A design method for motor sliding mode speed controller for aviation hybrid propulsion system

Abstract

The present invention discloses a design method of a motor sliding mode speed controller for an aviation hybrid propulsion system, comprising the following steps: modeling a permanent magnet synchronous propulsion motor and a propeller, respectively listing the voltage, flux, torque equations of the permanent magnet synchronous motor in a natural coordinate system, a stationary coordinate system, and a rotating coordinate system, as well as the thrust, torque, power, efficiency, and forward ratio formulas of the propeller; designing a variable exponential power reaching law to improve the convergence speed of the sliding mode variables; designing a sliding mode speed controller based on disturbance compensation; designing an adaptive chaos gray wolf optimization algorithm; and building a permanent magnet synchronous propulsion motor system simulation model based on a MATLAB / Simulink simulation platform. The present invention expands the sliding mode disturbance observer to estimate and compensate for disturbances, and uses an improved adaptive chaos gray wolf optimization algorithm to optimize the controller and observer parameters.

Description

Technical Field

[0001] The invention belongs to the field of aviation propulsion motor control, and in particular relates to a design method for a sliding mode speed controller of a propulsion motor. Background Art

[0002] In terms of motor control, many researchers and institutions have done a lot of research work to continuously optimize the control performance of permanent magnet synchronous motors in order to further improve the control effect of permanent magnet synchronous motors. The main control methods of permanent magnet synchronous motors are direct torque control and vector control. 【1】 Among them, direct torque control has a simple structure, but there will be torque pulsation problems when running at low speed. Vector control, on the other hand, separates the current and torque detected by the system and processes and controls them separately. In order to improve the control effect of vector control, domestic and foreign scholars have designed many improved control strategies based on the principle of vector control. Zeng Guohong et al. 【2】 A modular peer-to-peer control strategy is designed for dual-winding PMSM, with each three-phase winding as a unit, and a dual redundant structure of the controller and motor winding is constructed. 【3】 A permanent magnet synchronous motor self-disturbance weakening control method for more electric aircraft was designed, which achieved faster dynamic response speed and control effect. Li et al. 【4】 An adaptive internal model control method with two different adaptive rules was designed, and the disturbance observer was used to observe the disturbance information of PMSM for compensation. Sarsembayev B et al. 【5】 A discrete-time cascade PI control strategy with anti-saturation tracking is designed, and the experimental results demonstrate the feasibility of the proposed control scheme. Gao et al. 【6】 A direct compensation method is designed for the current change during the calculation delay time in PMSM model predictive control, which is better than the traditional delay compensation method. Liu et al. 【7】 A terminal sliding mode control method is designed for PMSM. By adopting a speed-current single-loop control structure instead of the traditional cascade control, it ensures that the actual speed can quickly respond to and track the command signal and can better suppress disturbances.

[0003] The permanent magnet synchronous propulsion motor of the aviation hybrid electric propulsion system is the main source of flight thrust and is the key to the entire electric propulsion system. Due to the extremely harsh high-altitude environment in which the propulsion motor works, the vibration during flight and the extremely low temperature environment at high altitude may cause the speed sensor to fail during use. In order to avoid the threat of sensor failure to flight safety, corresponding active fault-tolerant control measures need to be taken.

[0004] The goal of sliding mode control is to make the state trajectory reach the sliding mode switching surface set by itself and gradually converge to the system origin. However, the stability condition cannot reflect how the system reaches the sliding mode surface. Some scholars have proposed the use of the reaching law method, which can speed up the system response speed and improve the dynamic quality of the approaching motion.

[0005] Various optimization techniques inspired by animal behavior in nature have emerged in the past few decades and have been widely used in various fields. They have been proven to be effective in optimizing complex parameters and multi-dimensional optimization problems. At present, an important direction for improving optimization algorithms is the combination of different algorithms.

[0006] References

[0007] 【1】Luo Wen. Research on sensorless control strategy of permanent magnet synchronous motor based on three-sliding mode structure[D]. Lanzhou Jiaotong University, 2021.

[0008] 【2】Zeng Guohong, Dong Yukun, Wu Xuezhi, et al. Modular peer-to-peer control of dual-winding permanent magnet synchronous motor[J]. Acta Aeronautica Sinica, 2022, 1(1): 1-13.

[0009] 【3】Wang Yicheng. Research on active disturbance rejection control of high power density permanent magnet synchronous motor for more electric aircraft[D]. Southeast University, 2021.

[0010] 【4】Li S, Gu H.Fuzzy adaptive internal model control schemes for pmsmspeed-regulation system[J].IEEE Transactions on Industrial Informatics, 2012,8(4):767-779.

[0011] 【5】Sarsembayev B, Suleimenov K, Do T. High order disturbance observerbased PI-PI control system with tracking anti-windup technique for improvement of transient performance of PMSM[J]. IEEE Access, 2021,9:66323-66334.

[0012] 【6】Gao J, Gong C, Li W, et al. Novel compensation strategy for calculation delay of finite control set model predictive current control in PMSM [J]. IEEE Transactions on Industrial Electronics, 2020, 67(7): 5816-5819.

[0013] 【7】Liu X, Yu H, Yu J, et al.Combined speed and current terminal slidingmode control with nonlinear disturbance observer for PMSM drive[J]. IEEEAccess, 2018, 6: 29594-29601.

[0014] 【8】Li Peng. Research and application of traditional and high-order sliding mode control[D]. National University of Defense Technology, 2011.

[0015] 【9】Li

[0016]

[10] Kennedy J, Eberhart R.Particle swarm optimization[C].ICCN'95-international conference on neural networks,1995.

[0017]

[11] Mirjalili S, Mirjalili SM, Lewis A. Gray wolf optimizer[J]. Advances in Engineering Software, 2014: 46-61. Summary of the invention

[0018] The purpose of the present invention is to provide a design method for a motor sliding mode speed controller for an aviation hybrid propulsion system, an extended sliding mode disturbance observer is used to estimate and compensate for disturbances, and an improved adaptive chaotic grey wolf optimization algorithm is used to optimize the controller and observer parameters.

[0019] To achieve the above object, the present invention adopts the following technical solution:

[0020] A design method for a motor sliding mode speed controller for an aviation hybrid propulsion system includes the following steps:

[0021] Step 1: Model the permanent magnet synchronous propulsion motor and propeller, and list the voltage, flux, torque equations of the permanent magnet synchronous motor in the natural coordinate system, stationary coordinate system, and rotating coordinate system, as well as the thrust T, torque M, and power PW of the propeller. prop , efficiency η, forward ratio formula;

[0022] Step 2: The goal of sliding mode control is to make the state trajectory reach the sliding mode switching surface set by itself and gradually converge to the system origin. In order to improve the convergence speed of the sliding mode variable s, a variable exponential power reaching law is designed;

[0023] Step 3, design a sliding mode speed controller based on disturbance compensation;

[0024] Step 4, design an adaptive chaotic grey wolf optimization algorithm;

[0025] Step 5: Build a simulation model of the permanent magnet synchronous propulsion motor system based on the MATLAB / Simulink simulation platform.

