Control method based on mechanical angular velocity adjusting system

Abstract

The invention belongs to the technical field of PID (Proportion Integration Differentiation) control optimization, and particularly relates to a control method based on a mechanical angular velocity regulating system, which comprises the following steps of: 1, constructing a mechanical angular velocity regulating system model, 2, constructing a red tail and algorithm mathematical model, and improving the red tail and the algorithm, and mainly improving the red tail and the algorithm. The method specifically comprises the following steps: S1, introducing an exponential penalty mechanism into a red-tail plinth algorithm, S2, improving a transition factor TF oscillation convergence problem of high-altitude soaring by using a cosine adaptive transformation factor, and S3, introducing normal distribution disturbance in a diving stage, adding random noise to explore a solution space, and solving the solution space by using the random noise. 3, parameters of an angular velocity PID controller of the mechanical angular velocity adjusting system are optimized through the improved red tail plinth algorithm, and 4, simulation and contrast test are conducted on the improved mechanical angular velocity adjusting system through MATLAB, and performance is verified.

Description

Technical Field

[0001] The present invention belongs to the technical field of PID control optimization, and particularly relates to a control method based on a mechanical angular velocity regulation system. Background Technique

[0002] Under the wave of automation, the mechanical angular velocity regulation system is no longer limited to traditional manual operations, but realizes intelligent and autonomous operation by virtue of advanced technologies. The mechanical angular velocity regulation system is a device that realizes precise adjustment or dynamic control of angular velocity through mechanical structures, and is widely used in fields such as mechanical engineering, automation equipment, aerospace, and optical instruments. Its core function is to make components rotate around a fixed axis to a target angle through mechanical transmission, control logic, or external drive to meet the requirements of precise positioning, attitude adjustment, or motion trajectory control.

[0003] The PID controller is a classic closed-loop control algorithm that reduces the deviation between the target value and the actual output by adjusting the system input in real time, and is widely used in fields such as industrial automation, robotics, and process control. In the mechanical angular velocity regulation system, the PID controller is one of the core technologies to achieve high-precision angle control. By adjusting the output of the driving device in real time, the actual angular velocity of the mechanical structure stably tracks the target angular velocity. The angular velocity PID controller detects the deviation between the actual angular velocity and the target value in real time, and uses the proportional link to quickly respond to the deviation, the integral link to eliminate the steady-state error, and the differential link to suppress overshoot and improve the system stability. After algorithm calculation, the control quantity is output to achieve the dynamic closed-loop control of the angular velocity.

[0004] The Red-tailed Hawk Algorithm (RTH) is a meta-heuristic optimization algorithm inspired by the predation behavior of the red-tailed hawk. It simulates the three-stage behaviors of soaring at high altitude, hovering at low altitude, and diving attack, and realizes efficient search through mathematical modeling such as Lévy flight, spiral motion model, and acceleration factor. The algorithm shows better accuracy, robustness, and convergence speed than 8 comparison algorithms such as FO and MGO in 23 standard benchmark functions, the CEC2020 / 2022 test set, and 7 types of engineering optimization problems. It has significant advantages especially in iterative efficiency and dealing with complex non-linear problems, providing a new efficient solution for the optimization field. However, the key parameters on which the algorithm depends in different stages have a great impact on the algorithm performance, and it is easy for the algorithm to fall into a local optimum and be unable to jump out, resulting in an imbalance between the exploration and development stages of the algorithm. Summary of the Invention

[0005] The object of the present invention is: in order to achieve precise and efficient regulation of a mechanical structure to reach a specified angular velocity and meet the accuracy and stability requirements of mechanical angular velocity regulation in different application scenarios, the present invention proposes a control method based on a mechanical angular velocity regulation system. By improving the red kite algorithm to optimize the angular velocity PID controller, the problem of limited parameter adaptability of the traditional angular velocity PID controller is solved, and thus the dynamic response performance of the mechanical angular velocity regulation system in the face of different external disturbances is improved.

[0006] To achieve the above object, the present invention adopts the following technical solutions: A control method based on a mechanical angle regulation system, the specific steps are as follows:

[0007] Step 1: Build a mechanical angular velocity regulation system model.

[0008] Step 2: Construct a mathematical model of the red kite algorithm and improve the red kite algorithm. The improvement is mainly carried out in three places of the red kite algorithm, specifically as follows: S1: Introduce an exponential penalty mechanism in the red kite algorithm. By punishing out-of-bounds behavior, guide the algorithm to tend to solutions that meet the constraints, dynamically quantify the degree of out-of-bounds, and then match the exponential penalty strength. Specifically, calculate the deviation of the actual value of each solution in each dimension from the boundary range. If the solution exceeds the upper and lower bounds, it is determined as a violation. The farther the deviation distance, the higher the degree of violation, and then the degree of violation imposes a penalty on the solution, and the penalty strength increases exponentially with the degree of violation; S2: Use a cosine adaptive transformation factor to improve the problem of the transition factor TF oscillation convergence in high-altitude soaring. Specifically, utilize the monotonically decreasing characteristic of the cosine function in the interval, combine the iterative process with the changing trend of the cosine function, so that the value of the transition factor TF is adaptively adjusted based on the cosine function law as the number of iterations increases. Through the continuous waveform characteristic of the cosine function, guide TF to smoothly transition from the larger value required for the global search mode to the smaller value required for the local search mode; S3: Introduce a normal distribution perturbation in the diving stage and add random noise to explore the solution space. Specifically, the normal distribution perturbation is centered on the current optimal solution to generate random noise, so that the newly generated solutions are distributed near the current optimal solution with a high probability, ensuring that they will not deviate too far from the feasible region; at the same time, solutions far from the current optimal solution are generated with a low probability to explore the areas in the solution space that have not been discovered;

[0009] Step 3: Use the improved red kite algorithm to optimize the parameters of the angular velocity PID controller of the mechanical angular velocity regulation system.

[0010] Step 4: Use MATLAB to perform simulation and comparative experiments on the improved mechanical angular velocity regulation system to verify the performance.

