Simulation of Asynchronous Motor Control System Bad on BP Neural
Network PID Control Algorithm
LIU Di, Hu Chun-wan, Gao Yan-li
Department of Control Engineering
Naval Aeronautical and Astronautical University,
Yantai Shandong
China
Abstract:- In allusion to the effect that traditional asynchronous motor PID control system is vulnerable to uncertain factors of parameter variations and load disturbance, the disadvantage that system parameters can’t be adjusted timely following the diversification of motor speed, this paper introduces a PID control algorithm bad on the BP network by melting the regular PID control algorithm and the l
f-automatic learning neural network. Simulation results are provide to indicate that this method has the advantage of quick velocity respon, less overshoot, higher control precision and good robustness, has great control effect, is much better than that of traditional PID control algorithm.
Key words:-BP Neural network; PID control algorithm; Asynchronous motor; Simulation; Overshoot; Robustness;
1Introduction
Induction motor supplys from the AC power, becau of its simple structure, low cost, durable, easymaintenance, therefore, induction motor has gained a wide range of applications in the engineering,agriculture and other fields. Conventional induction motor control system commonly us PID controlalgorithm. PID control algorithm is simple, easy to adjust parameters, and there is a certain degree of control precision, but there are also inadequate.Conventional PID controller is vulnerable to theuncertainty factors impact of parameter variations and load disturbance. and is not well balanced betweenthe dynamic respon and anti-jamming capability.To overcome the deficiencies, a variety of controlmethods have been propod to eliminate the uncertainty. However, the policies are basically obtainedby the linear model,robustness is difficult to be guaranteed. BP n
eural network simulates human brainsystems from the structure, has lf-learning ability, can continuously modify the weights of network toadjust the output of network by online training, obtain the required output which we need at last. but theconventional BP neural network exists the problem of slow convergence and local minimum,will produceoscillations inevitablely. Improved BP neural network PID controller resolves the appeal issues, canachieve the good control effect about the uncertain factors of the object of change and randomperturbation. The system not only has fast dynamic respon, but also has a high degree of stability.However, due to neural network obtains the optimal control parameters by a period of time. So neuralnetwork can not achieve satisfactory performance in the early time of system into operation.The effect ofcontrol is not satisfactory.
2 The mathematical model of Induction motor
The mathematical model of AC induction motor is the basis for modeling and simulation, thedynamic mathematical model of induction motor is a high order, nonlinear and strong couplingmultivariable systems.
(1)、the voltage equation
the voltage balance equation of three-pha stator windings is:
A
A A s B
B B s C
C C s d u i R dt
d u i R dt
d u i R dt ψψψ⎧=+
⎪⎪⎪=+⎨⎪⎪=+⎪⎩ (1) Where: A u 、B u 、C u ——the instantaneous value of stator and rotor pha voltage; A i 、B i 、C i ——the instantaneous value of stator and rotor pha current; A ψ、B ψ、C ψ——all flux of the pha winding.
(2)、flux equation
Flux of each winding is the sum of its own lf-inductance flux and its other winding mutual inductance flux. Therefore, the expression of six winding flux is:
A AA A
B A
C Aa Ab Ac A B BA BB BC Ba Bb Bc B C CA CB CC Ca Cb Cc C a aA aB aC aa ab ac a
b bA bB bC ba bb b
c b
c cA cB cC ca cb cc c L L L L L L i L L L L L L i L L L L L L i L L L L L L i L L L L L L i L L L L L L i ψψψψψψ⎡⎤⎡⎤⎡⎤
⎢⎥⎢
⎥⎢⎥
⎢⎥⎢⎥⎢⎥
⎢⎥
⎢⎥⎢⎥
=⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥⎢⎥
⎢⎥⎢⎥⎢⎥
⎢⎥
⎢⎥⎢⎥
⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦⎣⎦ (2)
Where:AA L 、BB L 、CC L 、aa L 、bb L 、cc L ——lf-inductance of the relevant winding; the remaining is the mutual inductance between the windings.
(3)、the torque equation
According to principles of electromechanical energy conversion, in the multi-winding motor, under the conditions of the linear inductance, the sum of magnetic energy storage and magnetic energy is 'T T m m 11
W W 22===i Ψi Li (3)
(4)、equation of motion
In the conditions of ignoring torsional elastic of electric drive system transmission shaft and viscous friction, The equations of motion for the transmission is r
e L p d J t T n dt ω=+
(4) Here: L T is the load torque, p n is the number of motor pole pairs, J is the moment of inertia, r ωis electrical angular velocity. 3. Improved BP neural network algorithm description and the structure of PID controller 3. 1 The structure and characteristics of BP neural network Multi-layer forward BP neural network consists of an output layer and an input layer, one or more of the hidden layer. Transfer function of hidden layer is generally non-linear function, such as s transfer function.The transfer function of output layer can be non-linear, it can be linear, which is decided by the needs of
mapping relationship of input-output [2]. Multi-layer forward BP neural network can approximate any nonlinear function, it has a wide range of applications in the scientific field.The algorithm is bad on two hidden layer BP neural network as an example to carry out rearch. The specific structure is shown in Figure x
x x d i p Fig.1：The structure of BP neural network Among the many forward network, the most typical is the error back-propagation BP neural network. BP neural network introduces least squares learning algorithm, in the learning process of neural networks, the error of the output of network and expected output of network is back propagation while fixing connection strength (weighting coefficient), to make the mean square of error minimum.The learning process can be divided into prior computing of the network and backward error propagation ——fix the weights of connection, the two parts are repeated in a continuous succession, until the error meets the requirements. 3. 2 The description of improved BP neural network algorithm In learning algorithm of the BP neural network, it can make u of the idea of quadratic performance index in optimal control, becau that quadratic performance index is ud to calculate the control lawcan get the optimization effect that we desire, the idea of quadratic performance index is introduced in the adjustments of weighting coefficient, the sum of output error and control increment weighted squares
as the smallest adjusts the weighting coefficient, achieve the constraint control of output error and control increment weighting indirectly.