[0026] The step 1 comprises:

[0027] Step 1-1, first establish the mathematical model of the permanent magnet synchronous propulsion motor:

[0028] Assume that the ideal permanent magnet synchronous motor model conditions are as follows:

[0029] (1) The effects of skin effect, eddy current, hysteresis loss and magnetic saturation of the motor core are not considered;

[0030] (2) The three-phase windings in the stator are symmetrically distributed, and the influence of harmonics of various orders in the three-phase winding current is ignored;

[0031] (3) The flux generated by the permanent magnets of the rotor is constant and three-phase symmetrical;

[0032] Then the magnitude of the induced magnetic flux generated on the stator three-phase winding is:

[0033]

[0034] Among them, ψ fis the permanent magnet flux; ψ fA , fB , fC are the magnitudes of the induced flux generated on the stator A, B, and C phase windings, respectively; θ is the angle between the A phase stator winding and the permanent magnet flux, also called the rotor position angle;

[0035] According to Kirchhoff's voltage theorem, the voltage equation of the permanent magnet synchronous propulsion motor is:

[0036]

[0037] Among them, u x (x=a,b,c) is the stator three-phase winding voltage; i x (x=a,b,c) is the stator three-phase winding current; R s is the phase resistance of the stator three-phase winding; ψ x (x=a,b,c) is the flux linkage of the stator three-phase winding;

[0038] The flux of the three-phase winding consists of two parts, one is the induced flux generated by the permanent magnet flux in the winding, and the other is the armature flux generated by the armature current. The expression is as follows:

[0039]

[0040] Among them, L AA , L BB , L CC are the self-inductance of the three-phase stator windings; L AB , L BA , L AC , L CA , L BC , L CB are the mutual inductance of the three-phase stator windings;

[0041] The electromagnetic torque equation is:

[0042] T e =-n p ψ f [i a sinθ+i b sin(θ-2π / 3)+i c sin(θ+2π / 3) (4)

[0043] Among them, T e is the electromagnetic torque; n p is the number of magnetic pole pairs;

[0044] The equation of motion is:

[0045]

[0046] Among them, ω m is the mechanical angular velocity; J is the moment of inertia; B is the damping coefficient; T L is the load torque;

[0047] According to Clark transformation, the voltage equation, flux equation and torque equation of the permanent magnet synchronous propulsion motor in the two-phase stationary coordinate system are obtained as follows:

[0048]

[0049]

[0050] T e =n p ψ f (i β cosθ-i α sinθ) (8)

[0051] Among them, u α 、u β 、i α 、i β are the stator voltage and current components on the α and β axes respectively; ψ α , β is the component of the stator flux on the α and β axes; L α , L β is the inductance in the α and β coordinate systems; p is the differential operator; for the surface-mounted permanent magnet synchronous motor, L α =L β =L s ;ω is the rotor rotation angular velocity; Ls is the stator inductance;

[0052] According to equations (6)-(8) and combined with Park coordinate transformation, the voltage, flux linkage and torque equations of the permanent magnet synchronous propulsion motor in the synchronous rotating coordinate system are obtained as follows:

[0053]

[0054]

[0055]

[0056] Among them, u d 、u q 、i d 、i q are the stator voltage and current components on the d and q axes respectively; ψ d , q is the component of the stator flux on the d and q axes; L d , L q is the inductance of d and q axes;

[0057] Step 1-2: Propeller Modeling:

[0058] The dynamic characteristics of the propeller include thrust, thrust coefficient, torque, torque coefficient, power, power coefficient, and efficiency;

[0059] According to the aerodynamic characteristics and structural features of the propeller, the propeller thrust T is expressed as:

[0060] T=C t ρn s 2 D 4 (12)

[0061] Among them, C t is the tension coefficient; ρ is the atmospheric density; n s is the propeller speed, which is the motor speed when it is directly connected to the propulsion motor; D is the propeller diameter;

[0062] The propeller torque is the torque of the resistance that the propeller needs to overcome when rotating. The propeller torque M is expressed as:

[0063] M=C M ρn s 2 D 5 (13)

[0064] Among them, C M is the torque coefficient;

[0065] The propeller power is the power obtained by the propeller from the propulsion motor. The propeller power PW prop It is expressed as:

[0066] PW prop =C p ρn s 3 D 5 (14)

[0067] Among them, C p is the power coefficient;

[0068] The propeller propulsion efficiency η is expressed as:

[0069]

[0070] Among them, V 0 is the airspeed.

[0071] The propeller advance ratio λ can be expressed as:

[0072]

[0073] As can be seen from the previous formula, for a fixed-pitch propeller, after the structural parameters and flight conditions are determined, the propeller torque, power are related to the torque coefficient and power coefficient, and the torque coefficient, power coefficient and propulsion efficiency are all related to the propeller advance ratio.

[0074] In step 2, in order to improve the convergence speed of the sliding mode variable s, a variable exponential power reaching law is designed:

[0075]

[0076] where x is the state variable, which satisfies ε>0, k>0, 0 < b < 1, and the expression of α(s) is:

[0077]

[0078] where p 1 、q 1 、p 2 and q 2 are positive numbers, and p 1 > q 1 > 0, p 2 > q 2 > 0;

[0079] The sliding mode convergence process based on VEPRL is discussed in two cases of |s|≤1 and |s|>1. When |s|≤1, the traditional exponential reaching law slows down significantly due to the decrease of s, and in formula (17), sgn(|s|-1) = - 1 , then the variable exponential term becomes k|s| -b s, obviously k|s| -b s > k|s| b s. At this time, the sliding mode variable s converges directly to zero at . When the system is far from the sliding mode surface, that is, s > 1, then sign(|s|-1) = 1, α(s) > 1, and the system relies on and k|s| b s to jointly approach |s| = 1, and then converge to zero at ; by adding the power term α(s), when the system is far from the sliding mode surface, it can maintain a relatively fast speed to approach the sliding mode surface. When the system is close to the sliding mode surface, a smaller α(s) is ensured to reduce chattering, and thus the overall relatively fast approaching speed to s = 0 and the reduction of chattering can be guaranteed;

[0080] When the system approaches the sliding mode surface, the variable exponential power reaching law proposed based on formula (17) is simplified to Its discrete expression is:

[0081]

[0082] Where T is the sampling period;

[0083] When satisfied and When s(n)=0 at time n + ,but:

[0084]

[0085] Similarly, suppose that at time n, s(n) = 0 - ,but:

[0086]

[0087] Based on equations (20) and (21), the discrete sliding mode bandwidth is:

[0088]

[0089] The step 3 comprises:

[0090] Step 3-1, sliding mode speed controller design

[0091] In order to facilitate the design of the controller, the formula (9) is transformed into:

[0092]

[0093] Since the surface mounted permanent magnet synchronous propulsion motor has L d =L q , and adopt i d = 0, the torque equation (11) is simplified to:

[0094]

[0095] The mechanical motion equation is:

[0096]

[0097] make Considering the influence of interference and uncertainty factors in the permanent magnet synchronous motor model, the mechanical motion equation is expressed as:

[0098]

[0099] Now take g = △ai q -△bω m -△mT L , represent the internal parameter disturbance and external disturbance of the system respectively, then equation (26) can be expressed as:

[0100]

[0101] Among them, x 1 =ω m , The q-axis reference current of the current inner loop will be used to estimate the parameter disturbance using the adaptive law, and an extended sliding mode disturbance observer will be designed to estimate and compensate for the external disturbance.