[0011] Further, in the first step, as Figure 2 shown, a mechanical angular velocity regulation system model is built, including an improved red kite algorithm, an angular velocity PID controller, space vector pulse width modulation, an inverter, a permanent magnet synchronous motor, a sliding mode observer, a DC power supply, a load, and a mechanical angular velocity regulation system. The improved red kite algorithm is used to optimize the parameters of the angular velocity PID controller after improving the red kite algorithm. By adjusting the proportional coefficient, integral coefficient, and differential coefficient, the performance of the controller is made better. The angular velocity PID controller calculates the difference between the given speed and the rotor angular velocity feedback by the sliding mode observer, and outputs a control signal through proportional, integral, and differential operations to adjust the motor speed. Space vector pulse width modulation converts the output signal of the angular velocity PID controller into an inverter control signal. By controlling the switching state of the inverter, a voltage waveform is generated to drive the permanent magnet synchronous motor. The inverter converts the DC power of the DC power supply into three-phase alternating current under the control of the space vector pulse width modulation signal to supply power to the permanent magnet synchronous motor. The permanent magnet synchronous motor operates under the action of the three-phase alternating current output by the inverter to drive the load. The sliding mode observer collects the stator voltage and current signals of the motor, estimates the rotor angular velocity information, and feeds it back to the angular velocity PID controller to achieve closed-loop control. The DC power supply provides DC electrical energy for the inverter and is the energy source of the whole system. The load is the external resistance added during the test of the whole system and is used to judge the effect of the overall system. The mechanical angular velocity regulation system is used to regulate the angular velocity of the working machinery to make the motor operation more in line with the actual requirements.

[0012] Further, the mechanical angular velocity regulation system takes the DC power supply as the energy source, supplies power to the permanent magnet synchronous motor through the inverter, and the switching state of the inverter is controlled by the space vector pulse width modulation technology to generate a suitable voltage waveform to drive the motor. A sliding mode observer is used to estimate the angular velocity of the motor rotor in real time, compare the feedback actual angular velocity with the given speed, and input the difference into the angular velocity PID controller. After proportional, integral, and differential operations, a control signal is output to adjust the motor speed. To further improve the system performance, an improved red kite algorithm is introduced to optimize the parameters of the PID controller, dynamically adjust the proportional, integral, and differential coefficients to adapt to the load changes under different working conditions. The optimized control signal is modulated by SVPWM to drive the inverter, so that the permanent magnet synchronous motor outputs the corresponding electromagnetic torque to overcome the load resistance torque, realizing the precise regulation of the mechanical angular velocity, and thus constructing a high-efficiency, stable, and strong self-adaptive closed-loop mechanical angular velocity regulation system.

[0013] Further, the angular velocity PID controller is the core of the mechanical angular velocity regulation system, and its working principle is based on the given speed command and the actual speed fed back by the sliding mode observer The error between them generates a control signal through the weighted combination of the proportional, integral, and differential links , the rotational speed tracking is achieved by adjusting the input voltage or current of the motor, and the specific mathematical model is shown as follows: (1); In Equation (1), the proportional link instantaneously amplifies the current error and quickly responds to the rotational speed deviation. The integral link eliminates the static deviation by accumulating the historical error to ensure the steady-state accuracy of the system. The differential link predicts the future trend based on the error change rate, suppresses overshoot, and improves the system stability.

[0014] Further, the switching state of the inverter is controlled by the space vector pulse width modulation technology. By precisely combining the switching states of the three-phase bridge arms of the inverter, a reference voltage vector with any phase and amplitude is synthesized, and then the permanent magnet synchronous motor is driven. The switching state of the inverter is controlled by the space vector pulse width modulation technology, and the dq axis voltage command output by the current loop is converted into and in the two-phase stationary coordinate system to construct the reference voltage vector . After determining the sector where the vector is located through the sector judgment function, the action time of adjacent effective vectors and the zero vector time are calculated according to the volt-second balance principle, and the conduction and cutoff of the 6 switching devices of the inverter are controlled according to a specific switching sequence to make the average output voltage approximate , realizing the precise control of the permanent magnet synchronous motor. The mathematical model of the voltage vector is shown as follows: (2); In Equation (2), in the two-phase stationary coordinate system, , is the projection component of the voltage vector, j is the imaginary unit, is the expected synthesized average voltage vector, whose amplitude determines the voltage magnitude, and the phase angle θ determines the voltage direction, and .

[0015] Further, a sliding mode observer is used to estimate the angular velocity of the motor rotor in real time. The sliding mode observer constructs a sliding mode surface containing system uncertainties and uses high-frequency switching control to make the system state converge to the sliding mode surface to achieve real-time estimation of the angular velocity of the motor rotor. The observer mainly estimates the current and to approximate the actual current. The mathematical model is shown as follows: (3); In Equation (3), and is the current estimation error, and , , and are the sliding mode control rates, R is the stator resistance, L is the stator inductance, is the permanent magnet flux linkage, is the estimated value of the rotor angular velocity, is the estimated value of the rotor position angle.