The digital PID control of control increment is ud in this paper, the equation of control is
)()()()1()(2
k e k k e k k e k k u k u D I P ∆++∆+-= (5)
Where: D I P k k k 、、 is proportional, integral, differential coefficients, is the three output of BP neural network, )(k u is the output of the controller. Set performance indicators:
)())()((21
)(2k Mu k y k r k e +-= (6)
Where, M is the weighting coefficient of the control increment, )(k r and )(k y are the reference input and output of k times.
BP neural network contains an input layer, two hidden layers, one output layer. Three input nodes wh
ich are contained in input layer reprent 、)(k e ∆)()(2k e k e ∆、 parately. There are three nodes in output layer.They reprent the three parameters of controller D I P k k k 、、.
The output of the output layer of the network is:
∑==3
1)
()()(l h lh l k y k w k net (7)
3,2,1)],([)(==l k net g k o l l (8) P k k o =)(1，I k k o =)(2，D k k o =)(3 (9) According to performance indicators, the weighting coefficient of network is fixed in accordance with gradient descent method, and attach the global minimum inertia which makes arch fast convergence.The learning algorithm of output layer weight of network is
)()1()(k o k w k w l l lh lh ρδα+-∆=∆ (10) ))
(()()
())()(()('k net g k o k
u k u k y sign k e l l l ∂∆∂∆∂∂=δ 3,2,1=l (11)
Similarly, the learning algorithm of hidden layer weights of the network is
)()1()(k o k w k w j j hj hj ρδα+-∆=∆ (12)
∑==31')
())((h hj l h i k w k net g δδ3,2,1=h (13)
3. 3 PID controller structure of improved BP neural network
Classical PID controller is for the purpo of eliminating error and external disturbance, reduces errors and resist external disturbance with three different combinations of fixed form.However, the parameters of PID controller is often required to have the rich experience of control, is obtained by the determined mathematical model, given the transfer function of controlled object and the specific performance indicators. The methods are the approximation in a way, is difficult to obtain the optimal parameters. The BP neural network is combined with the traditional PID control algorithm, can play their advantages respectively, improve the performance of the control, produces intelligent PID control strategy. In this paper, the structure of improved BP neural network PID control induction motor has two parts: The first part is the traditional PID controller, control the induction motor in clod loop directly, andthree parameters D I P k k k 、、 is for online tuning; The cond part is the BP neural network improved, According to the operational status of the system, adjust the parameters of PID controller, achieve the performance of optimization. The output layer neuron's output state corresponds to the three adjustable parameters of PID controller, through the lf-learning of neural network 、adjusting the weighting coefficients, obtains the optimal PID controller parameters of steady state; The specific structure principle of the system is
Fig.2： The structure diagram of improved BP neural network PID controller 4. The results of simulation Matlab software package simulates the system discusd in this article, the identification of system us offline. Simulation parameters: rated voltage is 380V, Motor pole pairs is 0.6Ω，Rotor resistance is 0.8Ω，Stator and rotor inductance are equal 0.7H ，Mutual inductance between the stator and rotor is 0.4H ，Moment of inertia is 0.067kg*m^2. Simulation test: take the ttings of motor speed, n=200r/min.
Fig.3： unit step respon of conventional PID control system
Fig.4： unit step respon of bad on BP neural
network PID control system
Figure 3 shows the unit step respon of using the conventional PID control algorithm to control indu
ction motor. It can be en that overshoot of the system is large, fluctuations is large, over time is long.Figure 4 shows the unit step respon of the PID control algorithm of controlling induction motor bad on BP neural network. Compared with the conventional PID control algorithm, PID control algorithm bad on BP neural network reduces the overshoot of system largely, shortens the adjustment time of system. The respon of system is fast and stable. The system can reach a steady state quickly. The algorithm improves the performance of the
control system greatly.
Fig.5： speed change process of no-load starting
bad on conventional PID control algorithm Fig.6：speed change process of no-load starting bad on BP neural network PID control algorithm Figure 5 shows the speed change process of controlling induction motor no-load starting bad on the conventional PID control algorithm, it can be en that the fluctuation of speed is large at the beginning, overshoot is large, the time of adjustment is long; Figure 6 shows the speed change process of controlling induction motor no-load starting bad on BP neural network PID control algorithm. Compared with the former, In figure 6, the overshoot of speed is small, the time of transition is short, the speed reach a steady rapidly, does not occur oscillation. 5. Conclusion In this paper, it can be en from the simulation results of two control algorithms, compared with traditional PID control algorithm, PID control algorithm bad on BP neural network can improve the system's anti-jamming capability, suppress the error caud by the change of parameters through the intelligence factor of lf-adjusting, adaptive, lf-organization of the neural network itlf.it can be en from the simulation. The algorithm achieves the respon of step and controls starting speed of no-loading, has the advantage of short adjustment time 、small overshoot 、strong robustness ，has excellent control effect. References [1] wang zhe 、qu bai-da. the application of BP neural network in permanent magnet synchronous motor[J]. computer s
imulation,2009. [2] feng yu 、qiu xiang-yan 、ding hong. control of permanent magnet synchronous motor speed system bad on neural network[J]. Modern drive and control, 2007(2). [3] wang ting 、liu feng. automatic control components[M].Naval Aeronautical and Astronautical University, 1996,59-60 [4] liu di 、tang yong-hong 、wang jing 、liu xiao-lei. the rearch of PID control algorithm