[0102] The speed tracking error is defined as:

[0103]

[0104] in, Indicates a given reference speed;

[0105] The derivative of formula (28) is:

[0106]

[0107] In the speed control, the integral sliding surface is selected as follows:

[0108]

[0109] Where c is the integral coefficient, satisfying c>0;

[0110] The derivative of the sliding surface is:

[0111]

[0112] Combining the designed variable exponential power reaching law with equation (31) and performing corresponding transformations, the q-axis output reference current signal of the speed loop can be obtained:

[0113]

[0114] Where x = e; d is the estimate based on the extended sliding mode disturbance observer for feedforward compensation; the estimate of parameter uncertainty The derivative expression of is as follows:

[0115]

[0116] Step 3-2, design of extended sliding mode disturbance observer

[0117] In order to improve the control performance of permanent magnet synchronous motor in the presence of external disturbances, an extended sliding mode disturbance observer is designed to estimate the disturbance online, and then the estimated value is used for feedforward compensation.

[0118] The expansion of formula (25) is expressed as:

[0119]

[0120] Taking the motor speed and external disturbance as observations, the extended sliding mode disturbance observer (ESMDO) is designed as:

[0121]

[0122] Among them, y(ω e ) is the sliding mode control law; g is the sliding mode gain; is the estimated value of the motor speed; is the estimated value of the external disturbance;

[0123] Subtracting formula (36) from (37), we can get the observation error of ESMDO:

[0124]

[0125]

[0126] in, is the speed estimation error; is the disturbance estimation error;

[0127] Then design the sliding surface for ESMDO and select the integral sliding surface:

[0128] s ω =e ω +c 1 ∫e ω dt (40)

[0129] Among them, c 1 is the integral term coefficient; the derivative of the sliding surface is:

[0130]

[0131] At the same time, select the isokinetic reaching law:

[0132]

[0133] Among them, k 2 >0 is the switch gain coefficient;

[0134] E d / J is used as the disturbance term, and combined with equations (38), (41) and (42), the disturbance estimation of ESMDO is expressed as:

[0135]

[0136] The step 4 comprises:

[0137] The initial position of the gray wolf is generated by using Logistic chaotic mapping, so that the initial population is evenly distributed to improve the convergence speed at the initial moment. In the search process, chaotic randomness and ergodicity can be used to avoid falling into the local optimal solution.

[0138] The mapping equation of Logistic mapping is:

[0139] u k+1 =au k (1-u k ) (59)

[0140] Among them, a=4, at this time the output is widely distributed in the range of [0,1],

[0141] An adaptive convergence factor is designed to maintain a balance between global and local exploration capabilities. Its expression is as follows:

[0142]

[0143] Among them, a min and a max They represent the minimum and maximum values ​​of the convergence factor, respectively. i represents the current number of iterations, N is the total number of iterations, and n is the decreasing index. <n≤1;

[0144] The position of the leader wolf and the wolf pack is updated by combining the velocity vector of the particle swarm. The update formula after fusing the position and velocity is as follows:

[0145]

[0146] X ω (k+1)=X ω (k)+v ω (k+1) (62)

[0147] Among them, c 1 and c 2 is the acceleration constant, also known as the learning factor; X 1 , X 2 and X 3 They represent the distances that wolf ω has advanced to wolf α, wolf β, and wolf δ respectively;

[0148] Select the absolute error integral indicator as the objective function:

[0149]

[0150] Where, e(t) is the motor speed tracking error.

[0151] Beneficial effect: The present invention first builds the mathematical model of the permanent magnet synchronous motor and the propeller, and then designs a propulsion motor speed controller based on the variable exponential power reaching law (VEPRL), and uses the improved adaptive chaotic grey wolf optimization (ACGWO) algorithm to optimize the controller parameters. The designed permanent magnet synchronous propulsion motor sliding mode controller uses the improved variable exponential power reaching law to make the system have different approaching speeds at different stages. When it is far away from the sliding surface, it can approach the sliding mode at a higher speed. When the system approaches the sliding mode, a larger exponential coefficient is guaranteed to reduce the jitter and ensure the speed of approaching the sliding surface. The present invention designs a permanent magnet synchronous propulsion motor sliding mode controller, and uses the improved variable exponential power reaching law to make the system have different approaching speeds at different stages. When it is far away from the sliding surface, it can approach the sliding mode at a higher speed. When the system approaches the sliding mode, a larger exponential coefficient is guaranteed to reduce the jitter and ensure the speed of approaching the sliding surface. Then the controller parameters are optimized based on the improved adaptive chaotic grey wolf optimization algorithm. The simulation results verify the effectiveness of the fault-tolerant control strategy designed by the present invention, and provide a strong basis for the application of related theories in electric propulsion systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0152] Figure 1 It is a schematic diagram of the structure of a permanent magnet synchronous motor;

[0153] Figure 2 is the working characteristic curve of fixed pitch propeller;

[0154] Figure 3 is the sliding mode motion trajectory based on the variable exponential power reaching law when s approaches 0;

[0155] Figure 4 Optimize the algorithm flow chart for the gray wolf;

[0156] Figure 5 This is the flow chart of particle swarm optimization algorithm;

[0157] Figure 6 It is a comparison chart of convergence factors;

[0158] Figure 7 Flowchart of adaptive chaotic grey wolf optimization algorithm;

[0159] Figure 8 Comparison of the convergence effect of function curves;

[0160] Fig. 9 This is the control strategy block diagram of permanent magnet synchronous motor;

[0161] Fig.10 It is the control effect of VEPRL-SMC;

[0162] Fig.11 Comparison of three control strategies against load disturbances;

[0163] Fig.12 is the dq current based on PI control strategy;

[0164] Fig.13 is the dq current based on the ERL-SMC control strategy;

[0165] Fig.14 is the dq current based on the VEPRL-SMC control strategy. DETAILED DESCRIPTION

[0166] The present invention will be further explained below in conjunction with the accompanying drawings.

[0167] A design method of a motor sliding mode speed controller for an aviation hybrid propulsion system of the present invention comprises the following steps:

[0168] Step 1: Model the permanent magnet synchronous propulsion motor and propeller, and list the voltage, flux, torque equations of the permanent magnet synchronous motor in the natural coordinate system, stationary coordinate system, and rotating coordinate system, as well as the thrust T, torque M, and power PW of the propeller. prop , efficiency η, forward ratio formula;

[0169] Step 1-1: First, establish the mathematical model of PMSM: Since the actual PMSM model is complex and contains many nonlinear factors, the conditions are simplified and the ideal permanent magnet synchronous motor model conditions are assumed to be as follows:

[0170] (1) The effects of skin effect, eddy current, hysteresis loss and magnetic saturation of the motor core are not considered;

[0171] (2) The three-phase windings in the stator are symmetrically distributed, and the influence of harmonics of various orders in the three-phase winding current is ignored;

[0172] (3) The magnetic flux generated by the permanent magnet of the rotor is constant and three-phase symmetrical.

[0173] Then the magnitude of the induced flux generated on the stator three-phase winding is:

[0174]

[0175] Among them, ψ f is the permanent magnet flux; θ is the angle between the A-phase stator winding and the permanent magnet flux, also called the rotor position angle.