[0016] Furthermore, in the second step, a mathematical model of the red kite algorithm is constructed, which is characterized in that the red kite algorithm simulates the hunting process of the red kite and is divided into three stages: high-altitude soaring, low-altitude hovering, and dive attack, and corresponds to different strategies in the algorithm. The actions taken in each hunting stage are shown and modeled. The mathematical models of the three stages are as follows: D1. High-altitude soaring stage: The red kite flaps its wings at a low frequency and makes large-span circles at high altitude, uses the updraft to search for the prey position over a large range, explores the search space globally, and identifies potential prey areas. The high-altitude soaring stage mainly guides the search through Levy flight and the population mean position. The mathematical model of this stage is shown as the following formula: (4); In formula (4), is the position of the red kite at iteration number t, is the best position obtained so far, is the average of all position solutions, TF is the transition factor, Levy represents the Levy function, and the formula of the Levy function is as follows: (5); In formula (5), s is a constant with a value of 0.01, dim is the dimension of the problem, is a constant with a value of 1.5, and are random numbers within the range of [0,1]; D2. Low-altitude hovering stage: After locking the general area of the prey, the red kite reduces its flight altitude and circles around the prey in a spiral trajectory, narrowing the search range and determining the best attack position, corresponding to the local development stage in the optimization. The mathematical model of this stage is shown as the following formula: (6); In formula (6), StepSize( t ) is the step size, which is calculated based on the difference between the current position and the mean value to ensure convergence to the optimal solution. x(t) and y(t) are the spiral coordinates, and their mathematical formula is shown as the following formula: (7); In formula (7), R(t) is the radius, and , represents the initial radius when the red-tailed kite starts to fly around the prey, and its value ranges between [0.5, 3]. is the angle, and , A is the angle gain, with a value range between [5, 15], rand is a random number in the range of [0, 1], and r is the control gain, with a value in the range of [1, 2]. These parameters are necessary for the algorithm to simulate the spiral flight movement of the red-tailed kite around the prey. D3. Dive attack stage: The red-tailed kite will suddenly dive and attack the prey from the best position obtained in the low-altitude soaring stage, accurately hitting the prey, corresponding to the fast convergence stage of the optimization algorithm. The mathematical model of this stage is shown in the following formula: (8); In formula (8), and are both step size adjustment functions. They adjust the step size from two dimensions: the difference in population mean and the guidance of the optimal solution respectively. is the acceleration factor, used to accelerate the convergence speed, and ， is the gravity factor, used to reduce the search randomness, and .

[0017] Furthermore, in step two, the red-tailed kite algorithm is improved. There are mainly three improvements to the red-tailed kite algorithm: S1. Introduce an exponential penalty mechanism into the red-tailed kite algorithm to enhance the algorithm's ability to handle constraint conditions. S2. Use a cosine adaptive transformation factor to improve the oscillatory convergence problem of the transition factor TF in high-altitude soaring. S3. Introduce a normal distribution perturbation in the dive stage, add random noise to explore the solution space, and avoid the historical optimal solution falling into a local optimum. The specific steps are as follows: S1. Introduce an exponential penalty mechanism into the red-tailed kite algorithm to enhance the algorithm's ability to handle constraint conditions. When dealing with the problem of solutions exceeding the boundary, the red-tailed kite algorithm uses the method of forcibly pulling back to the boundary, completely ignoring the information of the overboundary direction and degree, which easily leads to the algorithm oscillating near the boundary and missing potential optimal solutions. After introducing the exponential penalty mechanism, it can dynamically adjust the penalty intensity according to the degree of solution overboundary. When the overboundary is slight, the penalty is small, allowing the algorithm to moderately explore the boundary area. When the overboundary is severe, the penalty increases exponentially, effectively preventing the algorithm from falling into an infeasible region and balancing the needs of global exploration and local development. The mathematical model of the exponential penalty mechanism introduced by the red-tailed kite algorithm is: (9); In formula (9), is the penalty value for the solution x, is the penalty factor, controlling the penalty intensity, is the problem dimension. is the violation degree of the i-th dimension, and the formula is as follows: (10); In formula (10), is the solution value on the i-th dimension, is the lower bound of the search space on the i-th dimension, is the upper bound of the search space on the i-th dimension; S2. Use the cosine adaptive transformation factor to improve the oscillation convergence problem of the transition factor TF in high-altitude soaring. The design of the transition factor TF in the high-altitude soaring stage of the red-tailed kite algorithm is not easy to change monotonically with the increase of the number of iterations, making it difficult to predict and control the exploration and exploitation balance of the algorithm. During the iteration process, periodic oscillations will occur, resulting in unstable TF parameters and prone to the phenomenon of suddenly switching from global search to local search, affecting the optimization efficiency. Using the cosine adaptive transformation factor to improve the transition factor TF in high-altitude soaring realizes a smooth transition from global search to local search, avoids the oscillation problem of the original transition factor TF, and optimizes the search dynamic characteristics of the red-tailed kite algorithm in the high-altitude soaring stage. The improved transition factor TF is: (11); In formula (11), represents the maximum number of iterations; S3. Introduce normal distribution perturbation in the diving stage, add random noise to explore the solution space, and avoid the historical optimal solution falling into the local optimum. The diving stage mainly relies on the current random direction for search. Although this strategy guides the algorithm to converge to the area close to the global optimal solution, it lacks sufficient randomness to jump out of the local optimal solution of complex problems. In the later stage of optimization, when the search focuses on the local area, the algorithm will be trapped in stagnation and unable to find the global optimum. By introducing normal distribution perturbation, the algorithm adds an independent random exploration ability to the original search mechanism. The normal distribution perturbation is triggered with a probability of 20%, and its intensity decays adaptively with the number of iterations. Larger perturbations are provided in the early stage to explore the global space, and fine perturbations are provided in the later stage to optimize the local solution. The mathematical model of the introduced normal distribution perturbation is: (12); In formula (12), is the perturbation intensity parameter, is a d-dimensional standard normal distribution random vector, is element-wise multiplication, and high and low respectively represent the upper and lower bound vectors of the search space.

