Permanent magnet synchronous motor algorithms based on nonlinear identification generalized predictive and Intelligent fuzzy control system

Abstract

A control strategy of permanent magnet-oriented field synchronous motor based on intelligent fuzzy control system and generalized predictive control with non-linear identification is proposed to develop the effectiveness of the controlling method of constant magnet-oriented field synchronous motor, the accessor can be split into stabilization control part and intelligent control part. The input of traditional feedback control is used as the stabilization control part, while the feed-forward is incorporated into the intelligent part to compensate for the uncertainties of repetitive load torque and model parameters. The proposed feed forward compensation term uses simple learning rules without any load torque disturbance observer. The additional learning feed forward term does not require information about motor parameters and load torque values, it is insensitive to load torque uncertainty and model parameters, and does not need to identify the system model. With that, the solidness and intermingling confirmation of the proposed control framework reaction is given. The exploratory outcomes demonstrate that the proposed technique has littler speed overshoot list, and the heap torque against aggravation capacity list is improved by over 30%.

Keywords

Nonlinear identification generalized predictive control permanent magnet synchronous motor intelligent fuzzy control system

1 Introduction

Nowadays, China has given great concentration to the improvement and usage of new energy sources, and large-scale wind power and nuclear power plants have been put into use. However, due to the increasing shortage of electric power resources, the price difference of peak and valley electricity has also been increasing day by day. Therefore, China is currently vigorously promoting the construction of generator set, aiming to achieve the effective balance of the electricity price between peak and valley [1]. Seeing from the current development situation, it is predicted that China’s permanent magnet synchronous generator set will achieve 120 million KWH of total installed capacity by 2026, accounting for about 5% of the total installed capacity [2]. Although the development process of the generator set in China is relatively late, after the government paid much attention to and strongly promoted, and through continuous technological innovation and technology introduction, China’s scientific research institutions have already had the ability to independently design and construct permanent magnet synchronous generator set. At present, it is of very important practical and economic significance to carry out relevant researches on permanent magnet synchronous generator sets [3, 4]. Fuzzy system is broadly utilized in device control. The equation “fuzzy” givesto the way that the system included. Albeit elective methodologies, for example, hereditary calculations and neural systems can done similarly just as fuzzy system much of the time [5], fuzzy system has the favorable position that the answer for the method can be given so their experience can be utilized in the structure of the controller. This makes it simpler to automate assignments that are as of now mainly done by people [6]. Generator motor is a key component of the design of generator set, and its performance directly affects the working efficiency of synchronous generator set [7 –11]. The main problem faced by the design of permanent magnet synchronous generator set is that the generator motor needs to switch between four different working conditions, including stop, work, pumping and phase modulation [12], and both switching frequency and work load of the generator motor are very high, so it requires that the designed generator motor should have a very excellent working performance. In this process, effectively establishing motor operation model plays a very important role in evaluating the motor’s working condition and adjusting the control strategy [13 –15]. However, because the structural form of generator set is very complicated, and the utilization of materials is diverse, the problems such as the saturation of magnetic circuit have a very complex impact on the electromagnetic. Therefore, all these factors made that the accurate mathematical model cannot be used to carry out the modeling of permanent magnet synchronous generator set, and how to more reasonably construct the model of set is a very meaningful research subject. On the other hand, the installed capacity of set is also increasing day by day, which is accompanied by the very serious terminal magnetic leakage problem of the generator set, thus leading to the accelerated end wear of the generator set [16, 17], which must be taken seriously in the design of set. In addition, the control performance of permanent magnet synchronous generator set plays a very important role in power generation efficiency, loss reduction and cost reduction, and the accuracy of generator set model is very important for the improvement of control performance [18]. Fuzzy controllers are exceptionally basic reasonably. They comprise of an information organize, a handling stage, and a yield arrange. The information stage maps sensor or different sources of info, for example, switches, thumbwheels, etc., to the suitable participation capacities and truth esteems [19, 22]. The handling stage conjures each fitting standard and produces an outcome for every, at that point consolidates the aftereffects of the guidelines. At last, the yield stage changes over the joined outcome once more into a particular control yield esteem [23].

The most widely recognized state of participation capacities is triangular, albeit trapezoidal and chime bends are likewise utilized, however the shape is commonly less significant than the quantity of bends and their position. From three to seven bends are commonly fitting to cover the required scope of an info esteem, or the “universe of talk” in fuzzy language [24, 25].