[0176] The schematic diagram of the permanent magnet synchronous motor structure combined with the three coordinate systems is shown in Figure 1As shown, the relevant parameters are as follows:

[0177] A, B, C——coordinate axes in the stator three-phase coordinate system;

[0178] α, β——coordinate axes of the stator two-phase stationary coordinate system;

[0179] d, q——coordinate axes in the synchronously rotating coordinate system;

[0180] θ——rotor position angle;

[0181] ω——rotor rotation angular velocity.

[0182] First, according to Kirchhoff's voltage theorem, the voltage equation of PMSM is:

[0183]

[0184] Among them, u x (x=a,b,c) is the stator three-phase winding voltage; i x (x=a,b,c) is the stator three-phase winding current; R s is the phase resistance of the stator three-phase winding; ψ x (x=a,b,c) is the magnetic flux of the stator three-phase winding.

[0185] The flux of the three-phase winding consists of two parts, one is the induced flux generated by the permanent magnet flux in the winding, and the other is the armature flux generated by the armature current. The expression is as follows:

[0186]

[0187] Among them, L AA , L BB , L CC is the self-inductance of the stator three-phase winding; L AB , L BA , L AC , L CA , L BC , L CB is the mutual inductance of the three-phase stator winding.

[0188] The electromagnetic torque equation is:

[0189] T e =-n p ψ f [i a sinθ+i b sin(θ-2π / 3)+i c sin(θ+2π / 3) (4)

[0190] Among them, T eis the electromagnetic torque; n p is the number of magnetic pole pairs.

[0191] The equation of motion is:

[0192]

[0193] Among them, ω m is the mechanical angular velocity; J is the moment of inertia; B is the damping coefficient; T L is the load torque.

[0194] According to Clark transformation, the voltage equation, flux equation and torque equation of PMSM in the two-phase stationary coordinate system can be obtained as follows:

[0195]

[0196]

[0197] T e =n p ψ f (i β cosθ-i α sinθ) (8)

[0198] Among them, u α 、u β 、i α 、i β are the stator voltage and current components on the α and β axes respectively; ψ α , β is the component of the stator flux on the α and β axes; L α , L β is the inductance in the α and β coordinate systems; p is the differential operator; for the surface-mounted permanent magnet synchronous motor, L α =L β =L s ; Ls is the stator inductance;

[0199] According to equations (6)-(8) and combined with Park coordinate transformation, the voltage, flux and torque equations of PMSM in the synchronous rotating coordinate system can be obtained as follows:

[0200]

[0201]

[0202]

[0203] Among them, u d 、u q 、i d 、i qare the stator voltage and current components on the d and q axes respectively; ψ d , q is the component of the stator flux on the d and q axes; L d , L q is the inductance of the d and q axes.

[0204] Step 1-2: Propeller modeling. The propeller is an important part of the hybrid electric propulsion system, used to generate thrust during flight. For hybrid UAVs or small general aviation aircraft, it is usually composed of two or three blades. It has a large inertia, which will affect the control effect of the propulsion motor and its control system during flight. Therefore, it is necessary to establish a mathematical model for the propeller to calculate the performance parameters of the propeller under different speed conditions, which will be used as the load of the propulsion motor to verify the subsequent control performance of the propulsion system.

[0205] There are many methods for mathematical modeling of propellers, which can be based on experimental data modeling, theoretical formula modeling, and three-dimensional flow field numerical simulation modeling. The present invention only regards the propeller as a motor load, makes reasonable simplifications, and uses fixed-pitch blades. Therefore, a method based on a mechanism formula is selected for modeling to more conveniently and quickly calculate the propeller-related parameters. The more important dynamic characteristics of the propeller include thrust, thrust coefficient, torque, torque coefficient, power, power coefficient, and efficiency.

[0206] According to the aerodynamic characteristics and structural characteristics of the propeller, the propeller thrust T can be expressed as:

[0207] T=C t ρn s 2 D 4 (12)

[0208] Among them, C t is the tension coefficient; ρ is the atmospheric density; n s is the propeller speed, which is the motor speed when directly connected to the propulsion motor; D is the propeller diameter.

[0209] The propeller torque is the torque of the resistance that the propeller needs to overcome when rotating. The propeller torque M can be expressed as:

[0210] M=C M ρn s 2 D 5 (13)

[0211] Among them, C M is the torque coefficient.

[0212] The propeller power is the power obtained by the propeller from the propulsion motor. The propeller power PWprop It can be expressed as:

[0213] PW prop = C p ρn s 3 D 5 (14)

[0214] Wherein, C p is the power coefficient.

[0215] The propeller propulsion efficiency η can be expressed as:

[0216]

[0217] Wherein, V 0 is the airspeed.

[0218] The propeller advance ratio λ can be expressed as:

[0219]

[0220] As can be seen from the previous formula, for a fixed-pitch propeller, after the structural parameters and flight conditions are determined, the propeller torque, power are related to the torque coefficient and power coefficient. And the torque coefficient, power coefficient and propulsion efficiency are all related to the propeller advance ratio, and their relationship is as shown in Figure 2 the propeller operating characteristic curve.

[0221] Step 2, the goal of sliding mode control is to make the state trajectory reach the self-set sliding mode switching surface and asymptotically converge to the system origin. To improve the convergence speed of the sliding mode variable s, a variable exponential power reaching law is designed;

[0222] The goal of sliding mode control is to make the state trajectory reach the self-set sliding mode switching surface and asymptotically converge to the system origin. However, the stability condition cannot reflect how the system reaches the sliding mode surface. Some scholars propose to use the reaching law method, which can accelerate the system response speed and improve the dynamic quality of the reaching motion at the same time.

[0223] To improve the convergence speed of the sliding mode variable s, a variable exponential power reaching law is designed:

[0224]

[0225] Wherein, x is the state variable, which satisfies ε > 0, k > 0, 0 < b < 1, and the expression of α(s) is:

[0226]

[0227] Wherein, p 1 、q 1 、p2 and q 2 is a positive number, and p 1 >q 1 >0,p 2 >q 2 >0.

[0228] The sliding mode convergence process based on VEPRL can be discussed in two cases: |s|≤1 and |s|>1. When |s|≤1, the traditional exponential convergence rate slows down significantly due to the decrease of s, while in formula (17), sgn(s-1)=- 1 , then the variable exponential term becomes k|s| -b s, obviously k|s| -b s>k|s| b s, at this time the sliding mode variable s is Directly converges to zero. When the system is far away from the sliding surface, that is, |s|>1, then sign(|s|-1)=1, α(s)>1, the system relies on and k|s| b s work together to approach |s| = 1, and then Converges to zero. By adding the power term α(s), the system can maintain a relatively fast speed approaching the sliding surface when it is far away from the sliding surface. When the system approaches the sliding surface, a smaller α(s) is ensured to reduce chattering, thereby ensuring a faster overall speed approaching s=0 and reducing chattering.

