Transition speed domain permanent magnet synchronous motor sensorless control method based on improved Hereum algorithm

Abstract

The invention discloses a permanent magnet synchronous motor sensorless transition speed domain control method based on an improved Hereum algorithm. According to the following innovative scheme, firstly, a random high-frequency square wave voltage injection method is combined with a sliding-mode observer method, and rotor position accurate estimation of a zero-low-speed domain and a medium-high-speed domain is achieved; and then, introducing an improved Ho algorithm (HO), adopting a Chebyshev chaotic mapping initialization population strategy, replacing an original exponential attenuation formula with a self-adaptive inverse proportion attenuation function, calculating an optimal weight coefficient corresponding to each discrete rotating speed point in a switching interval in an off-line manner, and generating a continuous and smooth weight distribution curve through polynomial fitting. Smooth transition of the two control strategies in the transition speed domain is achieved, and switching oscillation and position errors are remarkably reduced. According to the method, through transition speed domain model fusion and algorithm optimization, the problem of torque fluctuation caused by traditional linear weighted switching is solved, and the system robustness is improved.

Description

Technical Field

[0001] The present invention belongs to the field of permanent magnet synchronous motor control, and particularly relates to a sensorless control method for a permanent magnet synchronous motor in a transition speed range based on an improved Hippopotamus (HO) algorithm. Background Art

[0002] Permanent magnet synchronous motors (PMSMs) have advantages such as high efficiency, high power density, and wide speed regulation range, and are widely used in many fields. Among them, interior permanent magnet synchronous motors (IPMSMs) have less permanent magnet consumption, a strong structure, and a significant salient pole effect, and thus have greater application potential in terms of cost and performance balance. However, traditional PMSM drive systems rely on mechanical encoders or resolvers to obtain the rotor position, which are vulnerable to environmental interference, large in size, high in cost, and complex in circuit, affecting the reliability of the system.

[0003] Sensorless control technology estimates the rotor position through algorithms, and can construct a drive system with low cost, high reliability, and wide speed regulation. It has broad application prospects in fields such as industrial manufacturing, rail transit, aerospace, and household appliances. Especially in the field of new energy vehicles, it is an important development direction for lightweight and high-reliability drive systems.

[0004] Sensorless control methods are mainly divided into two categories: back electromotive force (EMF) estimation-based and high-frequency voltage signal injection methods based on the saliency of the motor. The signal-to-noise ratio of the back EMF is very small in the zero or low-speed region, making it difficult to obtain rotor position and speed information in real time, and it is mostly used in the medium and high-speed fields. The high-frequency voltage signal injection method is widely used in the zero and low-speed regions, but the fixed switching frequency leads to harmonic concentration and audible noise. Random frequency injection can broaden the power density spectrum and reduce sharp noise.

[0005] To achieve smooth switching between the low-speed and high-speed regions of the motor, it is necessary to combine the two control modes to give full play to their respective advantages in different speed regions. Traditional conversion algorithms include switch switching, hysteresis switching, and weighted switching, but there are problems of switching oscillation and insufficient stability in the transition speed region. These deficiencies not only limit the performance of the motor system in the transition speed region, but also affect its reliability in high-precision application scenarios. To address the above problems, the present invention proposes a variable weight coefficient switching method based on the Hippopotamus algorithm (HO), which adaptively adjusts the weight coefficient through an intelligent optimization algorithm. This design enables the intelligent fusion of the observation results of the two sensorless control strategies in the transition speed region, eliminates the oscillation phenomenon in traditional switching, significantly improves the position observation accuracy and system stability, and provides a breakthrough solution for smooth control in the transition speed region. Summary of the Invention

[0006] Aiming at the problems existing in the traditional hysteresis switching strategy and fixed-weight switching method in the transition speed range, a variable-weight coefficient switching method based on the improved Hippopotamus Optimization (HO) algorithm is proposed. This method adaptively adjusts the weight coefficient through an intelligent optimization algorithm, combines the Chebyshev chaotic mapping uniform initialization population strategy, improves the original exponential decay formula, replaces it with an adaptive inverse proportional decay function, effectively integrates the observation results of the zero-low speed range random high-frequency square wave voltage injection method and the medium-high speed range sliding mode observer method, and realizes the smooth transition of the two sensorless control strategies in the transition speed range.

