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Discussion on speed regulation algorithm of Brushless DC motor

discussion on speed regulation algorithm of Brushless DC motor Chen Jing 1, Xu Luping 2

(School of electronic engineering, Xi'an University of Electronic Science and technology, Xi'an 710071)

Abstract: Aiming at the speed closed-loop control of Brushless DC motor, this paper discusses three typical control algorithms: PI control, fuzzy control and fuzzy PI compound control, and analyzes their respective characteristics, The established control model is simulated, and the comparison results of control performance are obtained

keyword: control; Fuzzy; PI； Simulation

discussion of brush DC motor

speed adjustment arithmetic

chen 1 xuluping 2

(Electronic Engineering College of Xian University Xi'an 710071)

abstract: the arithmetic of PI control, fuzzy control, and the PI fuzzy control of the velocity loop in brush DC motor is discussed in this article., and the emulation has been done, which provides the comparision of their performance.

Keywords: Controll; Fuzzy; PI; emulation

1. Introduction in recent years, with the progress of power integrated circuit technology, the application of Brushless DC motor has been rapidly promoted. Many small brushless DC motors often need high speed control accuracy in applications. Therefore, the research on the speed closed-loop control method of Brushless DC motor is more and more in-depth, and many new control algorithms appear. In this paper, three typical control algorithms, digital PI algorithm, intelligent fuzzy control algorithm and fuzzy PI compound control algorithm, which are the most common in the control field at present, are used to adjust the speed of Brushless DC motor in closed loop respectively, and their respective control performance is obtained, and the simulation results are given

2. Where is the structure of the speed closed-loop system?

the speed loop structure model of Brushless DC motor is shown in Figure 1

Figure 1 Composition of speed loop of Brushless DC motor

Fig.1 constitution of brush DC motor

the model is composed of three parts: speed controller, motor armature and tachometer. The speed controller is the core part of the model, which converts the error signal between the given speed and the real-time speed fed back by the tachometer into a voltage signal to control the motor armature. Its embedded control algorithm determines the quality of control performance

the essence of the tachometer is the magnetic pole position detection sensor, which usually uses the switching element with Hall effect or electromagnetic induction sensor element. It can detect the position of the motor armature rotor, judge the motor speed at the same time, and feed back to the speed controller

as a controlled object, it is necessary to know its characteristic transfer function. The transfer function equation of motor armature is:

Chen Jing, born in 1979, female, Shaanxi, master's degree candidate

=+Ω=Ω=++=)()()()()()()()()()() (siksmsmsmjssmskseslsisrisumdldeds

where US: control voltage; R: armature circuit resistance; armature circuit inductance; electromagnetic torque; rotor moment of inertia; motor speed coefficient; electromagnetic torque constant; continuous current; lmdjekki Ω: rotor angular velocity. The motor parameters used in this paper are: Ω =14r, mh35l=, mmdn ⋅ =120, ia7=, sradv//7.20ke=, 2skm=2.0kgj=m ⋅ ⋅, a17m/⋅ n14. and this formula The equivalent motor armature transfer function model is shown in Figure 2 [.] 2

Figure 2 armature model of Brushless DC motor

Fig.2 model of brush DC motor

3 Discussion on control algorithm

3.1 digital PI control

digital PI control omits the differential link compared with the traditional PID control, and eliminates the weakening phenomenon of system anti sensitivity caused by the differential link. At present, it is widely used in the process of industrial control. The traditional digital position PI control algorithm is:

Σ= ⋅ + ⋅ =kjjekikekpku0) () (

where k is the sampling sequence number, k=0,1,2 * e (k) is the k-th sampling speed error; U (k) is the output control quantity at the k-th sampling time; KP is the proportional coefficient of PI controller; Ki is the integral coefficient. The system model of PI control motor speed loop is shown in Figure 3. Where motor is the motor model and step is the given speed

Figure 3 PI control system model

Fig.3 system model of PI control

3.2 fuzzy control algorithm

fuzzy control algorithm is a new control method developed in recent years and belongs to computer intelligent control. The structure of the control system is shown in Figure 4

Figure 4 structure of fuzzy control system

fig.4 the steps of designing a fuzzy controller are as follows: first, determine the structure of the fuzzy controller

select a two-dimensional fuzzy controller, and define the basic domains of input variable speed error E, error variation EC, and output variable control u as [-6, +6], [-3000, +3000], [-10, +10] respectively. By fuzzifying the basic universe, e and EC are discretized as [-6, -5, -4, -3, -2, -1,0, +1, +2, +3, +4, +5, +6], and u is discretized as [-6, -5, -4, -3, -2, -1, -0, +0, +1, +2, +3, +4, +5, +6]. The language variables e, EC and u corresponding to these three variables are defined as: {negative large [nb], negative medium [nm], negative small [ns], zero [zo], positive small [ps], positive medium [pm], positive large [bm]}

secondly, establish fuzzy control rules

to minimize the speed error, when the error is negative, the error change rate is also negative, indicating that the actual speed exceeds the specified value, and the error has an increasing trend, and the control quantity should be negative; The error is positive small, and the error change rate is positive center, which indicates that the speed is too small, and the system has the trend of eliminating the error. The control quantity should not be too large, and it is selected as the center. According to this relationship, all fuzzy control rules are obtained, as shown in Table 1