As examined before, the preparing stage depends on an accumulation of system manages as IF-THEN explanations, where the IF part is known as the “predecessor” and the THEN part is known as the “ensuing". Commonplace fuzzy control frameworks have many guidelines [26]. Based on this, aiming at the construction of the motor model of permanent magnet synchronous generator set, this study adopted subspace identification method to build the motor model, and it aimed to use numerical analysis method to regularly analyze the operational changing situation of electromagnetic parameters and relevant parameters of the motor of permanent magnet synchronous generator in various working conditions, so as to provide basic references for the motor’s design and control and further promote the research and development of new products [27, 28].

2 Generalized predictive control based on nonlinear identification of fuzzy system

According to relevant literature, if a better control effect of motor is obtained, the transient linearized model of motor must be identified first, and at the same time, online identification is required. At present, among parameter identification algorithms which can be used for online identification, the least square method is a simple and effective identification method. In addition, the commonly used method is the identification process of intelligent optimization algorithm, but its disadvantage is too high computation complexity and some defects of its application in online identification process. This is mainly because, for the control objects that require calculating the transient model, adopting optimization algorithm to optimize and identify the parameters identification of parameters generally requires multiple iterative processes before convergence, which is unrealistic for the online control system with high real-time requirements and has no engineering application value. In addition, there are also online model identification methods which have learning function and which adopt support vector machine and neural network, but they need higher computation complexity, because they require sufficient identification data accumulation to obtain a relatively accurate learning model. Especially for the control model of permanent magnet synchronous motor which is more complicated, there are higher requirements for the identification data, which will not only increase the difficulty of the data acquisition part but also greatly reduce the real-time performance of the control process.

In this study, in order to achieve the model predictive control method of permanent magnet synchronous motor which is more similar engineering use, the least squares method is most commonly used. Although it does not have advantages in identification accuracy, it can meet the needs of engineering design in terms of computational efficiency, but the problem of the inaccuracy of the least squares method can be solved by using the form of algorithm improvement.

Based on the above description, among the three different control methods mentioned above, for the PMSM to be studied in this study, the complexity of its model construction makes it impossible to adopt the second GPC control method for controller design. As far as the third control strategy, permanent magnet synchronous motor needs to frequently switch between various working conditions to acquire relatively sufficient identification data, which isn’t conductive to the safety of the controlled objects. Meanwhile, it needs to waste a lot of time and money, so its economic efficiency is poor and the real-time control efficiency cannot be guaranteed, which constrain its application in the design of GPC control method of motor in this study. Therefore, the controller design of motor in this study adopts the first GPC controller design method based on transient model linearization, and it mainly considers the simplicity of algorithm implementation in order to make it closer to engineering use.

Because the flying turbine and other components of permanent magnet synchronous motor have very complicated operation conditions and strong non-linearity, it is unrealistic to use mathematical theory to construct the models for them, which cannot be accurate. Therefore, the solution of this study is to construct the mode by using the operating characteristic curve of permanent magnet synchronous motor. Generally, the model can be constructed by adopting the way of given working conditions or taking sampling point as the stable working conditions of the model. The characteristic curve model of the flying turbine of PMSM can be established with fuzzy membership functions are described as follows in Equation 1: ${\begin{matrix} m_{t} (n, y, h) = e_{x} n + e_{y} y + e_{h} h \\ q (n, y, h) = e_{qx} n + e_{qy} y + e_{qh} h \end{matrix}$ (1)

Where e_x = ∂m_t/∂n is the transfer factor of the speed of the flying turbine in the permanent magnet synchronous motor as Equation 2: $e_{y} = (\partial m_{t} / \partial a) (\partial a / \partial y)$ (2) the transfer factor of the torque parameter relative to the opening parameter of the hydraulic servomotor in the flying turbine; and e_h = ∂m_t/∂h is the transfer factor of the torque parameter in the fly turbine relative to the operating condition of water pressure in the permanent magnet synchronous motor. e_qx = ∂q/∂n is the transfer factor of the water flow going through the flying turbine relative to the speed parameters of flying turbine in permanent magnet synchronous motor; e_qy = (∂a/∂a) (∂a/∂y) is the transfer factor of the water flow parameters in the flying turbine relative to the opening parameters of hydraulic servomotor; e_qh = ∂a/∂h is the transfer factor of the water flow parameters in the flying turbine relative to the hydraulic operation conditions in permanent magnet synchronous motor.