[0007] The technical solution provided by the present invention is as follows:

[0008] Step 1: For the permanent magnet synchronous motor system under random high-frequency square wave voltage injection, conduct mathematical modeling and characteristic analysis, and establish its high-frequency response model at zero and low speeds;

[0009] Step 2: Adopt the random high-frequency square wave voltage signal injection method, and realize the estimation of the rotor position and speed in the zero-low speed range through signal injection, position error signal demodulation, and position observation;

[0010] Step 3: Estimate the rotor position and speed in the medium-high speed range of the permanent magnet synchronous motor;

[0011] Step 4: Use the variable-weight coefficient switching method of the improved Hippopotamus Optimization (HO) algorithm to realize the smooth transition between the random high-frequency square wave voltage signal injection method and the sliding mode observer method.

[0012] Furthermore, in step 1, it includes: the high-frequency mathematical model of the permanent magnet synchronous motor in the zero-low speed range, which is characterized in that: under the random frequency high-frequency square wave voltage injection method, a high-frequency mathematical model is constructed.

[0013] Furthermore, step 2 includes the following steps:

[0014] (1) Signal injection: The random frequency high-frequency square wave voltage signal injected in the estimated dq-axis coordinate system is:

[0015]

[0016] In the above formula, V R is the amplitude of the random frequency voltage signal, and T R is the period of the random frequency voltage signal.

[0017] (2) Filter signal separation: According to the characteristics of the high-frequency response current and fundamental wave current under the random high-frequency square wave voltage signal injection method, separate the signals through a high-pass filter.

[0018] (3) Position error signal demodulation: In the estimation After injecting a random high-frequency square wave signal into the axis, a pair of high-frequency current signals related to the position of the motor rotor can be obtained in the stationary coordinate system. Establish a measurement rotor frame for d m q m , and through coordinate transformation, the high-frequency induced current in the d m q m coordinate system can be obtained and Multiplied by the demodulated g(t - TR / 4, T R ) signal, the high-frequency induced current and will have a positive amplitude. The high-frequency currents and are transformed into the stator frame. When Δθ e is small enough for normalization, the estimated position error is obtained through the heterodyne method.

[0019] (4) Position Observation

[0020] By constructing an observer or designing a phase-locked loop, the rotor position error is adjusted to 0, then the observed position will converge to the actual position, and the estimated rotor position and speed are observed.

[0021] Furthermore, step 3 includes the following steps:

[0022] (1) Extended back electromotive force: Perform a coordinate transformation on the mathematical model of the permanent magnet synchronous motor in the synchronous rotating coordinate system in step 1 to establish a mathematical model in the stationary two-phase coordinate system, where the extended back electromotive force [E α E β T is:

[0023]

[0024] (2) Design of a sliding mode observer based on a phase-locked loop: Design the SMO as the following formula:

[0025]

[0026] In the formula, is the observed value of the stator current; is the observed value of the extended back electromotive force. When the state variable of the observer reaches the sliding mode surface, the observer state will always remain on the sliding mode surface. At this time, the extended back electromotive force estimated by the observer is equal to the true extended back electromotive force E a 、E β . At this time, filter out the high-frequency components of E a and E β through a first-order low-pass filter to obtain continuous E a and E​β Position Observation: Instead of using the arctangent function, a PLL (Phase-Locked Loop) is adopted to estimate the rotor position. The orthogonal product method is used to obtain ΔE, and then the estimated rotor position and speed are observed through the PLL based on ΔE.

[0027] Furthermore, Step 4 includes the following steps:

[0028] (1) Determine the switching interval: The upper limit of the speed at which the random high-frequency square wave injection method can accurately estimate the rotor position is the lower limit ω of the switching interval L , and the lower limit of the speed at which the sliding mode observer method can accurately estimate the rotor position is the upper limit ω of the switching interval H .

[0029] (2) Establish the objective function and determine the parameters to be optimized: To ensure the rapidity of the algorithm, the designed objective function is solved for the optimal weight coefficient through multi-index fusion and dynamic weight adjustment.