[0018] Furthermore, in the step three, the improved red-tailed kite algorithm is used to optimize the parameters of the angular velocity PID controller of the mechanical angular velocity regulation system, wherein the core goal of the angular velocity PID controller parameter optimization is to adjust the three parameters of proportion, integration and differentiation so that the mechanical angular velocity regulation system can achieve comprehensive optimization in terms of tracking performance, stability and robustness. By reasonably selecting the fitness function and combining the improved red-tailed kite algorithm, a set of optimal PID parameter combinations in the mechanical angular velocity regulation system can be found. The specific steps are as follows: Step 1, parameter initialization: set the maximum number of iterations of the improved red-tailed kite algorithm and population size N, the angular velocity PID controller parameters \left [ {{K}_{p}, {K}_{i}, {K}_{d}} \right ] Encoded as the position vector of the individual red-tailed kite \left [ {{x}_{1}, {x}_{2}, {x}_{3}} \right ] , search space upper bound UB, lower bound LB, population dimension dim; Step 2, angular velocity PID controller parameter tuning: using the improved red-tailed kite algorithm, by simulating the three stages of high-altitude soaring, low-altitude circling and dive attack when the red-tailed kite is hunting, combined with spiral search and exponential penalty mechanism strategies, efficient optimization in complex parameter space, avoiding falling into local optimal, select the angular velocity PID controller parameter combination that achieves the best balance between the system dynamic response and steady-state performance. Considering the algorithm's adaptive balance characteristics for global and local searches, time multiplied by the absolute error integral is selected as the fitness function, and its mathematical formula is: (13); In formula (13), e(t) is the system error, which is the core indicator for evaluating the control effect and is used to measure the deviation between the actual output of the control system and the expected target; Step 3, parameter iteration: The Red-tailed Kite algorithm first evaluates the PID parameter combination represented by each Red-tailed Kite individual in the current population, and quantifies the system control performance corresponding to each Red-tailed Kite individual by calculating the time multiplied by the absolute error integral. After obtaining the fitness value of the current individual, the algorithm compares it with the optimal fitness value in the historical record. If the current fitness value is better, the historical optimal fitness value is updated to the current value, and the PID parameter combination corresponding to the individual is recorded as the new optimal solution. If the current fitness value does not exceed the historical optimal, the original optimal record is retained; Step 4, iterative stop judgment: judge whether the number of iterations t has reached the maximum number of iterations. If it has, stop and output the optimal solution. If it has not, continue to simulate the red-tailed kite predation process and the parameter iterative optimization process; Step 5, Parameter Deployment: Accurately map the obtained optimal solution to the parameters of the angular velocity PID controller to realize the transformation and deployment from the theoretical optimization result to the actual control system.

[0019] Furthermore, in the fourth step, MATLAB is used to conduct simulation and comparative tests on the improved mechanical angular velocity regulation system to verify its performance. It is characterized in that parameters are set in MATLAB using the improved red kite algorithm model to simulate the three stages of high-altitude soaring, low-altitude hovering, and diving attacks during the red kite's predation, optimize and find the optimal combination of angular velocity PID controller parameters. The mechanical angular velocity regulation system is modeled in MATLAB to observe the change in motor speed. The space vector pulse width modulation model receives the signal from the angular velocity PID controller and converts it into an inverter switching signal in MATLAB to invert the direct current provided by the DC power supply into three-phase alternating current to control the voltage and current of the permanent magnet synchronous motor, improving the control accuracy and system stability. The sliding mode observer estimates the rotor angular velocity based on the stator voltage and current signals of the permanent magnet synchronous motor and feeds it back to the angular velocity PID controller to provide accurate motor state information for other modules and ensure the precise control of the mechanical angular velocity regulation system.

[0020] In summary, due to the adoption of the above technical solutions, the beneficial effects of the present invention are: By introducing an exponential penalty mechanism in the red kite algorithm, the ability of the algorithm to handle constraint conditions is improved, and the problem of optimizing solutions beyond the boundary is solved. The cosine adaptive transformation factor is used to improve the TF oscillation convergence problem of the transition factor during high-altitude soaring. By controlling the exploration and exploitation balance, the search dynamic characteristics of the red kite algorithm during the high-altitude soaring stage are optimized. A normal distribution perturbation is introduced during the diving stage, and random noise is added to explore the solution space, thereby increasing the independent random exploration ability in the search mechanism. By optimizing the parameters of the angular velocity PID controller using the improved red kite algorithm, the problems of poor control accuracy and slow response of the mechanical angular velocity regulation system are solved. Description of the Drawings

[0021] Figure 1 It is a flowchart for optimizing the parameters of the angular velocity PID controller using the improved red kite algorithm.

[0022] Figure 2 It is a model diagram of the mechanical angular velocity regulation system.

[0023] Figure 3 It is a comparative curve graph of the effects of optimizing the angular velocity PID controller using the improved red kite algorithm and the original red kite algorithm.

[0024] Figure 4 It is a comparative curve graph of the fitness values of the improved red kite algorithm and the original red kite algorithm.

[0025] Figure 5This is the overall simulation effect diagram of the mechanical angular velocity regulation system. Specific implementation manners

[0026] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

[0027] The present invention provides a technical solution: a control method based on a mechanical angular velocity regulation system, and the specific steps are as Figure 1 shown.

[0028] Step 1: Build a mechanical angular velocity regulation system model.

[0029] Further, in the said Step 1, as Figure 2 shown, build a mechanical angular velocity regulation system model, including an improved red kite algorithm, an angular velocity PID controller, space vector pulse width modulation, an inverter, a permanent magnet synchronous motor, a sliding mode observer, a DC power supply, a load, and a mechanical angular velocity regulation system. The improved red kite algorithm is used to optimize the parameters of the angular velocity PID controller after improving the red kite algorithm. By adjusting the proportional coefficient, integral coefficient, and differential coefficient, the performance of the controller is made better. The angular velocity PID controller is based on the difference between the given speed and the rotor angular velocity fed back by the sliding mode observer, and outputs a control signal through proportional, integral, and differential operations to adjust the motor speed. Space vector pulse width modulation converts the output signal of the angular velocity PID controller into an inverter control signal, and generates a voltage waveform to drive the permanent magnet synchronous motor by controlling the switching state of the inverter. The inverter, under the control of the space vector pulse width modulation signal, converts the DC power of the DC power supply into three-phase alternating current to supply power to the permanent magnet synchronous motor. The permanent magnet synchronous motor operates under the action of the three-phase alternating current output by the inverter to drive the load. The sliding mode observer collects the stator voltage and current signals of the motor, estimates the rotor angular velocity information, and feeds it back to the angular velocity PID controller to achieve closed-loop control. The DC power supply provides DC electrical energy for the inverter and is the energy source of the whole system. The load is the external resistance added during the test of the whole system and is used to judge the effect of the whole system. The mechanical angular velocity regulation system is used to regulate the angular velocity of the working machinery to make the motor operation more in line with the actual requirements.