For the water diversion system of permanent magnet synchronous motor, a small model fluctuation interval is set at the selected sampling location, and the water hammer effect of the elastic or rigid permanent magnet synchronous motor can be used for model analysis. Therefore, the water diversion system of permanent magnet synchronous motor can be simplified at the selected sampling point. The transfer function of rigid and elastic water hammer effect mode with fuzzy membership function is derived as follows in Equation (4): $G_{h} (s) = \frac{h (s)}{q (s)} = - T_{w} s$ (3) $\frac{h (s)}{q (s)} = - h_{w} \frac{T_{r} s + T_{r}^{3} s^{3} / 24}{1 + (T_{r}^{2} s^{2} / 8) + (T_{r}^{4} s^{4} / 384)}$ (4)

Where fuzzy parameter T_w is the flow inertia parameter in the operation process of the motor; T_r is the pressure wave parameter of the water hammer component of the and h_w is the pipeline parameter of the motor.

For the above model setup, the model of motor can be described by using the first-order transfer function. For the selected single sampling point method, the dead zone part of the hydraulic actuator can be ignored. Meanwhile, it can be simplified into a general second-order transfer function model and linearized. Therefore, the simplified form of rigid water hammer model of the motor is shown in Fig. 1.

Fig. 1

Simplified form of rigid water hammer model of permanent magnet synchronous motor.

As for the simplified form of rigid water hammer model of motor shown in Fig. 1, if only the controlled part of permanent magnet synchronous motor is considered, the model can be described by the form of first-order transfer function. The specific form of fuzzy membership function is as follows in expression (5): $\frac{n (s)}{u (s)} = \frac{e_{y} - (e_{qy} \cdot e_{h} - e_{qh} \cdot e_{y}) T_{w} s}{(T_{y} B^{s} + 1) (e_{qy} T_{w} s + 1) (T_{a} s + e_{n}) T_{y} s}$ (5)

For the transfer function performing Z transformation process as shown in the above model (4), because model (5) has a higher model order than model (4), the model obtained by performing Z transformation is relatively complex, and the physical meaning of many parameters is unknown. There may be differences in the form of Z transformation models obtained by different calculation methods. In this study, it is calculated by“c2d”inherent function in MATLAB software as Equation 6: $\frac{n (s)}{u (s)} = \frac{b_{3} z^{2} + b_{2} z + b_{1}}{z^{3} + a_{3} z^{2} + a_{2} z + a_{1}}$ (6)

Model (5) is discretized, as shown in discrete model (6):

Through comparing formula (6) and formula (7), it can be found that formula (6) is the model result after the transient linearization of the nonlinear model of permanent magnet synchronous motor by using the CARIMA model. Considering that there is n_a = n_b = 3 in the rigid water hammer model of permanent magnet synchronous motor shown in Fig. 1. According to different forms of rigid water hammer model of motor, parameter n_b and n_b have different values, for example, if the water diversion system of motor has long pipe, it cannot simply the rigid water hammer model of motor, and if a second-order model is adopted to simply the elastic water hammer process of motor, then it can conclude that n_a = 5 and n_b = 4. In addition, the input and output of the rigid water hammer model of permanent magnet synchronous motor a₁, a₂, …, a_{n
_a}, b₁, b₂, …, b_nb can be obtained by Z transformation of the parameters of the simplified model of the rigid water hammer of permanent magnet synchronous motor, e_x, e_y, e_h, e_qx, e_qy, e_qh, T_p, T_w, T_a, T_g, T_y1. Since the parameters of the rigid water hammer model of motor are unknown, the above coefficients are actually uncertain. On the basis of the above analysis, after obtaining the parameter n_a and n_b and using the specific parameter identification process, the control rate of PMSM can be designed based on the following Equation 7: $\begin{matrix} u (k) = u (k - 1) + Δ u (k) = u (k - 1) + [10, \dots, 0] \\ {[F_{1}^{⊤} F_{1} + Γ)}^{- 1} F_{1}^{⊤} [Y_{r} - F_{2} Δ U (k - j) - GY (k)] \end{matrix}$ (7)