Table 1 fuzzy control rule table

tab 1 Fuzzy control rules

NB

NM

NS

ZO

PS

PM

PB

NB

NB

NB

NM

NM

NS

NS

PM

NM

NB

NM

NS

NS

NS

ZO

PM

NS

NB

NM

NS

NS

ZO

PS

PB

ZO

NB

NS

NS

ZO

PS

PS

PB

PS

NB

NS

zo

ps

ps

pm

pb

pm

nm

zo

ps

ps

pm

pb

pb

nm

ps

ps

pm

pm

pb

pb

e

u

ec

then establish the membership function of fuzzy language variables e, EC, u, as shown in Figure 5

e EC U

Figure 5 membership functions of fuzxy control

finally, a fuzzy control query table is established according to the control rules and membership functions, as shown in Table 2

Table 2 fuzzy control query table

tab 2 query rules of fuzzy the basis of this comparative experiment: control

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

-6

-5

-5

-5

-5

-2

-2

-1

1

1

1

1

-5

-5

-5

-5

-5

-5-2

-2

-2

-1

-1

-1

1

1

1

-4

-5

-5

-5

-5

-2

-2

-2

-1

-1

-1

1

1

1

-3

-5

-5

-5

-2

-1

-1

-1

-1

-1

0

1

1

1

-2

-5

-5

-5

-2

-1

-1

-1

-1

-1

0

1

1

1

-1

-5

-5

-5

-2

-1

-1

-1

0

0

2

5

5

5

0

-5

-5

-5

-1

-1

-1

0

2

2

2

5

5

5

1

-5

-5

-5

-1

0

0

2

2

2

1

5

5

5

2

0

0

0

0

2

2

2

2

2

1

5

5

5

3

-2

-2

-2

1

2

2

2

2

2

1

5

5

5

4

-2

-2

-2

2

2

2

1

1

1

5

5

5

5

5

-2

-2

-2

2

2

2

1

1

1

5

5

5

5

6

-2

-2

-2

2

2

1

1

1

5

5

5

5

e

u

ec

the control query table stored in the computer only needs to read the input information during real-time control, query the control strategy that should be adopted, and then the control quantity can be output

the control model of using fuzzy logic controller to control motor speed is shown in Figure 6. Ke is the quantization factor of speed error, KEC is the quantization factor of error change, and Ku is the proportional factor of output control quantity. Mold selection table:

Figure 6 fuzzy control system model

fig.6 system model of fuzzy control

3.3 fuzzy PI algorithm

fuzzy PI algorithm is a control algorithm that combines fuzzy and PI. The control idea of this compound controller is to adopt fuzzy control in case of large error, and switch to PI control in case of small error. The control model is shown in Figure 7. In the figure, | u | is the threshold value, which is compared with the constant K. when it is greater than k, fuzzy control is executed, and vice versa, PI control

Figure 7 Fuzzy PI control model

fig.7 system model of fuzzy PI control

4 Simulation results

the above established control model of controlling the speed loop of Brushless DC motor with three algorithms is simulated in the Simulink simulation environment of MATLAB. The adjustment parameters are as follows: in PI control, ki=2000, kp=10 are selected. In fuzzy control, Ke, KEC and Ku are 6/6 and 6/3000150 respectively. In fuzzy PI control, change Ku to 50, K to 1, and the other coefficients remain unchanged. Therefore, for the given speed curve in Figure 8 (a), a set of step response simulation curves shown in Figure 8 (b), (c) and (d) are obtained

analyze this group of graphs and list the comparison results in Table 3. It can be concluded that the digital PI control algorithm can meet the high control accuracy, but the response is slow and the transition time is long; The new fuzzy control algorithm not only has the advantages of strong adaptability to the controlled model, but also has a very fast response speed. The disadvantage is that its steady-state characteristics are not good, and the accuracy often does not meet the requirements; The fuzzy PI control, which combines the two algorithms, inherits the advantages of flexible and fast fuzzy control. At the same time, it has high control accuracy. It is a very effective control method for the speed loop control of Brushless DC motor

(a) (b) (c) (d)

figure 8 speed response simulation curve

Fig.8 step response result from simulation

Table 3 control performance comparison

tab 3 Comparison of the control performance

transition time (s)

static error

PI control

0.06

no

fuzzy control

0.015

Yes

Fuzzy - PI control

0.03

no

5 Conclusion

aiming at the speed regulation system of Brushless DC motor, this paper discusses several typical control algorithms in the field of modern control, and obtains the comparison results of their control performance.

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