[0030] Furthermore, the mechanical angular velocity regulation system uses a DC power supply as the energy source and supplies power to the permanent magnet synchronous motor through an inverter. The switching state of the inverter is controlled by space vector pulse width modulation technology to generate a suitable voltage waveform to drive the motor. A sliding mode observer is used to estimate the angular velocity of the motor rotor in real time. The actual angular velocity fed back is compared with the given speed, and the difference is input into the angular velocity PID controller. After proportional, integral, and derivative operations, a control signal is output to adjust the motor speed. To further improve the system performance, an improved red kite algorithm is introduced to optimize the parameters of the PID controller, dynamically adjust the proportional, integral, and derivative coefficients to adapt to the load changes under different working conditions. The optimized control signal is modulated by SVPWM to drive the inverter, so that the permanent magnet synchronous motor outputs the corresponding electromagnetic torque, overcomes the load resistance torque, and realizes the precise regulation of the mechanical angular velocity, thereby constructing a high-efficiency, stable, and strong self-adaptive closed-loop mechanical angular velocity regulation system.

[0031] Furthermore, the angular velocity PID controller is the core of the mechanical angular velocity regulation system, and its working principle is based on the given speed command and the actual speed fed back by the sliding mode observer The error generates a control signal through the weighted combination of the proportional, integral, and derivative links , and adjusts the input voltage or current of the motor to achieve speed tracking. The specific mathematical model is shown as follows: (1); In Equation (1), the proportional link instantly amplifies the current error and quickly responds to the speed deviation. The integral link eliminates the static deviation by accumulating the historical error to ensure the steady-state accuracy of the system. The derivative link predicts the future trend according to the error change rate, suppresses overshoot, and improves the system stability.

[0032] Furthermore, the switching state of the inverter is controlled by space vector pulse width modulation technology. By precisely combining the switching states of the three-phase bridge arms of the inverter, a reference voltage vector with any phase and amplitude is synthesized, and then the permanent magnet synchronous motor is driven. The switching state of the inverter is controlled by space vector pulse width modulation technology. The dq axis voltage command output by the current loop is converted to and in the two-phase stationary coordinate system through inverse Park transformation, constructs a reference voltage vector . After determining the sector where the vector is located through the sector judgment function, the action time of adjacent effective vectors and the zero vector time are calculated according to the volt-second balance principle, and the conduction and cut-off of 6 switching devices of the inverter are controlled according to a specific switching sequence, so that the average output voltage approaches , to achieve precise control of the permanent magnet synchronous motor, the mathematical model of the voltage vector is shown as follows: (2); In Equation (2), in the two-phase stationary coordinate system, , is the projection component of the voltage vector, j is the imaginary unit, is the expected synthesized average voltage vector, whose amplitude determines the voltage magnitude, and the phase angle θ determines the voltage direction, and .

[0033] Further, a sliding mode observer is used to estimate the angular velocity of the motor rotor in real time. The sliding mode observer constructs a sliding mode surface containing system uncertainties and uses high-frequency switching control to make the system state converge to the sliding mode surface, realizing the real-time estimation of the angular velocity of the motor rotor. The observer mainly estimates the currents and to approximate the actual currents, and the mathematical model is shown as follows: (3); In Equation (3), and are the current estimation errors, and , , and are the sliding mode control rates, R is the stator resistance, L is the stator inductance, is the permanent magnet flux linkage, is the estimated value of the rotor angular velocity, is the estimated value of the rotor position angle.

[0034] Step 2: Construct the mathematical model of the red kite algorithm and improve the red kite algorithm.

[0035] Further, in the above Step 2, the construction of the mathematical model of the red kite algorithm is characterized in that the red kite algorithm simulates the hunting process of the red kite and is divided into three stages: high-altitude soaring, low-altitude hovering, and dive attack, and each stage corresponds to different strategies in the algorithm. The actions taken in each hunting stage are shown and modeled. The mathematical models of the three stages are as follows: D1. High-altitude soaring stage: The red kite flaps its wings at a low frequency and makes large-span circles at high altitude, using the updraft to search for the prey position over a large range, exploring the global search space and identifying potential prey areas. The high-altitude soaring stage mainly guides the search through Levy flight and the population mean position. The mathematical model of this stage is shown as follows: (4); In Equation (4), is the position of the red kite at iteration t, is the best position obtained so far, is the average of all position solutions, TF is the transition factor, and Levy represents the Levy function. The formula for the Levy function is as follows: (5); In Equation (5), s is a constant with a value of 0.01, dim is the dimension of the problem, is a constant with a value of 1.5, and are random numbers in the range [0,1]; D2. Low-altitude hovering stage: After locking the general area of the prey, the red kite reduces its flight altitude and hovers around the prey in a spiral trajectory, narrowing the search range and determining the best attack position, corresponding to the local exploitation stage in the optimization. The mathematical model for this stage is shown in the following equation: (6); In Equation (6), StepSize( t ) is the step size, which is calculated based on the difference between the current position and the mean to ensure convergence to the optimal solution. x(t) and y(t) are the spiral coordinates, and their mathematical formulas are shown in the following equation: (7); In Equation (7), R(t) is the radius, and , represents the initial radius when the red kite starts flying around the prey, and its value ranges between [0.5, 3], is the angle, and , A is the angle gain, with a value range between [5, 15], rand is a random number in the range [0, 1], and r is the control gain, with a value between [1, 2]. These parameters are necessary for the algorithm to simulate the movement of the red kite flying around the prey in a spiral shape; D3. Dive attack stage: The red kite will suddenly dive from the best position obtained in the low-altitude soaring stage and attack the prey, accurately hitting the prey, corresponding to the fast convergence stage of the optimization algorithm. The mathematical model for this stage is shown in the following equation: (8); In Equation (8), and are both step size adjustment functions, which adjust the step size from two dimensions: the difference between the population mean and the guidance of the optimal solution respectively, is the acceleration factor, which is used to accelerate the convergence speed, and ， is the gravity factor, which is used to reduce the search randomness, and .