[0030]

[0031] In the above formula, ω e represents the actual electrical angular velocity, represents the estimated electrical angular velocity obtained through the high-frequency square wave voltage signal injection method, represents the estimated electrical angular velocity obtained through the sliding mode observer method. The α term: retains the sensitivity of the original objective function to the overall error and ensures the average accuracy of the estimated value. The β term: suppresses the influence of outliers and enhances the robustness of the algorithm in a noisy environment. The γ term: constrains the change range of the weight coefficient between adjacent moments, avoids sudden changes during the switching process, and improves the smoothness of the full-speed range transition. Zero low-speed range: mainly uses the high-frequency injection method (λ1 = 1), and the absolute error term suppresses the influence of current sampling noise. Transition domain: the smoothing term forces λ1 and λ2 to change slowly to avoid torque jumps during switching. High-speed domain: dominated by the sliding mode observer method (λ2 = 1), and the squared error term optimizes the steady-state accuracy. Let λ = λ1, and λ is used as the parameter to be optimized.

[0032] (3) Algorithm implementation: Calculate the optimal weight coefficient for each measurement point through the improved hippopotamus algorithm. The algorithm implementation process:

[0033] ① Initialize the hippopotamus population, including the initial position of the population, the number of iterations, etc. Calculate the optimal weight coefficient for each measurement point through the improved hippopotamus algorithm. Characteristics: Generate the initial population based on the Chebyshev chaotic map, and calculate the initial position of each individual in the hippopotamus population through the following formula:

[0034] x n+1 = cos(k·arccos(x n ))), (k≥2)

[0035]

[0036] In the above formula, X i is the position of the i-th hippopotamus in the search space, mapping the weight coefficient λ to the position variable x of the hippopotamus individual ij , N is the number of the population, ub j and lb j are the upper and lower limits of the search space respectively, that is, the value range of the optimal weight coefficient to be determined.

[0037] ② Use the improved hippopotamus algorithm to test the optimal weight coefficient, which mainly includes three stages: exploration stage, hippopotamus defending against predators, and hippopotamus escaping from predators.

[0038] Exploration stage: The hippopotamus dynamically evaluates the fitness of λ based on the objective function, and updates the positions of the hippopotamus population to search for the optimal λ combination. Map the weight coefficient λ to the position variable x ij of the hippopotamus individual, and adjust the candidate values of λ through the position update formula:

[0039]

[0040] In the formula, x ij directly represents the value of the candidate weight coefficient λ, Mhippo is the position of the male hippopotamus, is the current optimal λ value. I1 is an integer between 1 and 2, r1 - r4 are random vectors between 0 and 1, r5 is a random number between 0 and 1, including 1 and 0, and are integer random numbers, which can be 1 or 0.

[0041]

[0042] Improve the original exponential decay formula, replace it with an adaptive inverse proportional decay function, adjust the decay rate through the k value. The inverse proportional function has a higher decay rate in the initial stage of the algorithm (t is smaller), accelerating the preliminary optimization of the weight coefficient and quickly approaching the optimal solution region. As the number of iterations increases (t increases), the decay rate decreases, retaining a certain perturbation ability to avoid the algorithm converging to the local optimum prematurely. The steep decline of the exponential decay in the initial stage may cause mutations in the weight coefficient, resulting in rotational speed or position jitter during switching. The inverse proportional decay reduces the mutation probability through a smoothly transitioning decay curve. Dynamically adjust the search step size of λ through this function to accelerate convergence to the optimal solution.

[0043] ③ Hippopotamus defending against predators:

[0044] One of the main reasons for the gregariousness of hippos can be attributed to their safety. Due to their inherent curiosity, immature hippos may occasionally stray from the group and become potential targets for predators. Their strength is relatively weak during this time, and hippos adopt a defense behavior based on the FPredator j factor to protect themselves from predators. The purpose is to make predators or intruders aware of their presence within the territory.

