Balancing machine main shaft rotating speed control method for optimizing PID parameters

Abstract

The invention discloses a balancing machine main shaft rotating speed control method for optimizing PID parameters, and belongs to the technical field of balancing machine main shaft control optimization. In order to solve the problems that PID controller parameters need to be set depending on experience, parameter setting is complex, and the fitness is poor, the technical scheme provided by the invention is as follows: according to a mechanical structure of a dynamic balance detection system, a mathematical model for balancing machine main shaft rotating speed control is established, and a transfer function is solved; and the control model and the transfer function are imported into a PSO-BP-PID controller, the controller outputs a control quantity according to the input system deviation signal and the control parameter, and an execution mechanism adjusts the rotating speed of a main shaft of the balancing machine according to the control quantity. Wherein the PID parameter of the PSO-BP-PID controller is solved by a BP (Back Propagation) neural network; and then, using a PSO algorithm to optimize the training process of the BP neural network, and realizing stable control of the rotating speed of the balancing machine main shaft. The method is high in data identification precision, high in algorithm convergence speed and high in system stability, and the stability of balancing machine spindle control is improved.

Description

Technical Field

[0001] The invention relates to the technical field of balancing machine spindle control optimization, and in particular to a balancing machine spindle speed control method based on PSO-BP-PID. Background Art

[0002] In operation, the brake disc of an automobile is a high-speed rotating rotor. The rotor is the main component of a rotating machine. When the rotor is unbalanced, it is usually accompanied by vibration and noise. The abnormal vibration and noise caused by the rotor imbalance will cause the mechanical device to fail. Therefore, to ensure the smooth operation of the rotating machine, the rotor needs to be dynamically balanced. In recent years, although domestic dynamic balancing machines have made great progress, the dynamic balancing machine technology is still restricted by overseas companies. Therefore, it is of great significance to conduct research on dynamic balancing control technology. For the detection station of the balancing machine, ensuring the stability of the rotor speed during the sampling time is the prerequisite for the accurate extraction of the unbalanced signal, that is, it is necessary to achieve stable control of the spindle rotation and rotor positioning.

[0003] In order to reduce errors and improve the stability and control accuracy of the control system, proportional-integral-differential (PID) control is often used in industry to control the servo system. However, the traditional PID control method is based on the experience of engineers to adjust the PID parameters through the "trial and error method", so the control process error is relatively large and the control effect is not ideal. With the innovation and development of production technology, enterprises have put forward higher requirements on the stability, response speed and tracking accuracy of the balancing detection station. The traditional trial and error method can no longer meet the precise control requirements of the balancing machine, and there are many safety hazards. In addition, in the current efficient production process, the process does not allow operating engineers to conduct frequent trials. Therefore, in view of the problems that the PID controller parameters need to rely on experience to set, the parameter setting is complex, and the fitness is poor, the relevant intelligent algorithm is used to optimize the control system, and the development of a high-precision, fast-response balancing machine spindle speed controller has great application value. Summary of the invention

[0004] The present invention studies the control method of a dynamic balancing detection station servo system and designs a controller combining a particle swarm algorithm, a BP neural network and a PID algorithm. The controller can adaptively adjust three parameters of the PID control.

[0005] The technical solution of the present invention is: a balancing machine spindle speed control method based on PSO-BP-PID parameters, which specifically includes the following steps:

[0006] 1) According to the mechanical structure of the dynamic balancing detection system, a mathematical model for the spindle speed control of the balancing machine is established, and the transfer function is obtained;

[0007] 2) PID controller design:

[0008] The input and output of the system are respectively and , the deviation signal is defined as PID control output for:

[0009] u t = K P E t + K P K I ∫ 0 t [ K D d ( E t ) dt + E t dt ] (1)

[0010] in, is the proportionality coefficient, and They are the integral and differential constants related to the time variable t, and these three parameters will directly affect the performance of the PID controller. Therefore, the essence of this type of controller design is to determine the optimal three parameters so that the performance of the control system reaches the optimal solution.

[0011] The above is a position-based PID algorithm, but since the system needs to take into account the error between the previous moment and the previous moment, its shortcomings are obvious. Therefore, the present invention adopts an incremental PID algorithm, which records , the formula is as follows:

[0012] (2)

[0013] From the above formula, we can see that when , and After determination, the system output increment can be obtained .