[0036] Furthermore, in the second step, the red kite algorithm is improved in three steps: an exponential penalty mechanism is introduced into the red kite algorithm to enhance the algorithm's ability to handle constraint conditions; the cosine adaptive transformation factor is used to improve the oscillation convergence problem of the transition factor TF during high-altitude soaring; a normal distribution perturbation is introduced during the diving stage, and random noise is added to explore the solution space to prevent the historical optimal solution from falling into a local optimum. The specific steps are as follows: S1. An exponential penalty mechanism is introduced into the red kite algorithm to enhance the algorithm's ability to handle constraint conditions. When dealing with the problem of solutions exceeding the boundary, the red kite algorithm simply forces the solutions back to the boundary, completely ignoring the information about the direction and degree of overstepping the boundary, which easily leads to the algorithm oscillating near the boundary and missing potential optimal solutions. After introducing the exponential penalty mechanism, the penalty intensity can be dynamically adjusted according to the degree of overstepping the boundary of the solution. When the overstepping is slight, the penalty is small, allowing the algorithm to moderately explore the boundary region. When the overstepping is severe, the penalty increases exponentially, effectively preventing the algorithm from falling into an infeasible region and balancing the needs of global exploration and local development. The mathematical model of the exponential penalty mechanism introduced by the red kite algorithm is: (9); In formula (9), is the penalty value for solution x, is the penalty factor, controlling the penalty intensity, is the problem dimension, is the degree of violation of the i-th dimension, and the formula is as follows: (10); In formula (10), is the solution value on the i-th dimension, is the lower bound of the search space on the i-th dimension, is the upper bound of the search space on the i-th dimension; S2. The cosine adaptive transformation factor is used to improve the oscillation convergence problem of the transition factor TF during high-altitude soaring. The design of the transition factor TF during the high-altitude soaring stage in the red kite algorithm is not easy to monotonically change with the increase of the number of iterations, making it difficult to predict and control the balance between the exploration and development of the algorithm. Periodic oscillations will occur during the iteration process, resulting in unstable TF parameters and easily causing the phenomenon of suddenly switching from global search to local search, affecting the optimization efficiency. Using the cosine adaptive transformation factor to improve the transition factor TF during high-altitude soaring realizes a smooth transition from global search to local search, avoids the oscillation problem of the original transition factor TF, and optimizes the search dynamic characteristics of the red kite algorithm during the high-altitude soaring stage. The improved transition factor TF is: (11); In formula (11), denotes the maximum number of iterations; S3. Introduce a normal distribution perturbation during the dive phase, add random noise to explore the solution space, and avoid the historical optimal solution falling into a local optimum. The dive phase mainly relies on the current random direction for search. Although this strategy guides the algorithm to converge to the region close to the global optimal solution, it lacks sufficient randomness to jump out of the local optimal solution of complex problems. In the later stage of optimization, when the search focuses on a local area, the algorithm will be stuck and unable to find the global optimal solution. By introducing a normal distribution perturbation, the algorithm adds an independent random exploration ability to the original search mechanism. The normal distribution perturbation is triggered with a probability of 20%, and its intensity decays adaptively with the number of iterations. A larger perturbation is provided in the early stage to explore the global space, and a fine perturbation is provided in the later stage to optimize the local solution. The mathematical model of the introduced normal distribution perturbation is: (12); In formula (12), is the perturbation intensity parameter, is a d-dimensional standard normal distribution random vector, is element-wise multiplication, and high and low respectively represent the upper and lower bound vectors of the search space.

[0037] Step 3. Use the improved red kite algorithm to optimize the parameters of the angular velocity PID controller of the mechanical angular velocity regulation system.

[0038] Furthermore, in the said step 3, when using the improved red kite algorithm to optimize the parameters of the angular velocity PID controller of the mechanical angular velocity regulation system, it is characterized in that the core objective of the PID controller parameter optimization is to achieve comprehensive optimization in terms of tracking performance, stability, and robustness of the mechanical angular velocity regulation system by adjusting the three parameters of proportional, integral, and differential. By reasonably selecting the fitness function and combining the improved red kite algorithm, a set of optimal PID parameter combinations for the mechanical angular velocity regulation system can be found. The specific steps are as follows: step1. Parameter initialization: Set the maximum number of iterations of the improved red kite algorithm and the population size N, and encode the angular velocity PID controller parameters \(\left [ {{K}_{p}, {K}_{i}, {K}_{d}} \right ]\) as the position vector \(\left [ {{x}_{1}, {x}_{2}, {x}_{3}} \right ]\) of the red kite individual, the upper bound UB of the search space, the lower bound LB, and the population dimension dim; Step 2: Tuning of the angular velocity PID controller parameters: The improved red kite algorithm is adopted. By simulating the three stages of high-altitude soaring, low-altitude hovering, and dive attack during the red kite's predation, combined with the spiral search and exponential penalty mechanism strategy, efficient optimization is carried out in the complex parameter space to avoid falling into local optima. The parameter combination of the angular velocity PID controller that enables the best balance between the system's dynamic response and steady-state performance is selected. Considering the self-adaptive balance characteristics of the algorithm for global and local search, the integral of time multiplied by the absolute error is selected as the fitness function, and its mathematical formula is: (13); In Equation (13), e(t) is the system error, which is the core index for evaluating the control effect and is used to measure the deviation between the actual output and the desired target of the control system; Step 3: Parameter iteration: The red kite algorithm first evaluates the PID parameter combination represented by each red kite individual in the current population. By calculating the integral of time multiplied by the absolute error, the system control performance corresponding to each red kite individual is quantified. After obtaining the fitness value of the current individual, the algorithm compares it with the optimal fitness value in the historical record. If the current fitness value is better, the historical optimal fitness value is updated to the current value, and at the same time, the PID parameter combination corresponding to this individual is recorded as the new optimal solution. If the current fitness value does not exceed the historical optimum, the original optimal record is retained; Step 4: Iteration termination judgment: Determine whether the iteration number t has reached the maximum iteration number. If it has, stop and output the optimal solution. If not, continue to execute the process of simulating the red kite predation process and parameter iteration optimization; Step 5: Parameter deployment: The obtained optimal solution is accurately mapped into the parameters of the angular velocity PID controller to realize the transformation and deployment of the theoretical optimization result to the actual control system.

[0039] Step 4: Use MATLAB to conduct simulation and comparative experiments on the improved mechanical angular velocity regulation system to verify the performance.