3 Simulation analysis

Table 1 provides the parameters of motor, and the following Equation (8) is used for experiment: $\dot{ω} = 1679.4 i_{qs} - 0.2837 ω - 3782.4 T_{L}$ (8)

Table 1

Parameters of permanent magnet synchronous motor

Parameter item	Symbol	Value
Rated power	P _rated	750 W
Pole number	P	8
Stator resistance	R _s	0.43 Ω
Stator inductance	L _s	3.2 mH
Magnetic flux	λ _m	0.085 Vs/rad
Rotational inertia	J	0.0018 kgm2
Viscous friction coefficient	B	0.0002 Nms/rad

Referring to the derivation results showed in the previous section, the current control rate shown in the following formula (9) can be obtained: $i_{qsd} (t) = - 0.2 σ (t) + u_{ff} (t)$ (9)

Where the calculation form of σ (t) is:

u_ff (t) can be updated according to the following self-adaptive rules in (10)(12): $u_{ff} (t) = 0 .$ (10) $T_{c} 3 (Np / 2)$ (11) $μ_{pin} = 4 \sqrt{2 RLNAK}$ (12)

Figure 2 shows the overall block diagram of the learning control system of the proposed permanent magnet synchronous motor. point DSP calculation.

Fig. 2

Overall block diagram of learning control system of permanent magnet synchronous motor.

The bode diagram and speed step response of the system are tested and analyzed, as shown in Figs. 3 and 4. The proposed feed forward compensation term uses simple learning rules without any load torque disturbance observer. The additional learning feed forward term does not require information about motor parameters and load torque values, The exploratory outcomes demonstrate that the proposed technique has littler speed overshoot list.

Fig. 3

Step response of permanent magnet synchronous motor (PI controller and algorithm in this paper).

Fig. 4

Bode diagram of permanent magnet synchronous motor system (PI controller and algorithm in this paper).

According to the results shown in Figs. 3 and 4, the comprehensive analysis indicates that: 1) the permanent magnet synchronous motor system adopting the control strategy in this paper has a smaller overshooting index of speed than the permanent magnet synchronous motor system based on traditional PI control, reflecting the stability of the control algorithm, so it can obtain a smaller current impacting effect; 2) the PMSM system using the control strategy in this paper has a smaller phase angle lagging index than the PMSM system based on traditional PI control, reflecting the fast performance of the control algorithm, so it can achieve a faster speed adjustment.

Under the setting of the above parameters, the speed of the permanent magnet synchronous motor is set at 800 r/min, and the constant torque mode dynamometer is adopted to compare the anti-disturbance performance of the load torque of the controller in this paper (without intelligent learning rules) and the controller in this paper (with intelligent learning rules). The results are shown in Figs. 5-6.

Fig. 5

Load step response (no intelligent learning rules).

Fig. 6

Load step response (add intelligent learning rules).

According to the results shown in Figs. 5 and 6, it can be seen that, compared with the controller without the addition of intelligent learning rules, the load torque anti-disturbance ability of the controller with the addition of intelligent learning rules increased by more than 30% and the load torque anti-disturbance ability was improved.

4 Conclusion

The load identification problem of permanent magnet synchronous motor (PMSM) under stable operation condition was studied in this paper. It adopted the method of subspace identification strategy based on bilinear model, and verified the performance of the algorithm through simulation. Main innovations: 1) in order to solve the model nonlinear problem of motor, a subspace identification model of motor based on bilinear model was designed and its state-space model was provided. 2) To enhance the validity of subspace recursive likelihood identification method, a bilinear subspace recursive likelihood identification method for motor was put forward in this paper. Compared with the identification process of linear model adopting characteristic moment mode, the subspace identification process of bilinear model can more extensively describe the linear model, so it is a more effective identification method.

Simulation research results indicate that: 1) subspace identification strategy based on bilinear model can better realize the identification of permanent magnet synchronous motor model, and it has a higher identification accuracy; 2) the subspace identification strategy based on bilinear model can well process the historical data of PMSM, realize the effective identification of the model’s subsystem, and obtain a more accurate identification model; 3) the PMSM model obtained by this research identification method can be applied in the controller design of PMSM to improve the control effect of PMSM. Therefore, applying the designed identification model of motor to realize the optimal control of motor will be the follow-up research focus of this study.

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