[0014] 3) BP neural network design:

[0015] BP neural network consists of input layer, output layer and hidden layer, and its structure is as follows: Figure 1 As shown in the figure, all the neuron nodes between its layers are connected, and the nodes in the same layer are not connected. A complete BP neural network training includes two steps. The first is the propagation of information from left to right, which is called forward propagation, that is, putting the known data into the input layer, entering the hidden layer through the network and being processed in it, and then output by the output layer; the second is the back propagation of the error, that is, calculating the error between the actual output value and the expected output value, and then correcting the weight of the entire network and the threshold of each node until the error converges to the minimum.

[0016] The detailed steps of the BP neural network algorithm are as follows:

[0017] A. Initialization of weights

[0018] Assume that the number of neurons in the input layer is i, the number of neurons in the hidden layer is q, and the number of neurons in the output layer is j; the weight between the hidden layer and the input layer is recorded as , the weight between the output layer and the hidden layer is .

[0019] B. Forward Propagation Process

[0020] After clarifying the activation function and weight value of the neural network, the nth neuron node in the first layer has the following expression:

[0021] (3)

[0022] The input of the mth neuron in the hidden layer is:

[0023] (4)

[0024] The calculation results of the hidden layer need to be processed by functions before being output. * ) is the nonlinear activation function of the input layer:

[0025] (5)

[0026] The calculation formula of the kth node of the output layer is as follows, and the weighted sum of the output results of the hidden layer is obtained:

[0027] (6)

[0028] Next, we obtain the output result of the output layer, G( * ) is the nonlinear activation function of the output layer:

[0029] (7)

[0030] At the same time, the error between the output value and the input value can be calculated:

[0031] (8)

[0032] in, is the target setting value for the kth output node, is the actual output value of the kth output node.

[0033] C. Back Propagation Process

[0034] Since there is a deviation between the final output value and the given value during the forward propagation calculation process, if this error system does not allow, back propagation calculation is required. According to the chain rule and the gradient descent method, the threshold and weight in the network are updated to make the output result closer to the set value. In this method, the threshold and weight updated each time are shown in the following formula:

[0035] (9)

[0036] (10)

[0037] According to the rules of the gradient descent method, let r be the number of training of the algorithm, and the weight and threshold iteration formulas between the output layer and the hidden layer can be obtained respectively:

[0038] (11)

[0039] (12)

[0040] The weight and threshold iteration formulas between the output layer and the hidden layer are:

[0041] (13)

[0042] (14)

[0043] According to the above formula, the weight coefficient and threshold are continuously updated and iterated. After multiple iterations, the system error is continuously reduced to a reasonable threshold range, meeting the performance requirements of the system.

[0044] 4) PSO-BP-PID controller design:

[0045] The purpose of the PSO algorithm is to particle each individual in the population in a given D-dimensional search space, so that each particle has position and velocity attributes. After the algorithm is started, these particles will be located at the initial position and search for food in the direction of the initial velocity; during the iteration process, the fitness function defined in the algorithm is used to determine whether the particle is in a suitable position. If so, the position information will be recorded, otherwise the iteration will continue. The iterative process changes the position and velocity of the particle according to formula (15).

[0046] (15)

[0047] In the formula, represents the position of the particle at time t, represents the velocity of the particle at time t, represents the most suitable position found by the sth particle locally, represents the most suitable position of the i-th particle in the entire population, refers to the inertia weight, refers to the learning factor, Refers to a random number between 0 and 1.

[0048] When training the BP neural network using the PSO algorithm, follow the steps below:

[0049] A. Set PSO parameters: including the total number of particle swarms, number of iterations, weight factor, particle search range, and the position and speed of particles in the initial state;

[0050] B. Calculate the fitness of particles;

[0051] C. Compare the fitness of each particle with the local most suitable position , iterate it;

[0052] D. Compare the most suitable positions of each particle locally The most suitable position in the group , change ;

[0053] E. Adjust the position and speed of each particle;

[0054] F. Repeat steps B to E until the particle swarm optimization is completed;

[0055] G. Set the initial parameters of the BP neural network to The corresponding particles are trained according to the previous BP neural network process, running the forward propagation and back propagation algorithms, calculating the output of the neural network, then calculating the output error, and finally adjusting the basic parameters of the neural network.

