1 The excellent performance of the hybrid stepping motor closed-loop servo system has been paid more and more attention. At present, the research on the control strategy of self-controlled hybrid stepper motor servo system lags behind due to the fact that the internal control variables of the hybrid stepping motor are coupled with each other, and the motor structure is special. Different from the general types of motor writers, they have proposed a second method in the literature. Hybrid Stepping Motor Vector Control Position Servo System . This system adopts the neural network model reference adaptive control strategy to compensate the uncertain factors in the system in real time and achieve the high-efficiency control of the motor through the maximum torque/current vector control. Figure 1 shows the system block diagram. In the system, the input of the neural network controller is position error, velocity error, and model reference error. During operation of the system, the neural network controller gives the current given correction value in real time according to the change of the input quantity, and corrects the parameters such as its own weight. The reference model in the figure is determined based on the mathematical model of the two-phase hybrid stepper motor, the control system structure and performance requirements, and has a crucial role to the system performance. How to get a simple, accurate and feasible reference model is one of the key points of system design, and the problem is mainly focused on the establishment of a simple and accurate motor model.
This paper first gives a simple mathematical model of a two-phase hybrid stepper motor and proves its feasibility. That is, the model parameters can be selected appropriately to make the model more accurately reflect the dynamics of the motor. Static characteristics. Subsequently, the model parameters were obtained using the appropriate identification method. Experiments show that the model is relatively simple and accurate, and can meet the requirements of real-time and accuracy of the servo system.
2 Mathematical model of two-phase hybrid stepping motor The mathematical model of the motor can be expressed in many forms, such as equations of state, transfer functions, etc. For convenience of description, this paper uses the following basic equation of winding voltage to describe the electromagnetic process inside the motor. V V phase winding terminal voltage, unit V phase winding resistance, unit k phase winding current, unit A k phase winding self inductance (k = j), mutual inductance (kk phase winding back electromotive force, unit V above In fact, L is actually an incremental inductor. Normally, regardless of the saturation effect, it is considered that the L-winding inductance reflects the electromagnetic relationship within the motor and directly represents the change of the motor magnetic field, which is the most important parameter in the stepper motor model. With the axial and radial mixed magnetic system, the stator and rotor double convex structure, so the characteristics of the winding inductance parameters are different from the ordinary motor.The authors in the literature on the theoretical and experimental study of the hybrid stepper motor winding inductance, clarified Some concepts have yielded some results and laid the foundation for the further refinement of the inductance model.The inductance measurement method and measurement proposed in the literature The quantitative results are more complex and difficult to directly apply to the general servo system design, but it provides the theoretical and experimental basis for the servo system design, and it is possible to make the expression of the inductor simpler and more expressible as the formula, L is the undetermined constant .
In equation (1), the back EMF e is another key quantity. In the motor, the value of e is directly proportional to the electromagnetic torque of the motor and represents the magnitude of the electromagnetic power induced by the stator windings to the rotor. The expressions of the literature are deduced. The conclusion is as follows. k is the undetermined constant.
In this way, if six unfixed constants are determined, the winding voltage equation of the motor can be solved in real time. Coupled with the rotor motion equation, the motor model is also established.
3 Identification of model parameters of two-phase hybrid stepper motor The rapid development of microprocessors, power electronics and PWM technology has led to a large number of rectification and inverter devices used in modern servo systems Shi Jingzhuo and other two-phase hybrid stepper motor models. In the parameter identification, the applied voltage of the motor is a non-sinusoidal square wave signal. For a stepper motor, the open-loop control voltage itself is a square wave or a staircase wave. When applied to a closed-loop servo system, the application of the PWM technique causes the voltage to become a square wave signal with a variable pulse width and generates a series of harmonic voltage components in the motor. At the same time, the parameters of the motor will change due to changes in the operating frequency of the motor and the saturation of the magnetic field. Therefore, the motor parameters obtained by the conventional experimental methods do not describe the dynamic performance of the motor well. The motor parameters must be measured by simulating the actual operating conditions of the motor in order to obtain a more satisfactory result [7]. The literature is effective. Try.
This article proposes another way of thinking, that is, the above-mentioned six undetermined constants are obtained offline through the parameter identification method. The specific method is: Measure the winding current curve when the motor is running. Through simulation, adopt the identification method combining the least squares method and the improved genetic algorithm to identify the parameters of the motor model.
Least square method is a recursive optimization process that takes the sum of squared errors as an objective function. The parameters to be identified are obtained by online recursive operations.
For the problems discussed in this paper, because it is an off-line calculation and a multi-dimensional optimization process for multi-modal complex objects, more effective optimization algorithms such as genetic algorithms can also be used.
