are given.

[0197] Fig.13 The speed response comparison diagram of MFAFTSMC and PI control, SMC and MFASMC under the condition of zero load of the load motor in the motor drag experiment is given;

[0198] Fig.14 The output torque comparison diagram of MFAFTSMC, PI control, SMC and MFASMC under the condition of zero load of the load motor in the motor drag experiment is given;

[0199] from Fig.13 It can be seen from the figure that under zero load conditions, traditional PI control and SMC reach stability only after t = 3.74s. However, MFASMC and MFAFTSMC converge significantly faster, reaching stability at t = 3.66s, and MFAFTSMC has a smaller overshoot. Fig.14 It can be seen that the output torque of MFAFTSMC is more stable and has better steady-state performance compared with the other three methods.

[0200] Case 5: Comparison results of the motor-to-motor drag test when the load motor is loaded

[0201] The initial reference speed is set to 1000r / min and the load torque is 0.045N·m. At t=6s, the reference speed increases to 1500r / min and the load torque increases to 0.12N·m. 3.5s after the platform is started, the motor speed gradually increases to 1000r / min. At t=6s, the speed and load increase. All four methods reach the new given speed within t=0.2s. Experimental results based on PI control, sliding mode control, MFASMC and MFAFTSMC are given.

[0202] Fig.15 The speed response comparison diagram of MFAFTSMC and PI control, SMC and MFASMC under the condition that the load motor is loaded in the motor drag experiment is given;

[0203] Fig.16 The output torque comparison diagram of MFAFTSMC, PI control, SMC and MFASMC under the condition that the load motor is loaded in the motor drag experiment is given;

[0204] Fig.17 A comparison diagram of the speed errors of MFAFTSMC, PI control, SMC and MFASMC is given when the load motor is under load in the motor drag experiment.

[0205] from Fig.15 and Fig.16 It can be seen that when the motor is started under load, the traditional PI control method and SMC both have excessive overshoot and slow convergence speed in order to quickly reach a stable state. However, the MFASMC and MFAFTSMC methods converge and stabilize in a short time, and the MFAFTSMC method performs better in overshoot and convergence speed. At t=6s, after the reference speed and load torque change, PI control, SMC and MFASMC all have a certain degree of jitter, while the MFAFTSMC method has the smallest jitter amplitude and a more stable output torque. Fig.17 The average amplitudes of PI, SMC, and MFASMC are all between 4.5r / min and 5r / min, while the average amplitude of MFAFTSMC obviously does not exceed 4r / min. Although the starting performance of the data-driven MFASMC and MFAFTSMC methods is equally excellent, it can be seen that the speed error of MFASMC is large due to the use of linear sliding surface and exponential approach rate, while the speed error of MFAFTSMC is smaller than that of the other three control methods due to the use of improved approach rate.

[0206] From the above analysis, it can be seen that PI control and SMC need to obtain the precise parameters of the motor in real time during operation, and they are obviously insufficient in starting performance, convergence speed, anti-interference performance and overshoot suppression. MFASMC and MFAFTSMC are data-driven controllers. When starting, they can perform real-time control based on the output speed and q-axis current of the PMSM at the previous moment. Therefore, under complex working conditions, this type of control method has more obvious advantages. MFAFTSMC is optimized on the traditional MFASMC, and its convergence to the sliding surface is faster, and the estimation of pseudo-partial derivatives is more accurate.

[0207] In summary, compared with PI control, SMC and MFASMC, MFAFTSMC not only performs better in speed tracking performance, but also has more advantages in dynamic response and steady-state performance under complex working conditions.

[0208] The above embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Any equivalent substitution or change made by a person skilled in the art based on the present invention is within the protection scope of the present invention.