[0056] H. Repeat step G until the requirements of the BP neural network are met;

[0057] In summary, the spindle speed controller of PSO-BP-PID is as follows Figure 2 The controller consists of three parts: (1) a closed-loop PID controller is used to adaptively adjust the PID parameters using a BP neural network; (2) the PSO algorithm is used to optimize the BP neural network parameters, thereby accelerating the convergence of the algorithm; (3) after the BP neural network is optimized by the PSO algorithm, the PID parameters in the controlled system are adaptively adjusted until the PID parameters are obtained. , and The optimal value of . BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 BP neural network model

[0059] Figure 2 PSO-BP-PID controller

[0060] Figure 3 Mechanical structure of the swing frame system

[0061] Figure 4 The fixture structure diagram

[0062] Figure 5 Motor schematic diagram

[0063] Figure 6 Comparison diagram of system step response curve

[0064] Figure 7 Comparison chart of system error change curve

[0065] Figure 8 PID output parameter adjustment curve DETAILED DESCRIPTION

[0066] It should be noted that the following descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise expressly stated, all technical and scientific terms used in the present invention have the same meanings as those understood by those skilled in the art to which the present application belongs. Example

[0067] The embodiment of the present invention is based on the balancing machine swing frame system, and its simplified mechanical transmission mechanism model is as follows Figure 3 As shown, the rotation of the motor is used as the system input, the rotation of the fixture and the workpiece module is used as the output, and they are connected by a belt drive. According to an embodiment of the present invention, a balancing machine spindle speed control method based on PSO-BP-PID is disclosed, comprising the following steps:

[0068] 1) Construction of mathematical model for speed control of swing frame system

[0069] Assuming that the components of the swing frame system are rigid transmission, the rotational inertia of each part is equivalently converted to the motor shaft, and the rotational inertia formula is as follows:

[0070] (16)

[0071] When the center of the cylinder is used as the rotation axis, the formula for the moment of inertia of the cylinder is as follows:

[0072] (17)

[0073] in, is the moment of inertia of the motor rotor, which is 2.1×10 -2 kg·m 2 ;

[0074] is the moment of inertia of the small pulley, calculated by the above formula, its value is 3.929×10 -3 kg·m 2 ,in is the radius of the small pulley, which is 56 mm. The mass of the small pulley is calculated. The value is 2.506kg; is the motor shaft speed, the value is 1600r / min; is the rotation speed of the large pulley shaft, the value is 800r / min;

[0075] is the moment of inertia of the large pulley. Similarly, its value is 6.272×10 -2 kg·m 2 , where the pulley diameter is 112 mm, the mass is calculated The value of is 10.012kg;

[0076] is the moment of inertia of the fixture, and its value is calculated to be 8.428×10 -3 kg·m 2 , the structure diagram of the fixture is shown in Figure 4 , this part can be regarded as three cylinders with different diameters, whose diameters are 125mm, 85mm and 165mm respectively, and the mass is about 6.743kg;

[0077] is the moment of inertia of the workpiece module, and its value is calculated to be 1.585×10 -1 kg·m 2 The workpiece diameter is 286mm and the mass is approximately 7.75kg.

[0078] Finally, the equivalent moment of inertia of the motor shaft is converted to 0.0823 kg·m 2 .

[0079] In the servo control system used in this chapter, the permanent magnet DC motor is used as the control object, and the motor needs to be modeled. Taking the system designed in this section as an example, the motor is designed according to the main technical indicators. The schematic diagram of the motor is shown in Figure 5 shown.

[0080] Next, a mathematical model is established based on the motor's potential balance equation and torque balance equation.

[0081] The potential balance formula of the motor is:

[0082] (18)

[0083] in, is the armature current, is the armature inductance, is the armature voltage, is the armature resistance, is the motor shaft angle, is the back electromotive force of the motor, , is the motor related structural constant, is the armature speed.

[0084] The torque balance of the motor is:

[0085] (19)

[0086] in, is the moment of inertia of the motor shaft, is the viscosity coefficient of the motor. After sorting, we can get:

[0087] (20)

[0088] Ignore the effect of motor inductance and set the armature inductance Taking the approximate value 0, we can get:

[0089] (20)

[0090] The transfer function of the second-order system can be obtained by Laplace transforming the above equation, and the main parameters of the motor shown in Table 1 can be substituted into the equation (22):

[0091] G(s)=\frac {{θ}_{m}(s)} {U(s)}=\frac {{K}_{T}} {J{r}_{a}{s}^{2}+s[{r}_{a}{f}_{m}+{K}_{T}{K}_{e}]}=\frac {0.4895} {0.0905{s}^{2}+0.1525s} (twenty two)

[0092] Table 1 Main parameters of the motor

[0093] Motor parameters Parameter Value <![CDATA[Armature resistance r a > 1.1Ω <![CDATA[Armature inductance L a > 0.0043H Logarithm of level P 4 <![CDATA[Back electromotive force constant K e > 0.03437 (v / rad / s) <![CDATA[Torque constant K T > 0.4895 (N·m / A) <![CDATA[Viscosity coefficient f m > 0.1236 (N·s / m²)

[0094] 2) PSO-BP-PID controller parameter setting and simulation experiment

[0095] In the PSO-BP-PID controller, the total number of particle swarms is set to 50, the iterations are 100, and the learning factor is , the individual particle positions are set in the range [-0.3, 0.3], and the maximum weight , minimum weight .