In recent years, genetic algorithms have gained wide application in the field of control. Genetic algorithms can always maintain the evolution of the entire population. In this way, even if an individual loses useful features at a certain moment, this characteristic will be retained by other individuals and will continue to develop. Since the genetic algorithm only needs to know the information of the objective function, and does not need its continuous differentiable requirements, it has wide applicability. At the same time, it is also an intelligent search method using heuristic knowledge, so it is often able to achieve better results than the previous algorithms (such as the gradient method) in the highly complex search space. With the development of applications, researchers at home and abroad are The study of genetic algorithms is also getting deeper and deeper. Zhang Xiaoxuan pointed out in [9] that the binary code search capability is stronger than the decimal code. In order to overcome the premature problems brought about by ordinary binary coding, Schraudolph proposed DPE) to dynamically change the domain of variables. When it is known by some method that the population has converged, the variable definition domain is narrowed down to a certain extent, so that a more accurate search can be performed near the global best point. The basic genetic algorithm uses only single-point crossover operation for a single chromosome, and uses multi-point crossing Help improve search efficiency. Commonly used multi-point crossings are two-point crossings and even crossings. In general, the uniform crossover is better than the two-point crossover to identify the parameters of the motor model. The sum of squared error is the objective function, and the genetic algorithm is used to optimize.
The genetic algorithm uses 60-bit binary coding, and L six pending constants each occupy 10 bits, as shown in Figure 2. The measured average inductance of the 86BH250B motor winding is 11 26mH, and the back EMF coefficient is 1 827V s. According to the theoretical analysis of the literature and [6], it can be seen that L is generally about 10% of L and generally k. Therefore, the initial domain of each variable is selected as follows: [ 0, 0 500]. Since the values ​​of the six pending constants are approximately: L 0 183V s. The initial population should be near this point (ie in the defined initial domain Medium) is selected uniformly and should contain this point. The number of chromosomes in the population was set to 60, and 59 randomly selected, plus the above-mentioned one chromosome.
The conversion from actual values ​​to 10-bit binary codes uses the equidistant method. For example, the domain of the variable x is [a, b], and the value x is encoded as, for example, the aforementioned chromosome using dynamic variable coding and uniform crossover techniques in the calculation of the genetic algorithm. The dynamic variable coding is set as follows: if the current domain of a variable is [a] and the corresponding 50 out of the optimal 50 chromosomes in the current population is [a], the variable domain is changed. For [a]. Uniform crossover is set to randomly select alleles from parental chromosomes with a certain probability (0 4) to form two progeny chromosomes to improve search efficiency. In addition, a random single-point crossover operation is used inside each gene, and the basic crossover probability is selected to be 0. 3. To make the cross-generational individual's optimization variables uniformly distributed in the multidimensional search space, and to use the non-equal probability selection for the cross positions. The specific setting is: the probability of the highest 2 digits of each inter-gen (10-bit binary coded) intercross electrotechnical journal is 2 times the cross probability of the remaining 8 digits. At the same time, in order to achieve the goal of global optimization and advanced protection, it is stipulated that the optimal individual of the father can always survive to the next generation, and this optimal individual will replace the worst individual in the offspring. The mutation probability in genetic computation is chosen as 0 05. Figure 3 shows the flow diagram of the genetic algorithm. The objective function of each chromosome in the genetic algorithm is calculated by the motor simulation software, and the model parameters specified by the chromosome are used in the calculation. The simulation calculation of the motor model uses the author's simulation software SMSS [12], and corresponding improvements are made. When measuring the winding current waveform, a system consisting of a constant total flow driver and an 86BH250B motor was used to measure the current waveforms at multiple operating frequencies to identify and verify motor model parameters. It should be pointed out that there are differences in the operating conditions when the motor is unloaded and loaded. When testing the current waveform, it covers the operating frequency range that the motor may reach and takes into account different load conditions. The corresponding motor model parameters obtained by the identification are: L-test results. The solid line in the figure shows the measured winding current waveform, and the dotted line shows the model calculation result. It can be seen that the established motor model and the identified model parameters have high accuracy over a wide frequency range.
4 Conclusions In this paper, a simple and accurate motor model using parameter identification is proposed and a corresponding identification algorithm is proposed. Shi Shijing and other two-phase hybrid stepper motor model parameter identification practice proves that for complex stepping motor model parameter identification such complex issues, genetic algorithm is an ideal optimization algorithm.
At the same time, experiments have shown that this method of using parameter identification to obtain a motor model is feasible, and it is also a relatively simple method that can be used for servo system design.
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