[0040] Further, in the fourth step, MATLAB is used to conduct simulation and comparative tests on the improved mechanical angular velocity regulation system to verify its performance. It is characterized in that parameters are set in MATLAB using the improved red kite algorithm model, simulating the three stages of high-altitude soaring, low-altitude hovering, and dive attack when the red kite preys, optimizing and searching for the optimal parameter combination of the angular velocity PID controller. The mechanical angular velocity regulation system is modeled in MATLAB, observing the change in motor speed. The space vector pulse width modulation model receives the signal of the angular velocity PID controller and is converted into an inverter switching signal in MATLAB, converting the direct current provided by the DC power supply into three-phase alternating current to control the voltage and current of the permanent magnet synchronous motor, improving the control accuracy and system stability. The sliding mode observer estimates the rotor angular velocity based on the stator voltage and current signals of the permanent magnet synchronous motor and feeds it back to the angular velocity PID controller, providing accurate motor state information for other modules and ensuring the precise control of the mechanical angular velocity regulation system.

[0041] Figure 3 It is a comparative curve graph of the effects of the improved red kite algorithm and the original red kite algorithm on optimizing the angular velocity PID controller. By optimizing the parameters of the angular velocity PID controller, under the condition of reaching the set target value of 1, the improved red kite algorithm has a smaller oscillation amplitude, a faster initial response speed, and a shorter time to reach the steady state than the original red kite algorithm. All aspects indicate that the improved red kite algorithm has a better control effect on the angular velocity PID controller.

[0042] Figure 4 It is a comparison of the fitness value curve graphs of the improved red kite algorithm and the original red kite algorithm. Throughout the iteration cycle, the fitness value obtained by the improved red kite algorithm has been continuously smaller than that obtained by the original red kite algorithm after the second iteration. The fitness value is the target orientation for algorithm optimization. According to the principle that the smaller the fitness value, the better the algorithm performance, and the lower the fitness value, usually representing a higher quality of the solution, the improved red kite algorithm performs better in jumping out of local optima and continuously exploring better solutions.

[0043] Figure 5 It is the overall simulation effect diagram of the improved red kite algorithm optimizing the angular velocity PID controller to control the mechanical angular velocity regulation system, showing the law of the change of the rotational speed of the mechanical angular velocity regulation system over time. The set speed of the system is 1000. After the simulation starts, the rotational speed quickly climbs to around 1200, then rapidly drops and stabilizes at 1000 in a short time, and then remains stable, indicating that the system can respond quickly and tend to a stable rotational speed, demonstrating good dynamic response characteristics and steady-state control effects of the mechanical angular velocity regulation system.

Claims

1. A control method based on a mechanical angular velocity regulation system, characterized in that, By improving the red kite algorithm to optimize the angular velocity PID controller, the problem of limited parameter adaptability of the traditional angular velocity PID controller is solved, and further, the dynamic response performance of the mechanical angular velocity regulation system in the face of different external disturbances is improved. The specific steps are as follows: Step 1: Build a mechanical angular velocity regulation system model; Step 2: Construct a mathematical model of the red kite algorithm and improve the red kite algorithm. There are mainly three improvements to the red kite algorithm, which are as follows: S1: Introduce an exponential penalty mechanism into the red kite algorithm. By punishing out-of-bounds behaviors, the algorithm is guided towards solutions that meet the constraints, dynamically quantifying the degree of out-of-bounds and then matching the exponential penalty intensity. Specifically, calculate the deviation of the actual value of each solution in each dimension from the boundary range. If the solution exceeds the upper and lower bounds, it is determined as a violation. The farther the deviation distance, the higher the degree of violation, and then the degree of violation imposes a penalty on the solution, and the penalty intensity increases exponentially with the degree of violation; S2: Use the cosine adaptive transformation factor to improve the problem of the TF oscillation convergence of the transition factor during high-altitude soaring. Specifically, utilize the monotonically decreasing characteristic of the cosine function within the interval, combine the iterative process with the change trend of the cosine function, so that the value of the transition factor TF is adaptively adjusted based on the cosine function law as the number of iterations increases, and guide TF to smoothly transition from the larger value required for the global search mode to the smaller value required for the local search mode through the continuous waveform characteristic of the cosine function; S3: Introduce a normal distribution perturbation during the dive phase and add random noise to explore the solution space. Specifically, the normal distribution perturbation is centered on the current optimal solution to generate random noise, so that the newly generated solutions are distributed near the current optimal solution with a high probability, ensuring that they will not deviate too far from the feasible region; at the same time, solutions far from the current optimal solution are generated with a low probability to explore the areas in the solution space that have not been discovered yet; Step 3: Use the improved red kite algorithm to optimize the parameters of the angular velocity PID controller of the mechanical angular velocity regulation system; Step 4: Use MATLAB to conduct simulation and comparison tests on the improved mechanical angular velocity regulation system to verify the performance.

2. The control method of a mechanical angular velocity adjustment system according to claim 1, characterized in that, In the first step, a mechanical angular velocity adjustment system model is built, which includes an improved red kite algorithm, an angular velocity PID controller, space vector pulse width modulation, an inverter, a permanent magnet synchronous motor, a sliding mode observer, a DC power supply, a load, and a mechanical angular velocity adjustment system. The improved red kite algorithm is used to optimize the parameters of the angular velocity PID controller after improving the red kite algorithm. By adjusting the proportional coefficient, integral coefficient, and differential coefficient, the performance of the controller is made better. The angular velocity PID controller calculates the difference between the given rotational speed and the rotor angular velocity feedback from the sliding mode observer, and through proportional, integral, and differential operations, outputs a control signal to adjust the motor speed. Space vector pulse width modulation converts the output signal of the angular velocity PID controller into an inverter control signal. By controlling the switching state of the inverter, a voltage waveform is generated to drive the permanent magnet synchronous motor. The inverter, under the control of the space vector pulse width modulation signal, converts the DC power of the DC power supply into three-phase alternating current to supply power to the permanent magnet synchronous motor. The permanent magnet synchronous motor operates under the action of the three-phase alternating current output by the inverter, drives the load to work. The sliding mode observer collects the stator voltage and current signals of the motor, estimates the rotor angular velocity information, and feeds it back to the angular velocity PID controller to achieve closed-loop control. The DC power supply provides DC electrical energy for the inverter and is the energy source of the entire system. The load is the external resistance added during the test of the entire system and is used to judge the effect of the overall system. The mechanical angular velocity adjustment system is used to adjust the angle of the working machinery to make the motor operation more in line with the actual requirements.