[0096] The effectiveness of the controller designed by the present invention in the detection station control system is verified by simulation. In the MATLAB environment, unit step response simulation experiments are performed on the PID controller, BP-PID controller and PSO-BP-PID controller respectively. Specifically, a unit step signal is input to the system, and the controller performance is evaluated by parameters such as the system adjustment time and the system overshoot. The system overshoot and the system adjustment time in the unit step signal simulation experiment can be obtained, as shown in Table 2.

[0097] Table 2 Step signal simulation experiment results

[0098] parameter PID BP-PID PSO-BP-PID Overshoot (%) 20% 16% 10.2% Adjustment time (s) 1.35 0.53 0.24

[0099] Figure 6 The advantages and disadvantages of the three algorithms are reflected. In the unit step simulation experiment, the controller with the best performance is the PSO-BP-PID controller, which has the lowest overshoot in the simulation and the shortest adjustment time. The optimization effect of applying the PSO-BP-PID controller to the servo system control is obvious. It can not only reach a steady state in a short time, but also has a low vibration frequency and small amplitude during the adjustment process, and the control effect is good. Figure 7 shown.

[0100] Figure 8 It shows the output of the PSO-BP-PID controller after particle swarm optimization. , and , that is, the PSO-BP-PID controller uses autonomous learning and adaptive adjustment to make the optimized , and Three parameters enable the system to achieve optimal performance.

[0101] The above examples are only used to illustrate the technical solution of the present application, rather than to limit it; the above examples are used to help understand the method of the present invention and its core ideas; at the same time, there will be certain modifications and substitutions in the specific implementation methods and application scope for general technical personnel in this field; and these substitutions or modifications do not make the essence of the corresponding technical solution deviate from the protection scope of the technical solution of the embodiment of the present invention.

Claims

1. A balancing machine spindle speed control method for optimizing PID parameters, characterized in that: The specific steps include: (1) According to the mechanical structure of the dynamic balancing detection system, a mathematical model for the spindle speed control of the balancing machine is established, and the transfer function is obtained; (2) Design PID controller and BP neural network, and use particle swarm optimization to optimize BP neural network. When using particle swarm algorithm to train BP neural network, follow the steps below: a. Set the particle swarm parameters: including the total number of particle swarms, number of iterations, weight factor, particle search range, and the position and speed of particles in the initial state; b. Calculate the fitness of particles; c. Compare the fitness of each particle with the local most suitable position , iterate it; d. Compare the most suitable positions of each particle locally The most suitable position in the group , change ; e. Adjust the position and speed of each particle; f. Repeat step (b) to step (e) until the particle swarm optimization is completed; g. Set the initial parameters of the BP neural network to The corresponding particles calculate the output of the BP neural network, then calculate the output error, and finally adjust the basic parameters of the neural network; h. Repeat step (g) until the requirements of the BP neural network are met; (3) The mathematical model obtained in step (1) is used as the transfer function of the control system, and the PSO algorithm is used to optimize the parameters of the BP neural network in the control system to find the optimal , and Input into the PSO-BP-PID controller to realize the spindle speed control of the dynamic balancing machine.

2. A balancing machine spindle speed control method for optimizing PID parameters as claimed in claim 1, characterized in that: The PID controller design adopts an incremental PID algorithm, which is determined by , and Obtain the system control increment to achieve smooth control of the spindle speed of the dynamic balancing machine.

3. A balancing machine spindle speed control method for optimizing PID parameters as claimed in claim 1, characterized in that: The BP neural network is composed of an input layer, an output layer and a hidden layer, and the nodes in the same layer are not connected. The trained neural network is used to control the real-time input and output of the control system to solve the PID controller. , and .

4. A balancing machine spindle speed control method for optimizing PID parameters as claimed in claim 1, characterized in that: The PSO algorithm uses the system deviation as the fitness function, by defining , and The value range of the parameters is then determined, and the three parameters are adjusted according to the fitness function.

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