INTRODUCTION
Inductively Coupled Power Transfer (ICPT) technology is a new mode of power
supply, which utilizes high frequency magnetic fields to transmit power from
the source to the receiver in the form of electrical isolation (Cannon
et al., 2009; Valtchev et al., 2009;
Sun et al., 2012). It effectively solves the
seamless access problem and changes traditional supply mode that transmit power
directly via electric conductor. ICPT technology has extensive application prospects
in various industries, such as manufacturing (Moradewicz
and Kazmierkowski, 2010), medicine (Madawala and Thrimawithana,
2011) and electric vehicles (Tian et al., 2012)
since it is environmental friendly, convenient and flexible.
An ICPT system has a primary side and a secondary side. When the secondary
impedance varies, the reflected impedance will be introduced in the primary
coil due to the electromagnetic coupling effect. Hence, the primary exciting
current will decrease and the operating frequency of Zero Voltage Switching
(ZVS) will drift (Hu et al., 2000), which weakens
the capability of transmission power and reduces the transmission efficiency.
If the frequency drift is too large, multicycle working points phenomenon will
appear and cause big influence on operational stability of system. When the
frequency offsets the inherent frequency and the primary input voltage remains
constant, the pickup voltage will drop sharply and generate bigger fluctuation,
causing hidden danger for the normal load operations (Li
et al., 2012). Therefore, to ensure the operational stability of system
and to improve its transmission efficiency, it is important to stabilize the
secondary output voltage.
Current control strategies for the secondary output voltage are mainly based
on the primary phaseshifted control (Yugang et al.,
2008), the primary detuning control (Si et al.,
2008) and the primary energy injection control (Li et
al., 2009). Although no auxiliary circuit is needed for the primary
phaseshifted control as it regulates the voltage via flexible power switches
to change the phaseshift angle, the switching loss and switching stress increases
because of the hard switching mode. As for the primary detuning control, its
demand for an auxiliary circuit not only increases the control difficulty and
system weight but also reduces the total efficiency. Besides, the primary energy
injection control will cause sharp decrease of frequency when the system is
in light running, not to mention that only when the pickup voltage is higher
than the regulated voltage needed, the output voltage of ICPT system can be
regulated via utilizing the decoupling method for the short circuit of auxiliary
coil.
In addition, the ICPT system usually presents complex higherorder switch nonlinear
behavior, for it comprises a number of nonlinear switching devices and energy
storage components. Hence, modeling and control design are rather complex, particularly
when the dynamic behavior of ICPT system is under the action of external disturbance.
By contrast, neural network control doesn’t rely on accurate mathematical
model of system and it reflects complex nonlinear objects that are difficult
to describe accurately at arbitrary precision (Coban, 2004;
Bigdeli et al., 2008; Keshavarzi
et al., 2012). Thus, neural network control is entitled to the abilities
of learning and adaptation, as well as practical value in the applied control
system.
Based on the review above, this study proposes a neural workbased control strategy to stabilize the secondary output voltage of ICPT system. During the control period, the system will work in the softswitching mode and utilize nonlinear function approximation character of the neural network to build a neural networkbased control model when the system gains input disturbance and load step. This model will then dynamically regulate the primary input DC voltage by detecting the actual secondary output voltage, and thus it will keep the secondary voltage at the desired value. Finally, simulation and experimental results have verified the feasibility of this neural workbased control strategy to stabilize output voltage of the ICPT system.
IMPROVED πTYPE ICPT SYSTEM
Figure 1 shows the circuit topology of an ICPT system with improved πtype resonant link. Similar to traditional ICPT system, it also consists of the primary and the secondary sides. At the primary side, a quasicurrent source is built on the input DC source E_{dc} and the filter inductance L_{d}, while a high frequency energy conversion link is made of two power switch pairs (S_{1}, S_{4}) and (S_{3}, S_{2}). Therefore, the forward and backward energy injection modes can be triggered by alternating breakover of the switch pairs. When the power switch pairs are switched at the zerocrossing of capacitor voltage, a ZVS operation would be realized in the system. At this moment, the effective value of the capacitor voltage u_{p} can be calculated by:
In this system, capacitor C_{b} and inductance L_{b} form the
bias network as an improved part of the πtype seriesparallel resonant
circuit (Dai et al., 2010), which eliminates
the harmonic distortion, improves the resonant quality of system and operation
stability, increases the rated power of reactive circulatingcurrent, reduces
the dynamic effect caused by parameter uncertainty of system and load switching,
and eliminates the EMI interference.