[0229] When the system approaches the sliding surface, the variable exponential power reaching law proposed based on equation (17) can be simplified to Its discrete expression is:

[0230]

[0231] Where T is the sampling period;

[0232] When satisfied and When s(n)=0 at time n + ,but:

[0233]

[0234] Similarly, suppose that at time n, s(n) = 0 - ,but:

[0235]

[0236] Based on equations (20) and (21), the discrete sliding mode bandwidth is:

[0237]

[0238] The motion trajectory designed based on VEPRL is as follows Figure 3 shown.

[0239] from Figure 3 It can be seen from the figure that the sliding mode motion trajectory stably approaches the equilibrium point in the fan-shaped area under the action of the reaching law. This advantage is conducive to eliminating the speed tracking error and chattering for the speed controller designed for the present invention.

[0240] Step 3, design a sliding mode speed controller based on disturbance compensation;

[0241] Step 3-1: Sliding mode speed controller design

[0242] In order to facilitate the design of the controller, the formula (9) is transformed into:

[0243]

[0244] The present invention uses a surface-mount PMSM, which has L d =L q , and adopt i d = 0, the torque equation (11) can be simplified to:

[0245]

[0246] The mechanical motion equation is:

[0247]

[0248] make Considering the influence of interference and uncertainty factors in the permanent magnet synchronous motor model, the motion equation can be expressed as:

[0249]

[0250] Now take g = △ai q -△bω m -△mT L , represent the internal parameter disturbance and external disturbance of the system respectively, then equation (26) can be expressed as:

[0251]

[0252] Among them, x 1 =ω m , It is the q-axis reference current of the current inner loop. The adaptive law will be used to estimate the parameter disturbance later, and the extended sliding mode disturbance observer will be designed to estimate and compensate the external disturbance.

[0253] The speed tracking error is defined as:

[0254]

[0255] in, Indicates the given reference speed.

[0256] The derivative of formula (28) is:

[0257]

[0258] In the speed control, the integral sliding surface is selected as follows:

[0259]

[0260] Wherein, c is the integral coefficient, satisfying c>0.

[0261] The derivative of the sliding surface is:

[0262]

[0263] Combining the designed variable exponential power reaching law with equation (31) and performing corresponding transformations, the q-axis output reference current signal of the speed loop can be obtained:

[0264]

[0265] Where x = e; d is the estimate based on the extended sliding mode disturbance observer for feedforward compensation; the estimate of parameter uncertainty The derivative expression of is as follows:

[0266]

[0267] The stability of the designed sliding mode control law is analyzed below.

[0268] First, define the estimation error of parameter uncertainty as Then there is

[0269] Select the Lyapunov function as:

[0270]

[0271] Combining formulas (17), (31) and (33), the derivative of the Lyapunov function yields:

[0272]

[0273] Because ε>0, k>0, sgn(s) has the opposite sign to s, then -εs|x| α(s) sgn(s)-ks 2 |s| b·sgn(|s|-1)<0, The stability of the system is proven.

[0274] Step 3-2: Design of extended sliding mode disturbance observer

[0275] In order to improve the control performance of permanent magnet synchronous motor in the presence of external disturbances, an extended sliding mode disturbance observer is designed to estimate the disturbance online, and then the estimated value is used for feedforward compensation.

[0276] The expansion of formula (25) can be expressed as:

[0277]

[0278] Taking the motor speed and external disturbance as observations, the extended sliding mode disturbance observer (ESMDO) is designed as:

[0279]

[0280] Among them, y(ω e ) is the sliding mode control law; g is the sliding mode gain; is the estimated value of the motor speed; is the estimated value of the external disturbance.

[0281] Subtracting formula (36) from (37), we can get the observation error of ESMDO:

[0282]

[0283]

[0284] in, is the speed estimation error; is the disturbance estimation error.

[0285] Then design the sliding surface for ESMDO and select the integral sliding surface:

[0286] s ω =e ω +c 1 ∫e ω dt (40)

[0287] Among them, c 1 is the integral term coefficient. The derivative of the sliding surface is:

[0288]

[0289] At the same time, select the isokinetic reaching law:

[0290]

[0291] Among them, k 2>0 is the switching gain coefficient.

[0292] E d / J is used as the disturbance term, and combined with equations (38), (41) and (42), the interference estimation of ESMDO can be expressed as:

[0293]

[0294] The stability of ESMDO is analyzed below.

[0295] Select the Lyapunov function as:

[0296]

[0297] The derivative of the Lyapunov function is:

[0298]

[0299] It can be seen that when k 2 >0, the designed ESMDO meets the stability condition.

[0300] From formula (32), it can be seen that when there is a disturbance in the system, the disturbance observed based on ESMDO is fed forward to the q-axis reference current, and a smaller sliding mode switch gain can be used to ensure the q-axis reference current required for load changes. Therefore, the external disturbance compensation based on ESMDO can effectively reduce the impact of the disturbance on the propulsion motor on the system. At the same time, because the sliding mode control switching amplitude is reduced, the impact of jitter is further weakened, which is conducive to improving the dynamic performance of the propulsion motor speed control.

[0301] Step 4, design an adaptive chaotic grey wolf optimization algorithm;

[0302] Various optimization techniques inspired by animal behavior in nature have emerged in the past few decades and have been widely used in various fields. They have been proven to be effective in optimizing complex parameters and multi-dimensional optimization problems. At present, an important direction for improving optimization algorithms is the combination of different algorithms. An adaptive chaotic grey wolf optimization algorithm is designed. First, the chaotic algorithm is applied to the grey wolf optimization (GWO) algorithm. During the initialization process, the diversity of the initial population can be maintained through chaotic randomness and ergodicity to improve the subsequent convergence speed; at the same time, the particle swarm optimization (PSO) algorithm has the advantages of fast convergence speed and strong local search ability of the grey wolf optimization algorithm. The grey wolf optimization algorithm is used as a search tool, and its search mechanism is used to start the search process. Then, the particle swarm algorithm is used to improve the position of the alpha grey wolf to achieve a balance between local and global search.

[0303] Step 4-1: Grey Wolf Optimization Algorithm

[0304] As a swarm intelligence optimization algorithm, the gray wolf optimization algorithm is inspired by the process of gray wolves hunting prey. Due to its simple structure and easy implementation, it has been successfully used to deal with a variety of optimization problems. In reality, gray wolves usually consist of 5-12 individuals, and they like to go out in groups and hunt together. Inspired by the social structure and group activities of gray wolves, the gray wolf optimization algorithm divides the gray wolves in the wolf pack into four categories, represented as α, β, δ and ω. Among them, α wolf is the first-level wolf, also known as the dominant wolf, which commands the entire wolf pack and is responsible for leading the entire wolf pack in hunting activities. It also represents the current optimal solution position from the prey; the second-level wolf in the gray wolf social hierarchy is called β wolf, which is most likely to replace α wolf. They help α wolf make decisions and guide the lower wolf pack; δ wolf is at the third level, and the rest are ω wolf.

[0305] The hunting process of gray wolves can be divided into two stages: surrounding prey and attacking prey. In order to facilitate the mathematical modeling of the gray wolf optimization algorithm, the social hierarchy, tracking and hunting process of gray wolves are introduced below. The flowchart of the gray wolf optimization algorithm is as follows: Figure 4 shown.

[0306] (1) Social class

[0307] To facilitate mathematical modeling, it is stipulated that α wolf represents the current optimal solution position, the second and third optimal solutions are β wolf and δ wolf respectively, and the remaining solutions are ω wolf, which will follow these three types of wolves to evolve.