Claims

1. A model-free adaptive fast terminal sliding mode control method for a permanent magnet synchronous motor, characterized in that: The following steps are involved: Step 1: Establish a first-order model of the permanent magnet synchronous motor control system based on a compact dynamic linearization format, which is specifically expressed as Δn(k+1)=φ(k)Δi q (k); Among them, Δn(k+1)=n(k+1)-n(k), Δn(k+1) is the speed difference between the speed n(k+1) at time k+1 and the speed n(k) at time k; φ(k) is the pseudo partial derivative at time k; Δi q (k) = i q (k)-i q (k-1), Δi q (k) is the q-axis current i at time k q (k) and the q-axis current i at time k-1 q (k-1) current difference; Step 2: Design an improved pseudo partial derivative estimation algorithm: The specific process of designing the improved pseudo partial derivative estimation algorithm in step 2 is as follows: Step 2.1, designing an estimation criterion function of pseudo partial derivatives for the permanent magnet synchronous motor speed control system; Among them, J(φ(k)) is the estimation criterion function of the pseudo partial derivative φ(k) at time k; n(k-1) is the speed at time k-1, is the estimated value of the pseudo partial derivative at time k-1; μ is the weight factor, μ>0; By finding the extreme value of J(φ(k)), we can obtain the estimation algorithm of the traditional pseudo partial derivative: in, is the estimated value of the pseudo partial derivative at time k, is the estimated value of the pseudo partial derivative at time k-1; λ is the step size factor, 0<λ<1; Δn(k)=n(k)-n(k-1), Δn(k) is the speed difference between the speed n(k) at time k and the speed n(k-1) at time k-1; Step 2.2: Add an adjustment term to the traditional pseudo-partial derivative estimation algorithm Where κ is a positive constant; e(k) = n d (k)-n(k), e(k) is the expected speed n at time k d The error between the speed at time k and n(k); e(k-1) = n d (k-1)-n(k-1), e(k-1) is the expected speed n at time k-1 d The error between the speed n(k-1) and the speed at time k-1; Step 2.3, the specific expression of the pseudo partial derivative estimation algorithm can be obtained as follows: Among them, sgn(·) is the sign function; Step 2.4, the algorithm reset mechanism is: Where φ(1) is The initial value of ε0 is a sufficiently small positive number, usually 10 to the power of -n, and its exponent is adjusted appropriately according to the complexity of the system; if any of the reset mechanisms is met, The value of is reset to make the algorithm more capable of tracking time-varying parameters; The improved pseudo partial derivative parameter estimation algorithm only collects the input and output data of the permanent magnet synchronous motor to obtain the estimated value of the pseudo partial derivative at the current moment, and outputs it to the model-free adaptive fast terminal sliding mode control module; Step 3: Design a model-free adaptive fast terminal sliding mode controller for the speed loop The specific process of designing the speed loop model-free adaptive fast terminal sliding mode controller module in step 3 is as follows: Step 3.1, define the state error as e(k)=n d (k)-n(k); where n d (k) is the expected speed at time k, n(k) is the speed at time k; Step 3.2, select the discrete fast terminal sliding surface s(k) Where, ξ>0, ξ is the coefficient of the error exponential term; c0>0; p, q>0, and p, q are odd numbers; c>0; The discrete fast terminal sliding surface is rewritten one step forward as Where ξ>0, ξ is the coefficient of the error exponential term; e(k+1)=n d (k+1)-n(k+1), e(k+1) is the error between the expected speed nd(k+1) at time k+1 and the speed n(k+1) at time k+1; c0>0; p, q>0, and p, q are odd numbers; c>0; γ1=c0 / T s , γ2=c-γ1; Step 3.3, select a new type of fast power reaching law as s(k+1)=s(k)-CT s |s(k) α sgn(s(k))-ε2T s |e(k) β s(k); Where, T s is the sampling period, C≥0 is an adjustable coefficient; 0<α<1, 0<β<1, ε2>0; In order to further reduce the chattering, the sign function sgn(s(k)) is improved to obtain a new sign function H(s), and its function expression is: Among them, k is a coefficient; Step 3.4, the specific expression of the designed speed loop model-free adaptive fast terminal sliding mode controller module is: In the formula, The control law of the speed loop model-free adaptive fast terminal sliding mode controller; Step 3.5 When k ≥ 0, select the Lyapunov function as V = s(k) 2 / 2, the derivative yields: in, is the derivative of V; Therefore, it can be proved that the state error of the speed loop model-free adaptive fast terminal sliding mode controller module (8) is e(k) and will converge in a finite time, and the designed controller is stable; Step 4: Output of the q-axis current from the model-free adaptive fast terminal sliding mode controller Input to the current loop based on PI control, and output the d-axis reference voltage Reference voltage of q axis Transmitted to the Park inverse transformation module (4) to obtain the α-axis reference voltage β-axis reference current Will The voltage is transmitted to the SVPWM control module (3), and the trigger pulse is transmitted to the three-phase inverter module (2), which outputs a three-phase voltage to drive the permanent magnet synchronous motor (1).

2. A model-free adaptive fast terminal sliding mode control system for a permanent magnet synchronous motor, characterized in that: The pseudo partial derivative parameter estimation module (11) and the model-free adaptive fast terminal sliding mode control module (8) include: The pseudo partial derivative parameter estimation module (11) is connected to the PMSM module (1) and the model-free adaptive fast terminal sliding mode controller module (8) respectively, and according to the speed n(k-1) at the k-1 moment output by the PMSM module (1), n(k-1) and the expected speed n at the k-1 moment d The error e(k-1) of (k-1) and the q-axis current i at time k-1 output by the model-free adaptive fast terminal sliding mode controller module (8) q (k-1), online estimation of pseudo partial derivatives and will Input into the model-free adaptive fast terminal sliding mode controller module (8); The speed loop model-free adaptive fast terminal sliding mode controller module (8) is connected to the PMSM module (1), the pseudo partial derivative parameter estimation module (11) and the current loop module (9) based on PI control, and the speed n(k) at the time k output by the PMSM module (1) is calculated according to the desired speed n at the time k. d (k) and the online estimated pseudo partial derivative output by the pseudo partial derivative parameter estimation module (11) Output d-axis reference voltage Q-axis reference voltage The permanent magnet synchronous motor model-free adaptive fast terminal sliding mode control system adopts the permanent magnet synchronous motor model-free adaptive fast terminal sliding mode control method described in claim 1.

3. A permanent magnet synchronous motor model-free adaptive fast terminal sliding mode control system according to claim 2, characterized in that: The speed loop model-free fast terminal sliding mode controller module (8) outputs a q-axis current Input into the current loop based on PI control, and obtain the reference voltage of the d-axis Reference voltage of q axis Transmitted to the Park inverse transformation module (4) to obtain the α-axis reference voltage β-axis reference current Will The voltage is transmitted to the SVPWM control module (3), and the trigger pulse is transmitted to the inverter module (2), which outputs a three-phase voltage to drive the permanent magnet synchronous motor (1).

4. A model-free adaptive fast terminal sliding mode control system for a permanent magnet synchronous motor according to any one of claims 2-3, characterized in that: The permanent magnet synchronous motor model-free adaptive fast terminal sliding mode control system does not require any PMSM model information and is only based on the expected speed n at time k. d (k), the motor speed n(k) at time k, and the output i of the model-free adaptive fast terminal sliding mode control system at time k-1 q (k-1), the estimated value of the online pseudo partial derivative at time k And input into the speed loop model-free fast terminal sliding mode controller module (8), and finally obtain the q-axis current at time k

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