Fig. 1: 
The circuit topology of πtype ICPT system 
The bias inductance and capacitor are shown below:
where, m is the bias facto, I_{Lb} is the current across the bias inductance, I_{Cb} is the current on the bias capacitor.
C_{p} and L_{p} comprise the series high frequency resonant
link. The sinusoidal exciting current with low distortion degree is produced
at the primary side. According to the electromagnetic induction principle, the
high frequency sinusoidal power is transferred from the transmitter to the pickup
by mutual inductance M.
At the secondary side, the parallel resonant network with the same frequency at the primary side includes the capacitor C_{s} and the receiver coil L_{s}. The output high frequency power u_{cs} realizes the bidirectional rectification of high frequency sinusoidal current by uncontrollable rectifier full bridge. As the filter choke of the rectifier bridge, L_{f} filters out the high frequency AC current effectively, and only allows low frequency AC current and DC current to pass. Then, the power across the choke is output on the load R_{L}.
THE VOLTAGESTABILIZING CONTROL STRATEGY OF ICPT SYSTEM
To get the main factor which influences the secondary output voltage, rectifier link, filter link and load resistance R_{L} can be equivalent to the equivalent resistance R_{eq}, as shown in Fig. 2, while the power losses of rectifier and filter link in the secondary are ignored.
The total impedance of the secondary coil is shown in Eq. 3:
The reflected impedance from the secondary to the primary is shown in Eq.
4:

Fig. 2: 
Equivalent mode of the secondary side 

Fig. 3: 
Control configuration 
Equation 4 shows that the reflected impedance varies with the equivalent resistance R_{eq} which will lead to the drift of primary resonant current. In this case, the input voltage value is changed dynamically to meet the requirement of secondary output power. Hence, an output voltagestabilizing control strategy based on the Back Propagation (BP) neural network is proposed. Its core mechanism is as follows: When the voltagestabilizing U_{ref} is set, error rate and error change rate are collect by comparing detected practical output voltage and referenced voltage as sample data to input into the neural network control. Meanwhile, the system is driven by the variation module of duty cycles whose output power switches are transformed as a controller. Consequently, a closed loop control system is formed to dynamically stabilize the output voltage on the condition of parameter disturbance and load step. The control configuration is shown in Fig. 3.
BP NEURAL NETWORK MODEL
The BP neural network is a multilayered feedforward network with unidirectional
propagation (Eriki and Udegbunam, 2008; Hsieh,
2010). It is the core of forward networks and the essence of artificial
neural networks. It’s named as the BP neural network, for it uses the errors
back propagation algorithm which modifies the connection weights and thresholds
of each output and input layers to reduce the difference between target output
and practical output. The BP neural network is made of an input layer, a single
or multiple hidden layers and an output layer. There is no connection among
neurons at the same layers but neurons from different layers are connected with
their next layer. According to the approximation theory of neural network, in
the case of reasonable hidden neuron numbers, any nonlinear complex function
with limited discontinuous points can be approximated at an arbitrary precision.
As a nonlinear modeling method, it has favorable fitting precision, nonlinear
quality and generalization ability (Abdalla and Deris, 2005;
Dutta et al., 2012).
A generalized threelayered feedforward network is shown in Fig. 4. This network includes neurons like ‘n’ as the input layer, ‘p’ as the hidden layer, and ‘q’ as the output layer.
Assuming the input vector of neural is X = [x_{1}, x_{2},…x_{k},…,x_{n}] and the output vector is Y = [y_{1},…,y_{m},…,y_{q} ]. As the selection of excitation function through the hidden layer to the output layer has significant influence on the network performance and learning speed Stype activation function is used in the current model due to it resembles to the inputoutput features of human brain and thus has ideal bionic effects. As shown in Fig. 4, module g is the Stype activation function and the first floor has no activation function. Taking the output neuron m as an example to show how this neural network works. Assuming its input weight is W_{lm.3} and its value is calculated based on the signal g_{l2} from Neuron 1. The square of the difference e_{m} between the practical output y_{m} and the target value D_{m} is defined as the index function of this neural network algorithm, as shown in Eq. 5:
Based on gradient descent, the modifier formula of weight coefficient between output layer node m and hidden layer node 1 is shown below:
where, η>0 is the learning rate and usually remains at a small constant value. Then the online adjustment law of network weights can be obtained by:
where, Stype excitation function is shown in Eq. 8:
The signal S_{m3} is determined by all signals from input to the neuron m, as shown in Eq. 9:
The online network weight adjustment is shown in Eq. 10:
where, k is the iteration times.
So far, it has been shown that the BP algorithm is a kind of static optimization
learning algorithm with gradient descent, which modifies the weights in the
opposite direction of the gradient of error performance function without consideration
of accumulation of previous experiences. Hence, the BP algorithm has some defects.
For example, if parameters are not set properly, the neural network may oscillate
during the training process, and slow down error elimination, or make the system
sank into local extremum. Therefore, to improve the standard BP algorithm, this
paper uses the momentum BP algorithm instead. This algorithm can decrease modification
value to ensure that modification is moving towards the convergence direction
in case overmodification happens during the training process. Besides, the
momentum of BP algorithm usually speeds up the modification at the same gradient
direction (Mao et al., 2007; Chen
et al., 2010). When adjusting weights with the BP algorithm, momentum
factor increases so as to filter out the high frequency oscillation generated
during the training process, thus training time is shortened, but the learning
rate and astringency is improved. The regulation formula is shown in Eq.
11:
where, w(k) is connection weight vector, D(k) is the negative gradient at k time, and a is the momentum factor. As the added momentum term is equivalent to the damping term, the tendency to oscillate will decrease during the learning process.
DESIGN OF THE BP NEURAL NETWORK CONTROLLER
A threelayered feedforward neural network is designed in this section, where
the input layer has two neurons, corresponding to the voltage error e and its
change rate e_{c} of the pickup coil; the output layer has one neuron,
corresponding to the change rate of duty cycle. The amount of hidden layers
and their neuron influence the functional approximation of the network. Nevertheless,
the more hidden layers and hidden neurons, the longer the training time and
the lower fault tolerance. Thus, the value function evaluating the BP neural
network performance may not be optimal unless the number of hidden neurons is
calculated based on the empirical formula:
where n_{j} is the number of input neurons, n_{l} is the number
of output neurons, and k is the random integer from [1,10]. Thus, the number
of hidden neurons should be limited to [2, 12]. To find the optimal number of
hidden neurons, a BP network with variable numbers of hidden neurons is designed,
then the error size with experiments is compared, and ten is found as the optimal
number. The vector of the outputs of each neural node in the hidden layers is
defined as [O_{3} O_{4},…, O_{12} ], while the
output of BP network is defined as O_{13}. The hyperbolic tangent Stype
function is used to as the excitation function for the input layer to hidden
layers, while “tansig” and linear excitation function “purelin”
is used for hidden layers to the output layer. The learning rate is set to 0.05,
maximum training times is 500 and target error is 0.000001. The output vector
of hidden layers is shown in Eq. 12:

Fig. 5: 
Mean squared error (MSE) curve of training 
The output vector of network is shown in Eq. 13:
As it has shown above, when the value of the input vector is known, the practical output of the network can be figured out based on the adjustment law of weight coefficients.
Therefore, this paper uses the MATLAB neural network toolbox function to establish an untrained threelayer BP neural network, and construct input (e and e_{c}) training sample set and output (Δd) target set based on the simulation results of the ICPT system. The selected training function is the momentum BP algorithm (Traingdm). The selected weight adjustment law is the gradient descent learning function with momentum (Learngdm). The number of training time is set and then the BP network is trained offline. The value function is used to evaluate whether the neural network training is optimal or not. The Mean Square Error (MSE) of the performance function is selected as the value function to evaluate the network’s performance. The MSE curve during training is shown in Fig. 5.
Figure 5 demonstrates that MSE curve meets the requirement of target error in the 54th iteration and the designed neural network has fast convergence which approximates for the complex nonlinear functional relations of input and output with certain degree of precision.
ANALYSIS OF SIMULATION RESULT
In the MATLAB simulation environment, the simulation circuit in Fig.
6 was established according to the control structure in Fig.
3.