[0308] (2) Surrounding the prey

[0309] The first stage of hunting for gray wolves is to track and surround their prey. The following equation can be used to express the gray wolf's encirclement:

[0310] X(t+1)=X p (t)-A·D (46)

[0311] D=|C·X p (t)-X(t)| (47)

[0312] Among them, t represents the current iteration number; X p and X represent the current positions of the prey and the gray wolf respectively; D is the distance between the gray wolf and the prey; A and C are vector coefficients, and their specific expressions are:

[0313] A=2a·r 1 -a (48)

[0314] C=2r 2 (49)

[0315] Among them, a is the convergence factor, which is a linearly decreasing parameter from 2 to 0; r 1 and r 2 are all random numbers between [0,1].

[0316] (3) Attacking prey

[0317] The gray wolf hunting process is led by wolf α, and other wolves update their positions according to the optimal solution searched by wolf α, wolf β, and wolf δ. This process can be expressed as follows:

[0318]

[0319]

[0320] Among them, X α , X β and X δ Respectively represent the current positions of α wolf, β wolf and δ wolf; A 1 , A 2 , A 3 and C 1 , C 2 , C 3 is the vector coefficient; D α , D β , D δ Respectively represent the distances of ω wolf from α wolf, β wolf and δ wolf; X 1 , X 2 and X 3 They represent the distances that ω wolf has advanced toward α wolf, β wolf, and δ wolf respectively.

[0321] The formula for updating the position of ω wolf by using α, β and δ wolf is as follows:

[0322]

[0323] Step 4-2: Particle Swarm Optimization Algorithm

[0324] Particle swarm optimization is another popular optimization algorithm, which is inspired by the social behavior of bird flocks. PSO is derived from simulating the foraging behavior of birds and was proposed by scholars such as Eberhart and Kennedy in 1995. PSO is initially a group of particles with random positions. It continuously searches for the optimal solution of the group through iteration according to the optimization rules. In the evolution process of each generation, the particles update themselves according to the global optimal solution and the individual optimal solution.

[0325] Assume that in a D-dimensional search space, there are N p A particle swarm consists of particles, where the position of the i-th particle can be recorded as:

[0326] x i=(x i1 ,x i2 ,…,x iD ),i=1,2,...,N p (53)

[0327] The velocity of the i-th particle can be written as:

[0328] v i =(v i1 ,v i2 ,…,v iD ),i=1,2,...,N p (54)

[0329] The optimal value found by the i-th particle can be recorded as:

[0330]

[0331] Let the global optimal value of PSO be:

[0332] g best =(g 1 ,g 2 ,…,g D ) (56)

[0333] When you get g best and After that, all particles update themselves according to formulas (57) and (58) combined with the optimal solution:

[0334] v id (k+1)=ω 1 ·v id (k)+c 1 ·rand·[p id (k)-x id (k)]+c 2 ·rand·[g d (k)-x id (k)] (57)

[0335] x id (k+1)=x id (k)+v id (k+1) (58)

[0336] Among them, ω 1 is the inertia weight coefficient, when ω 1 When it is smaller, the particle swarm has stronger local search ability, and when it is larger, the global search ability is stronger; d=1,2,...,D,i=1,2,...,n p ; k represents the current number of iterations; c 1 and c 2is the acceleration constant, also known as the learning factor; rand is a random number with a value range of [0,1].

[0337] Reasonable selection of particle swarm optimization algorithm parameters can maximize the advantages of particle swarm optimization. The main parameters of particle swarm optimization include inertia weight coefficient ω 1 , which is mainly used to control the algorithm's search and development capabilities, directly affecting the algorithm's sensitivity to the global optimal solution, and usually ranges from [0.8, 1.2]; the number of particle swarm individuals N p , relatively speaking, N p The larger the value, the higher the accuracy of the iterative calculation, but at the same time the iteration time will also be longer. Usually, N p Set between 20-50; learning factor c 1 and c 2 , which is used to control the intensity of particle learning from the optimal individual and the previous iteration, and can ensure the reasonable distribution of global and local search intensities. It is usually taken as 2; the particle speed range v∈[v min ,v max ], which is similar to the inertia weight coefficient. It is usually fixed after being set, and its effect is achieved by adjusting the inertia weight coefficient. Figure 5 shown.

[0338] Step 4-3: Adaptive Chaos Grey Wolf Optimization Algorithm

[0339] Since the GWO algorithm randomly generates the initial population, it may lead to a lack of diversity in the initial population. In order to maintain the diversity of particles, the present invention uses Logistic chaotic mapping to generate the initial position of the gray wolf, so that the initial population is evenly distributed to improve the convergence speed at the initial moment. In the search process, the chaotic randomness and ergodicity can be used to avoid falling into the local optimal solution.

[0340] The mapping equation of Logistic mapping is:

[0341] u k+1 =au k (1-u k ) (59)

[0342] Among them, a=4, at this time the output is widely distributed in the range of [0,1],

[0343] From formula (48), we can see that the size of A is affected by the convergence factor a. From the literature, when |A|>1, GWO will perform a global search; when |A|≤1, it will perform a local search. The traditional linear convergence factor cannot fully reflect the optimization process in practice. The present invention designs an adaptive convergence factor to maintain a balance between global and local exploration capabilities. Its expression is as follows:

[0344]

[0345] Among them, a min and a max Respectively represent the minimum and maximum values ​​of the convergence factor. In the present invention, a min =0,a max =2, i represents the current iteration number, N is the total iteration number, n is the decreasing index, 0 <n≤1。

[0346] When the number of iterations is 200 and n=1, the comparison chart is as follows: Figure 6 As shown in the figure, the improved adaptive convergence factor a changes in a quasi-sine law. In the early stage of iteration, the convergence factor is large and decreases at a small rate, which can improve the efficiency of global search; in the late stage of iteration, the convergence factor is small and decreases at a faster rate, which is conducive to improving the local accuracy of search.

[0347] The gray wolf optimization algorithm only updates the positions of the prey and the gray wolf when updating the position, which does not reflect the direction of optimization. In order to avoid reverse optimization, the present invention combines the velocity vector of the particle swarm to update the position of the alpha wolf and the wolf pack. The update formula after integrating the position and velocity is as follows:

[0348]

[0349] X ω (k+1)=X ω (k)+v ω (k+1) (62)

[0350] The calculation process of the adaptive chaotic gray wolf optimization algorithm is as follows: Figure 7 shown.

[0351] In order to verify the performance of the ACGWO algorithm designed in the present invention, the PSO algorithm, GWO algorithm and ACGWO algorithm are tested respectively based on the 5-dimensional Rastrigin test function, and the average values ​​of the objective functions obtained after 100 operations are 2.511, 0.091 and 0.002 respectively. Figure 8(b) shows the change curves of the objective function values ​​based on the three algorithms. It can be seen that the ACGWO algorithm is significantly better than the other two optimization algorithms in terms of convergence speed and convergence accuracy, and has good stability, indicating that the designed adaptive chaotic gray wolf optimization algorithm has superior optimization performance.