[0045]

[0046] The above formula represents the distance from the i-th hippo to the predator. ⊕ represents a position update operation, f represents a random number between 2 and 4, c is a uniform random number between 1 and 1.5, D is a uniform random number between 2 and 3. g represents a random number between -1 and 1. is a random vector with a dimension of 1×m. RL is a random vector with a Levy distribution, used for the sudden change of the predator's position when attacking the hippo. The mathematical model of the random movement of Levy motion is calculated as follows:

[0047]

[0048] w and v are random numbers between 0 and 1, σ w is an abbreviation of the gamma function, σ w can be calculated by the following equation:

[0049]

[0050] According to the above formula, if is greater than it means that this hippo has been hunted, and another hippo will replace it in the group. Otherwise, the hunter will flee and this hippo will return to the group. In the second stage, a significant improvement in the global search process was observed. The first stage and the second stage complement each other, effectively reducing the risk of falling into local minima.

[0051] ④ Hippos fleeing from predators:

[0052] Another behavior of hippos when facing predators is that when hippos encounter a group of predators or cannot repel the predators with defensive behavior. In this case, the hippos try to leave the area. It is modeled according to the following equation. When the newly created position improves the cost function value, it indicates that the hippo has found a safer position near its current position and changes its position accordingly. t represents the current iteration number, while T represents the maximum iteration number:

[0053]

[0054] From the above equation, The position of the hippopotamus searched to find the nearest safe location.

[0055]

[0056]

[0057] s1 is a vector or number randomly selected from three scenario equations. The scenarios considered have stronger local search capabilities. In the above formula represents a random vector between 0 and 1, while r 10 and r 13 represent random numbers generated within the range of 0 and 1. In addition, r 12 is a random number following a normal distribution. Calculate the fitness value and record the optimal position. After each iteration, calculate the fitness value through the fitness function and record the optimal position.

[0058] (4) Function fitting

[0059] Based on the improved Hippopotamus Optimization (HO) algorithm, calculate the optimal weight coefficients corresponding to each discrete speed point offline within the switching interval, and then generate a continuous and smooth weight distribution curve through polynomial or piecewise function fitting to replace the traditional linear weighted switching function for switching between the random high-frequency square wave voltage signal injection method and the sliding mode observer method.

[0060] Beneficial effects: It can make the switching between the high-frequency square wave voltage signal injection method and the sliding mode observer method smoother. Improve the traditional Hippopotamus Optimization (HO) algorithm by introducing the Chebyshev chaotic map to initialize the population, which solves the problems of poor diversity and uneven distribution of the initialized population and the problem of falling into local optimal solutions in the traditional Hippopotamus Optimization algorithm. Improve the original exponential decay formula and replace it with an adaptive inverse proportional decay function to improve the performance of the Hippopotamus Optimization algorithm. Compared with the previous weighted switching method that may cause chattering phenomena during the switching process from the zero and low-speed regions to the medium and high-speed regions of the permanent magnet synchronous motor, the method adopted in the present invention estimates the speed and rotor position more accurately. Generate a continuous and smooth weight distribution curve through polynomial fitting, which can achieve seamless transition between the two control modes, effectively suppress the torque and speed chattering caused by sudden changes in weights in the traditional method, and at the same time improve the dynamic accuracy of position observation in the transition speed range and the system stability. Description of the drawings

[0061] Figure 1 It is a control block diagram for random high-frequency square wave voltage injection.

[0062] Figure 2 It is a phase-locked loop structure.

[0063] Figure 3 It is a sliding mode observer based on a phase-locked loop.

[0064] Figure 4 To improve the flowchart of the hippopotamus algorithm.

[0065] Figure 5 For the expected fitting effect.

[0066] Figure 6 It is a control block diagram of a sensorless control method for a permanent magnet synchronous motor in the transition speed range based on an improved hippopotamus algorithm. Specific implementation manners

[0067] The present invention will be further specifically described below with reference to the accompanying drawings and embodiments.

[0068] The sensorless control method for a permanent magnet synchronous motor in the transition speed range based on the improved hippopotamus algorithm of the present invention includes the following steps:

[0069] Step 1: Analyze and evaluate the mathematical model of the permanent magnet synchronous motor after injecting a random high-frequency square wave voltage signal, and construct a high-frequency mathematical model of the permanent magnet synchronous motor in the zero and low-speed ranges.