3. The control method of a mechanical angular velocity adjustment system according to claim 2, characterized in that, In S1, an exponential penalty mechanism is introduced into the red kite algorithm to enhance the algorithm's ability to handle constraint conditions. When dealing with the problem of solutions beyond the boundary, the red kite algorithm simply forces them back to the boundary, completely ignoring the information about the direction and degree of overstepping the boundary, resulting in the algorithm oscillating near the boundary and missing potential optimal solutions. After introducing the exponential penalty mechanism, the penalty strength can be dynamically adjusted according to the degree of solution overstepping the boundary. When the overstepping is slight, the penalty is small, allowing the algorithm to moderately explore the boundary region. When the overstepping is severe, the penalty increases exponentially to prevent the algorithm from falling into an infeasible region, balancing the needs of global exploration and local exploitation. The mathematical model of the exponential penalty mechanism introduced by the red kite algorithm is as follows: （9）； In Equation (9), is the penalty value for the solution x, is the penalty factor, which controls the penalty intensity, is the problem dimension, is the degree of violation of the i-th dimension, and the formula is as follows: （10）； In formula (10), is the solution at the i-th dimension, is the lower bound of the search space at the i-th dimension, is the upper bound of the search space at the i-th dimension.

4. A control method for a mechanical angular velocity regulation system according to claim 3, characterized in that, In S2, a cosine adaptive transformation factor is used to improve the oscillation convergence problem of the transition factor TF during high-altitude soaring. The design of the transition factor TF during the high-altitude soaring stage in the red kite algorithm is not easily monotonically changed with the increase in the number of iterations, making it difficult to predict and control the balance between the exploration and exploitation of the algorithm. Periodic oscillations will occur during the iteration process, resulting in unstable TF parameters and prone to sudden transitions from global search to local search, affecting the optimization efficiency. Using a cosine adaptive transformation factor to improve the transition factor TF during high-altitude soaring achieves a smooth transition from global search to local search, solves the oscillation problem of the original transition factor TF, and optimizes the search dynamic characteristics of the red kite algorithm during the high-altitude soaring stage. The improved transition factor TF is as follows: （11）； In formula (11), represents the maximum number of iterations.

5. A control method based on a mechanical angular velocity regulation system according to claim 4, characterized in that, S3 introduces a normal distribution perturbation during the dive phase, adding random noise to explore the solution space and prevent the historical optimal solution from falling into a local optimum. The dive phase mainly relies on the current random direction for search. Although this strategy guides the algorithm to converge to the region close to the global optimal solution, it lacks randomness to jump out of the local optimum of complex problems. In the later stage of optimization, when the search focuses on a local area, the algorithm will be unable to find the global optimal solution due to being trapped in stagnation. By introducing a normal distribution perturbation, the algorithm adds an independent random exploration ability to the original search mechanism. The normal distribution perturbation is triggered with a probability of 20%, and its intensity decays adaptively with the number of iterations. A large perturbation is provided in the early stage to explore the global space, and a fine perturbation is provided in the later stage to optimize the local solution. The mathematical model of the introduced normal distribution perturbation is as follows: （12）； In formula (12), is the perturbation intensity parameter, is a d-dimensional standard normal distribution random vector, is element-wise multiplication, and high and low respectively represent the upper and lower bound vectors of the search space.

6. The control method of a mechanical angular velocity adjustment system according to claim 5, wherein In step three, the improved red kite algorithm is used to optimize the parameters of the angular velocity PID controller of the mechanical angular velocity regulation system. The core objective of optimizing the parameters of the angular velocity PID controller is to achieve an overall optimum in terms of tracking performance, stability, and robustness of the mechanical angular velocity regulation system by adjusting the three parameters of proportional, integral, and differential. By reasonably selecting the fitness function and combining it with the improved red kite algorithm, a set of optimal PID parameter combinations for the mechanical angular velocity regulation system can be found. The specific steps are as follows: step1. Parameter initialization: Set the maximum number of iterations of the improved red kite algorithm and the population size N, and encode the angular velocity PID controller parameters as the position vector of the red kite individuals , the upper bound UB of the search space, the lower bound LB, and the population dimension dim; Step 2: Tuning of the angular velocity PID controller parameters: The improved red kite algorithm is adopted. By simulating the three stages of high-altitude soaring, low-altitude hovering, and dive attack during the red kite's predation, combined with the spiral search and exponential penalty mechanism strategy, efficient optimization is carried out in the complex parameter space to avoid falling into a local optimum. The angular velocity PID controller parameter combination that makes the dynamic response and steady-state performance of the system reach the best balance is selected. Considering the adaptive balance characteristics of the algorithm for global and local search, the time multiplied by the integral of the absolute error is selected as the fitness function, and its mathematical formula is: （13）； In Equation (13), e(t) is the system error, which is the core index for evaluating the control effect and is used to measure the deviation between the actual output and the expected target of the control system. Step 3: Parameter iteration: The red kite algorithm first evaluates the PID parameter combinations represented by each red kite individual in the current population. By calculating the time multiplied by the integral of the absolute error, the system control performance corresponding to each red kite individual is quantified. After obtaining the fitness value of the current individual, the algorithm compares it with the optimal fitness value in the historical record. If the current fitness value is better, the historical optimal fitness value is updated to the current value, and at the same time, the PID parameter combination corresponding to this individual is recorded as the new optimal solution. If the current fitness value does not exceed the historical optimum, the original optimal record is retained. Step 4: Iteration termination judgment: It is judged whether the number of iterations t has reached the maximum number of iterations. If it has, the iteration stops and the optimal solution is output. If not, the process of simulating the red kite's predation process and parameter iteration optimization continues. Step 5, Parameter Deployment: Accurately map the obtained optimal solution to the parameters of the angular velocity PID controller to achieve the transformation and deployment of the theoretical optimization results to the actual control system.

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