[0352] For the propulsion motor, its main goal is to achieve stable control of the speed. Based on the designed adaptive chaotic gray wolf optimization algorithm, in order to better achieve the unified optimization of overshoot, adjustment time and other indicators of speed tracking, the present invention selects the absolute error integral indicator as the objective function:

[0353]

[0354] Where, e(t) is the motor speed tracking error.

[0355] The overall control strategy block diagram of the permanent magnet synchronous motor designed by the present invention is as follows: Fig. 9 The permanent magnet synchronous motor is shown in Figure 1, in which a speed loop and a current loop form a series structure controller. The speed control loop is a sliding mode controller designed based on the variable exponential power reaching law, and combined with ESMDO to suppress interference. At the same time, in order to find the optimal parameters to achieve the best control performance, the adaptive chaos gray wolf optimization algorithm is combined to optimize the controller parameters. The current loop uses two PI controllers to control the tracking error of the dq axis current respectively.

[0356] Step 5: Simulation Analysis

[0357] Based on the MATLAB / Simulink simulation platform, a simulation model of the permanent magnet synchronous propulsion motor system is built. The inverter of the permanent magnet synchronous propulsion motor is powered by the DC bus. The simulation is mainly carried out from two aspects. First, the control effect of the designed variable exponential power reaching law sliding mode control (VEPRL-SMC) strategy combined with ESMDO is compared with the exponential reaching law sliding mode control (ERL-SMC) and the double closed-loop PI control strategy under the condition of propeller load speed change; secondly, the three control strategies are simulated and compared under the condition of sudden load disturbance. The parameters of the permanent magnet synchronous propulsion motor used in the simulation are shown in Table 1.

[0358] Table 1 Permanent magnet synchronous propulsion motor parameters

[0359]

[0360] According to the objective function (63), the smaller the fitness function value under different control methods, the better the control effect. From the previous comparative analysis, it can be seen that compared with the other two optimization algorithms, the adaptive chaos gray wolf optimization algorithm has the best optimization ability. In order to avoid the control difference caused by optimizing a single controller, the adaptive chaos gray wolf optimization algorithm is used to optimize the three controllers. Table 2 shows the optimization results of the controller parameters based on the adaptive chaos gray wolf optimization algorithm.

[0361] Table 2 Optimization results of adaptive chaotic grey wolf optimization algorithm

[0362]

[0363] Step 5-1: Propeller load simulation analysis

[0364] The simulation conditions are that at the initial moment, the three-phase AC of the generator is rectified by the Vienna rectifier. After the DC bus voltage stabilizes, the reference speed of the propulsion motor is given to be 1500r / min at 0.1s, and the motor starts with the propeller load. Then, the speed suddenly changes to 1150r / min at 0.25s, and then to 1650r / min at 0.45s. Fig.10 Shown

[0365] Based on the above analysis, it can be seen that the VEPRL-SMC control strategy combined with the disturbance observer has a good dynamic response speed and steady-state accuracy in the speed control under propeller load conditions. It can maintain fast, stable and non-overshoot tracking of the reference instruction when the speed changes suddenly, and reduces the current fluctuation amplitude, further improving the dynamic performance of the system.

[0366] Step 5-2: Anti-load disturbance simulation analysis

[0367] In order to further verify the designed control strategy's suppression effect on load disturbance, the three control strategies are simulated for load disturbance resistance. The simulation conditions are that the reference speed of the permanent magnet synchronous motor is given to be 1500r / min at 0.1 seconds, the motor starts without load, and then a load torque of 10N·m is suddenly added at 0.25 seconds, and then the load torque of 10N·m is suddenly unloaded at 0.35 seconds. Fig.11 This is a simulation comparison of the load disturbance resistance capabilities of the three control strategies of VEPRL-SMC, ERL-SMC and PI. Figure 12-14 These are the dq-axis currents of the three control strategies, PI, ERL-SMC and VEPRL-SMC, under load disturbance.

[0368] The VEPRL-SMC control strategy has the smallest q-axis current fluctuation amplitude when facing a sudden change in external load, and recovers to a steady state faster, followed by the ERL-SMC control strategy, and the worst is the PI control strategy.

[0369] From the above analysis, it can be seen that the VEPRL-SMC control strategy has better dynamic response performance under load mutation conditions. By using the extended sliding mode disturbance observer to observe the load torque, the control system's ability to resist load disturbances is enhanced. When the control system is subjected to load disturbances, the speed fluctuation is reduced, and the speed of the system returning to stability is accelerated.