[0070] Step 2: Estimate the rotor position and speed of the permanent magnet synchronous motor in the zero and low-speed ranges: Adopt the random high-frequency square wave voltage signal injection method of filter signal separation, and realize the estimation of the rotor position and speed in the zero and low-speed ranges through signal injection, filter signal separation, position error signal demodulation, and position observation. The control block diagram of the random high-frequency square wave voltage injection is as Figure 1 shown.

[0071] (1) Signal injection: Inject a random high-frequency square wave voltage signal in the estimated dq-axis coordinate system.

[0072] (2) Filter signal separation: According to the characteristics of the high-frequency response current and the fundamental wave current under the high-frequency square wave voltage signal injection method, separate the signals through a high-pass filter.

[0073] (3) Position error signal demodulation: After injecting a random high-frequency square wave signal on the estimated axis, a pair of high-frequency current signals related to the rotor position of the motor will be obtained in the stationary coordinate system. Establish a measurement rotor frame, denoted as d m q m , where the d m -axis lags behind the estimated d-axis by π / 4. Through coordinate transformation, the high-frequency induced current m q m in the coordinate system and and are multiplied by the demodulation g(t - T R / 4, T R ), and we obtain the high-frequency induced current and The amplitude in is positive. High-frequency current and are transformed into the stator frame when Δθ e is small enough, then normalized, and the estimated position error is obtained by heterodyning.

[0074] (4) Position observation: By constructing an observer or designing a phase-locked loop, the rotor position error is adjusted to 0, then the observed position will converge to the actual position, and the estimated rotor position and speed are observed. The structure of the phase-locked loop is as Figure 2 shown.

[0075] Step 3: Estimation of rotor position and speed in the medium and high speed ranges of a permanent magnet synchronous motor: The improved sliding mode observer method based on the PLL phase-locked loop is used to achieve the estimation of rotor position and speed in the medium and high speed ranges. The structure of the sliding mode observer is as Figure 3 shown.

[0076] (1) Extended back electromotive force: The mathematical model of the permanent magnet synchronous motor in the synchronous rotating coordinate system in step 1 is subjected to coordinate transformation to establish a mathematical model in the stationary two-phase coordinate system, where the extended back electromotive force [E α E β T is:

[0077]

[0078] (2) Establishment of a sliding mode observer design based on a phase-locked loop: The SMO is designed as the following formula:

[0079]

[0080] In the above formula, is the stator current; is the observed value of the extended back electromotive force. When the state variable of the observer reaches the sliding mode surface, the observer state will always remain on the sliding mode surface. At this time, the extended back electromotive force estimated by the observer is a equal to the true extended back electromotive force E β . Then, E a and E β are filtered by a low-pass filter to remove the high-frequency components, and the continuous E a and E β are obtained.

[0081] (3) Position observation: The PLL phase-locked loop is used to replace the arctangent function to estimate the rotor position, the orthogonal product method is used to obtain ΔE, and then the estimated rotor position and speed are observed through the PLL for ΔE.

[0082] ​Step 4: Use the variable weight coefficient switching method of the improved Hippopotamus Optimization (HO) algorithm to achieve a smooth transition between the random high-frequency square wave voltage signal injection method and the sliding mode observer method.

[0083] (1) Determine the switching interval: Measure that the upper limit of the rotational speed at which the random high-frequency square wave injection method can accurately estimate the rotor position is the lower limit ω of the switching interval L , and the lower limit of the rotational speed at which the sliding mode observer method can accurately estimate the rotor position is the upper limit ω of the switching interval H .

[0084] (2) Establish the objective function and determine the parameters to be optimized: To ensure the rapidity of the algorithm, the designed objective function is solved for the optimal weight coefficient through multi-index fusion and dynamic weight adjustment.

[0085]

[0086] In the above formula, ω e represents the actual electrical angular velocity, represents the estimated electrical angular velocity obtained by the high-frequency square wave voltage signal injection method, represents the estimated electrical angular velocity obtained by the sliding mode observer method. The α term: retains the sensitivity of the original objective function to the overall error and ensures the average accuracy of the estimated value. The β term: suppresses the influence of outliers and enhances the robustness of the algorithm in a noisy environment. The γ term: constrains the change amplitude of the weight coefficient at adjacent moments, avoids sudden changes during the switching process, and improves the smoothness of the full-speed range transition. Zero low-speed range: mainly uses the high-frequency injection method (λ1 = 1), and the absolute error term suppresses the influence of current sampling noise. Transition domain: the smoothing term forces λ1 and λ2 to change slowly to avoid torque jumps during switching. High-speed domain: the sliding mode observer method dominates (λ2 = 1), and the squared error term optimizes the steady-state accuracy. Let λ = λ1, and take λ as the parameter to be optimized.