[0370] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A design method for a motor sliding mode speed controller for an aviation hybrid propulsion system, characterized by: The following steps are involved: Step 1: Model the permanent magnet synchronous propulsion motor and propeller, and list the voltage, flux, torque equations of the permanent magnet synchronous motor in the natural coordinate system, stationary coordinate system, and rotating coordinate system, as well as the propeller's thrust T, torque M, and power PW. prop , efficiency η, forward ratio formula; The step 1 comprises: Step 1-1, first establish the mathematical model of the permanent magnet synchronous propulsion motor: Assume that the ideal permanent magnet synchronous motor model conditions are as follows: (1) The effects of skin effect, eddy current, hysteresis loss and magnetic saturation of the motor core are not considered; (2) The three-phase windings in the stator are symmetrically distributed, and the influence of harmonics of various orders in the three-phase winding current is ignored; (3) The flux generated by the permanent magnets of the rotor is constant and three-phase symmetrical; Then the magnitude of the induced magnetic flux generated on the stator three-phase winding is: Among them, ψ f is the permanent magnet flux; ψ fA , fB , fC are the magnitudes of the induced flux generated on the stator A, B, and C phase windings, respectively; θ is the angle between the A phase stator winding and the permanent magnet flux, also called the rotor position angle; According to Kirchhoff's voltage theorem, the voltage equation of the permanent magnet synchronous propulsion motor is: Among them, u x (x=a,b,c) is the stator three-phase winding voltage; i x (x=a,b,c) is the stator three-phase winding current; R s is the phase resistance of the stator three-phase winding; ψ x (x=a,b,c) is the flux linkage of the stator three-phase winding; The flux of the three-phase winding consists of two parts, one is the induced flux generated by the permanent magnet flux in the winding, and the other is the armature flux generated by the armature current. The expression is as follows: Among them, L AA , L BB , L CC are the self-inductance of the three-phase stator windings; L AB , L BA , L AC , L CA , L BC , L CB are the mutual inductance of the three-phase stator windings; The electromagnetic torque equation is: T e =-n p ψ f [i a sinθ+i b sin(θ-2π / 3)+i c sin(θ+2π / 3) (4) Among them, T e is the electromagnetic torque; n p is the number of magnetic pole pairs; The equation of motion is: Among them, ω m is the mechanical angular velocity; J is the moment of inertia; B is the damping coefficient; T L is the load torque; According to Clark transformation, the voltage equation, flux equation and torque equation of the permanent magnet synchronous propulsion motor in the two-phase stationary coordinate system are obtained as follows: T e =n p ψ f (i β cosθ-i α sinθ) (8) Among them, u α 、u β 、i α 、i β are the stator voltage and current components on the α and β axes respectively; ψ α , β is the component of the stator flux on the α and β axes; L α , L β is the inductance in the α and β coordinate systems; p is the differential operator; for the surface-mounted permanent magnet synchronous motor, L α =L β =L s ;ω is the rotor rotation angular velocity; Ls is the stator inductance; According to equations (6)-(8) and combined with Park coordinate transformation, the voltage, flux linkage and torque equations of the permanent magnet synchronous propulsion motor in the synchronous rotating coordinate system are obtained as follows: Among them, u d 、u q 、i d 、i q are the stator voltage and current components on the d and q axes respectively; ψ d , q is the component of the stator flux on the d and q axes; L d , L q is the inductance of d and q axes; Step 1-2: Propeller Modeling: The dynamic characteristics of the propeller include thrust, thrust coefficient, torque, torque coefficient, power, power coefficient, and efficiency; According to the aerodynamic characteristics and structural features of the propeller, the propeller thrust T is expressed as: T=C t ρn s 2 D 4 (12) Among them, C t is the tension coefficient; ρ is the atmospheric density; n s is the propeller speed, which is the motor speed when it is directly connected to the propulsion motor; D is the propeller diameter; The propeller torque is the torque of the resistance that the propeller needs to overcome when rotating. The propeller torque M is expressed as: M=C M ρn s 2 D 5 (13) Among them, C M is the torque coefficient; The propeller power is the power obtained by the propeller from the propulsion motor. The propeller power PW prop It is expressed as: PW prop =C p ρn s 3 D 5 (14) Among them, C p is the power coefficient; The propeller propulsion efficiency η is expressed as: Where V0 is the airspeed; The propeller advance ratio λ is expressed as: From the previous formula, we know that for a fixed pitch propeller, when the structural parameters and flight conditions are determined, the propeller torque and power are related to the torque coefficient and power coefficient, while the torque coefficient, power coefficient and propulsion efficiency are all related to the propeller advance ratio; Step 2: The goal of sliding mode control is to make the state trajectory reach the sliding mode switching surface set by itself and gradually converge to the origin of the system. In order to improve the convergence speed of the sliding mode variable s, a variable exponential power reaching law is designed; In order to improve the convergence speed of the sliding mode variable s, a variable exponential power reaching law is designed: Among them, x is the state quantity, which satisfies ε>0,k>0,0,<b<1, the expression of α(s) is: Among them, p1, q1, p2 and q2 are positive numbers, and p1>q1>0, p2>q2>0; The sliding mode convergence process based on VEPRL is divided into two cases: |s|≤1 and |s|>1. When |s|≤1, the traditional exponential convergence rate slows down significantly due to the decrease of s. In formula (17), sgn(|s|-1)=-1, and the variable exponential term becomes k|s| -b s, obviously k|s| -b s>k|s| b s, at this time the sliding mode variable s is Directly converges to zero; when the system is far away from the sliding surface, that is, |s|>1, then sign(|s|-1)=1, α(s)>1, the system relies on and k|s b s work together to approach |s| = 1, and then Converge to zero; by adding the power term α(s), the system can maintain a faster speed to approach the sliding surface when it is far away from the sliding surface. When the system approaches the sliding surface, a smaller α(s) is ensured to reduce chattering, thereby ensuring a faster overall speed to approach s=0 and reducing chattering; When the system approaches the sliding surface, the variable exponent power reaching law proposed based on equation (17) is simplified to Its discrete expression is: Where T is the sampling period; When satisfied and When s(n)=0 at time n + ,but: Similarly, suppose that at time n, s(n) = 0 - ,but: Based on equations (20) and (21), the discrete sliding mode bandwidth is: Step 3, design a sliding mode speed controller based on disturbance compensation; The step 3 comprises: Step 3-1, sliding mode speed controller design In order to facilitate the design of the controller, the formula (9) is transformed into: Since the surface mounted permanent magnet synchronous propulsion motor has L d =L q , and adopt i d = 0, the torque equation (11) is simplified to: The mechanical motion equation is: make Considering the influence of interference and uncertainty factors in the permanent magnet synchronous motor model, the mechanical motion equation is expressed as: Now take g = Δai q -Δbω m -ΔmT L , represent the internal parameter disturbance and external disturbance of the system respectively, then equation (26) can be expressed as: Where x1 = ω m , The q-axis reference current of the current inner loop will be used to estimate the parameter disturbance using the adaptive law, and an extended sliding mode disturbance observer will be designed to estimate and compensate for the external disturbance. The speed tracking error is defined as: in, Indicates a given reference speed; The derivative of formula (28) is: In the speed control, the integral sliding surface is selected as follows: Where c is the integral coefficient, satisfying c＞0 ; The derivative of the sliding surface is: Combining the designed variable exponential power reaching law with equation (31) and performing corresponding transformations, the q-axis output reference current signal of the speed loop can be obtained: Where x = e; d is the estimate based on the extended sliding mode disturbance observer for feedforward compensation; the estimate of parameter uncertainty The derivative expression of is as follows: Step 3-2, Design of Extended Sliding Mode Disturbance Observer In order to improve the control performance of permanent magnet synchronous motor in the presence of external disturbances, an extended sliding mode disturbance observer is designed to estimate the disturbance online, and then the estimated value is used for feedforward compensation. The expansion of formula (25) is expressed as: Taking the motor speed and external disturbance as observation quantities, the extended sliding mode disturbance observer is designed as: Among them, y(ω e ) is the sliding mode control law; g is the sliding mode gain; is the estimated value of the motor speed; is the estimated value of the external disturbance; Subtracting formula (36) from (37), we can get the observation error of ESMDO: in, is the speed estimation error; is the disturbance estimation error; Then design the sliding surface for ESMDO and select the integral sliding surface: s ω =e ω +c1∫e ω dt (40) Among them, c1 is the integral term coefficient; the derivative of the sliding surface is: At the same time, select the isokinetic reaching law: Among them, k2>0 is the switch gain coefficient; E d / J is used as the disturbance term, and combined with equations (38), (41) and (42), the disturbance estimation of ESMDO is expressed as: Step 4, design an adaptive chaotic grey wolf optimization algorithm; The step 4 comprises: The initial position of the gray wolf is generated by using Logistic chaotic mapping, so that the initial population is evenly distributed to improve the convergence speed at the initial moment. In the search process, chaotic randomness and ergodicity can be used to avoid falling into the local optimal solution. The mapping equation of Logistic mapping is: in k+1 =au k (1-in k ) (59) Among them, a=4, at this time the output is widely distributed in the range of [0,1], An adaptive convergence factor is designed to maintain a balance between global and local exploration capabilities. Its expression is as follows: Among them, a min and a max They represent the minimum and maximum values ​​of the convergence factor, respectively. i represents the current number of iterations, N represents the total number of iterations, and n represents the decreasing index, 0<n≤1; The position of the leader wolf and the wolf pack is updated by combining the velocity vector of the particle swarm. The update formula after fusing the position and velocity is as follows: X ω (k+1)=X ω (k)+v ω (k+1) (62) Among them, c1 and c2 are acceleration constants, also known as learning factors; X1, X2, and X3 represent the distances that the ω wolf moves toward the α wolf, β wolf, and δ wolf, respectively; Select the absolute error integral indicator as the objective function: Where, e(t) is the motor speed tracking error; Step 5: Build a simulation model of the permanent magnet synchronous propulsion motor system based on the MATLAB / Simulink simulation platform.

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