[0087] (3) Algorithm implementation: Calculate the optimal weight coefficient for each measurement point through the improved Hippopotamus Optimization (HO) algorithm. The algorithm implementation process (as Figure 4 shown) is as follows:

[0088] ① Initialize the hippopotamus population, including the initial position of the population, the number of iterations, etc.

[0089] Calculate the optimal weight coefficient for each measurement point through the improved Hippopotamus Optimization algorithm. Characteristics: Generate the initial population based on the Chebyshev chaotic map, and set the current iteration number t to 0; calculate the initial position of the hippopotamus population through the following formula:

[0090] x n+1 = cos(k·arccos(x n ))), (k≥2)

[0091]

[0092] In the above formula, X i is the position of the i-th hippopotamus in the search space, N is the population size, ub j and lb j are the upper and lower bounds of the search space, respectively, that is, the value range of the optimal weight coefficient to be determined.

[0093] ② An improved hippopotamus algorithm is used to test the optimal weight coefficient, which mainly includes three stages: exploration stage, hippopotamus defending against predators, and hippopotamus escaping from predators.

[0094] Exploration stage: Dynamically evaluate the fitness of λ based on the objective function, and update the positions of the hippopotamus population to search for the optimal λ combination. Map the weight coefficient λ to the position variable x of the hippopotamus individual ij , and adjust the candidate values of λ through the position update formula:

[0095]

[0096] where x ij directly represents the value of the candidate weight coefficient λ, Mhippo is the position of the male hippopotamus, is the current optimal λ value. I1 is an integer between 1 and 2, r1 - r4 are random vectors between 0 and 1, r5 is a random number between 0 and 1, including 1 and 0, and are integer random numbers, which can be 1 or 0.

[0097]

[0098] Improve the original exponential decay formula and replace it with an adaptive inverse proportional decay function. Adjust the decay rate through the k value. The inverse proportional function has a higher decay rate at the initial stage of the algorithm (t is smaller), accelerating the preliminary optimization of the weight coefficient and quickly approaching the optimal solution region. As the number of iterations increases (t increases), the decay rate decreases, retaining a certain perturbation ability to avoid the algorithm converging to a local optimum prematurely. The steep decline of the exponential decay at the initial stage may cause mutations in the weight coefficient, resulting in speed or position oscillations during switching. The inverse proportional decay reduces the mutation probability through a smoothly transitioning decay curve.

[0099] ③ Hippopotamus defending against predators: According to the distance between the predator position and the hippopotamus individual, introduce the Levy distribution random perturbation mechanism to simulate the hippopotamus defense behavior, avoid local optima, and ensure that the hippopotamus individual can jump out of the local optimal weight coefficient trap and continue to search for the global optimal weight coefficient. The hippopotamus adopts a method based on FPredator jThe defensive behavior of the factor is to protect itself from predators, aiming to make the predator or intruder aware of its presence within the territory.

[0100]

[0101]

[0102] The above formula represents the distance from the i-th hippopotamus to the predator. ⊕ represents a position update operation, f represents a random number between 2 and 4, c is a uniform random number between 1 and 1.5, D is a uniform random number between 2 and 3. g represents a random number between -1 and 1. is a random vector with a dimension of 1×m. RL is a random vector with a Levy distribution, used for the sudden change of the predator's position when attacking the hippopotamus. The mathematical model of the random movement of Levy motion is calculated as follows:

[0103]

[0104] w and v are random numbers between 0 and 1, σ w is the abbreviation of the gamma function, σ w can be calculated by the following equation:

[0105]

[0106] According to the above formula, if is greater than it means that the hippopotamus has been hunted, and another hippopotamus will replace it in the population, otherwise this hippopotamus will return to the population. In the second stage, a significant improvement in the global search process was observed. The first stage and the second stage complement each other, effectively reducing the risk of falling into local minima.

[0107] ④ Hippopotamus escaping from predators: Dynamically narrow the parameter range through a local search strategy, combine normal distribution random numbers to generate safe positions, optimize the escape path of the hippopotamus, ensure the smooth switching of the weight coefficient, and make the hippopotamus individuals move in a direction more conducive to finding the optimal weight coefficient. t represents the current iteration number, while T represents the maximum iteration number.

[0108]

[0109] From the above equation, is the position of the hippopotamus searching for the nearest safe location.

[0110]

[0111] s1 is a vector or number randomly selected from three scenarios s equations. The considered scenarios have stronger local search capabilities. In the above formula represents a random vector between 0 and 1, while r 10 and r 13 represent random numbers generated within the range of 0 and 1. Additionally, r 12 is a random number following a normal distribution. During the iterative process of the entire hippopotamus algorithm, the position of each hippopotamus individual is continuously updated, corresponding to the continuous optimization and adjustment of the coefficient weights. By calculating the objective function value corresponding to each position (weight coefficient combination), its pros and cons are evaluated, gradually approaching the optimal weight coefficient, and finally realizing the smooth transition control of the random high-frequency square wave injection method and the sliding mode observer method in the transition speed range.

[0112] (4) Function fitting: Based on the improved hippopotamus algorithm (HO), calculate the optimal weight coefficients corresponding to each discrete speed point offline within the switching interval, and then generate a continuous and smooth weight distribution curve through polynomial fitting to replace the traditional linear weighted switching function for switching between the random high-frequency square wave voltage signal injection method and the sliding mode observer method.

[0113] In summary, the solution provided by the present invention can achieve the stable operation of the permanent magnet synchronous motor in the transition speed range. By improving the traditional hippopotamus algorithm and introducing the Chebyshev chaotic map to initialize the population, the problems of poor diversity and uneven distribution of the initialized population and being trapped in local optimal solutions existing in the traditional hippopotamus algorithm are solved, and the performance of the hippopotamus algorithm is improved. By replacing the decay exponential function with an adaptive inverse proportional decay function, the inverse proportional function has a higher decay rate in the initial stage of the algorithm, accelerating the preliminary optimization of the weight coefficients and quickly approaching the optimal solution region. As the number of iterations increases, the decay rate decreases, retaining a certain perturbation ability to avoid the algorithm converging to the local optimum prematurely. By adopting the variable weight coefficient switching strategy of the improved hippopotamus algorithm, the switching between the random high-frequency square wave voltage signal injection method and the sliding mode observer method is smoother. Then, a continuous and smooth weight distribution curve is generated through polynomial fitting. Finally, based on the accurately fitted weight function, seamless transition between the two control modes can be achieved, effectively suppressing the torque and speed chattering caused by weight mutation in the traditional method, and at the same time improving the dynamic accuracy of position observation and the system stability in the transition speed range.

Claims

1. The present invention provides a sensorless control method for a permanent magnet synchronous motor in a transition speed range based on an improved hippopotamus algorithm, comprising the following steps: Step 1: Determine the switching interval. Set the maximum speed at which the random high-frequency square wave injection method can accurately estimate the rotor position as the lower limit ω of the switching interval L , and the minimum speed at which the sliding mode observer method can accurately estimate the rotor position as the upper limit ω of the switching interval H ; Step 2: Establish the objective function and determine the parameters to be optimized. Design an objective function that integrates multiple indicators and has dynamic weight adjustment to solve for the optimal weight coefficient; Step 3: Combine the Chebyshev chaotic mapping uniform initialization population strategy for parameter setting; Step 4: Use the improved hippopotamus algorithm for parameter optimization. Finally, perform error correction according to the objective function, output the optimal weight coefficient, and achieve a smooth transition between the random high-frequency square wave voltage signal injection method and the sliding mode observer method.

2. As described in claim 1, characterized in that: Step 1 includes: measuring that the upper limit of the rotational speed at which the random high-frequency square wave injection method can accurately estimate the rotor position is ω, which is the lower limit of the switching interval L , and the lower limit of the rotational speed at which the sliding mode observer method can accurately estimate the rotor position is ω, which is the upper limit of the switching interval H , where ω L is 5%-10% of the rated speed, and ω H is 15%-20% of the rated speed, and it satisfies ω L < ω H Ensure that the two methods can accurately estimate the rotor position and speed information within the interval.

3. As described in claim 1, characterized in that: Step 2 includes: To ensure the rapidity of the algorithm, a target function that integrates multiple indicators and has dynamic weight adjustment is designed to solve for the optimal weight coefficient. The target function is as follows: In the above formula, ω e represents the actual electrical angular velocity, represents the estimated electrical angular velocity obtained by the high-frequency square-wave voltage signal injection method, represents the estimated electrical angular velocity obtained by the sliding mode observer method. The α term: retains the sensitivity of the original objective function to the overall error and ensures the average accuracy of the estimated value. The β term: suppresses the influence of outliers and enhances the robustness of the algorithm in a noisy environment. The γ term: constrains the change amplitude of the weight coefficients at adjacent moments, avoids sudden changes during the switching process, and improves the smoothness of the full-speed range transition. Zero low-speed range: mainly uses the high-frequency injection method (λ1 = 1), and the absolute error term suppresses the influence of current sampling noise. Transition range: the smoothing term forces λ1 and λ2 to change slowly to avoid torque jumps during switching. High-speed range: the sliding mode observer method dominates (λ2 = 1), the squared error term optimizes the steady-state accuracy, let λ = λ1, and take λ as the parameter to be optimized.

4. As described in claim 1, characterized in that: Step 3 includes: Calculating the optimal weight coefficient for each measurement point through an improved hippopotamus algorithm, generating an initial population based on the Chebyshev chaotic map; calculating the initial positions of each individual in the hippopotamus population through the following formula: x n+1 = cos(k·arccos(x n )), (k ≥ 2) In the above formula, X i is the position of the i-th hippopotamus in the search space, and the weight coefficient λ is mapped to the position variable x ij of the hippopotamus individual. N is the number of the population, ub j and lb j are the upper and lower limits of the search space, respectively, that is, the value range of the optimal weight coefficient to be determined.

5. As described in claim 1, characterized in that: Step 4 includes: Three stages of the hippopotamus algorithm: exploration stage, hippopotamus defending against predators, and hippopotamus escaping from predators. Improve the original exponential decay formula in the exploration stage of the first stage of the hippopotamus algorithm and replace it with an adaptive inverse proportional decay function. Exploration stage: Dynamically evaluate the fitness of λ based on the objective function, update the positions of the hippopotamus population to search for the optimal λ combination. Map the weight coefficient λ to the position variable x of the hippopotamus individuals ij , and adjust the candidate values of λ through the position update formula: where x ij directly represents the value of the candidate weight coefficient λ, Mhippo is the position of the male hippopotamus, is the current optimal λ value, and I1 is an integer between 1 and 2. The original exponential decay formula is improved and replaced with an adaptive inverse proportional decay function as follows: Dynamically adjust the search step size of λ through this function to accelerate convergence to the optimal solution. Hippopotamus defending against predators: According to the distance between the predator position and the hippopotamus individual, introduce a Levy distribution random perturbation mechanism to simulate the hippopotamus defense behavior, avoid local optima, and ensure that the hippopotamus individual can jump out of the local optimal weight coefficient trap and continue to search for the global optimal weight coefficient; Hippopotamus escaping from predators: Dynamically narrow the parameter range through a local search strategy, combine normal distribution random numbers to generate a safe position, optimize the escape path of the hippopotamus, ensure the smooth switching of the weight coefficient, and make the hippopotamus individual move in a direction more conducive to finding the optimal weight coefficient; During the iterative process of the entire hippopotamus algorithm, the position of each hippopotamus individual is continuously updated, corresponding to the continuous optimization and adjustment of the coefficient weight. By calculating the target function value corresponding to each position (weight coefficient combination), evaluate its pros and cons, gradually approach the optimal weight coefficient, and finally achieve the smooth transition control of the random high-frequency square wave injection method and the sliding mode observer method in the transition speed range.

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