Fig. 6: 
Simulation model of process 

Fig. 7: 
Output voltage under load disturbance 
The effect of voltage stabilizing control on the condition of input disturbance
and load change will be discussed.
The system detected the secondary output voltage in realtime and compared it with the reference voltage to get the error and its change rate as the input sample data for the neural network controller. Meanwhile, the output of the neural network had been in duty cycle variation and served as the duty cycle of Buck circuit to regulate voltage. Hence, the Buck circuit adjusted the trans formation link and then the input voltage of the ICPT system. Table 1 shows the simulation parameter values.
The system started simulation from the steady state, with the simulation time
being 0.02 sec, the expected voltagestabilizing being 50 V. The load value
was changed from 30 to 20 Ω at t = 0.01 sec. Figure 7
shows the simulation waveforms of the neural network controller under load disturbance,
where the output voltage of the ICPT system becomes steady after an overshoot
of 0.003 sec and the voltage stays within the range of ±0.4 V during
the adjustment process.
Table 1: 
Simulation parameters of the ICPT system 

The nether region in Fig. 7 demonstrates the voltagestabilizing
performance waveform during 0.01~0.02 sec after load change when the overshoot
has been within the range of ±1 V during the short adjustment process.
When load changes, the controller has restrain voltage fluctuation effectively
within the overall voltagestabilizing range, showing good control performance
and satisfying the requirement of control accuracy.
When an ICPT system is under operation, it will meet disturbance from the input source. To verify the inhibitory action of the neural network controller under input disturbance, a 50 V DC disturbance was added to the dc source at t = 0.01 sec. Figure 8 shows the simulation waveform of output voltage. When the system was under input disturbance, the output voltage waveform became steady after an overshoot of 0.004 sec with the help of the neural network controller. The overshoot is small and the waveform is quickly stabilized. Besides, the system had fast response speed and kept amplitude of voltage error within the range of ±0.6 V at the steady state. Hence, the neural network controller meet the requirement of accurately stabilize the output voltage.
These simulation results have proven that the neural network controller can effectively help the ICPT system to resist load change and input disturbance, showing small overshoot and strong adjustment performance and robustness of the output voltagestabilizing curves. Thus, it is feasible to use the topology of the system and the neural network controller.
EXPERIMENTAL DEMONSTRATION
Based on Fig. 6, an experimental ICPT system with neural network controller was built, as shown in Fig. 9.
The Buck circuit was used as the regulator to control the input voltage E_{dc},
with the value of filter inductance L_{a} being 5 mH, the value of output
capacitor C_{a} 100 μF and the chopping frequency 20 kHz. The control
circuit detected the secondary resonant voltage U_{cs} and coupled back
to the neural network controller via RFLink. To facilitate the discrete data
processing with DSP, the neural network controller was discretized.

Fig. 8: 
Output voltage under input disturbance 

Fig. 9: 
Block diagram of experiment system 

Fig. 10: 
Experiment waveforms when load jumped from 3520 Ω 
The TMS320F2812 was used as the main control unit to compute error, realize
the neural network algorithm and calculate the duty cycle. The PWM signal was
used to control the Buck circuit to adjust the output voltage.
To go a step further and validate the effect of neural network controller, two groups of load change was set in the experiment, including a resistance load transformed from 3520 Ω and one transformed from 2035 Ω. The expected output voltage of experiment system was assumed to be 13 V, while the input voltage E_{in} was 30 V. The waveforms of output voltage of load u_{o}, control input voltage E_{dc} and the primary current i_{Lp} are shown in Fig. 10 and 11.

Fig. 11: 
Experiment waveforms when load jumped from 2020 Ω 
In Fig. 10, the secondary output voltage has been stabilized
within 30 msec EC after an overshoot of 4 V due to the load change, that is
to say, the overshoot is about 30%. In Fig. 11, the secondary
output voltage reaches the given target state within 28 msec after an overshoot
3.6 V due to the load change, that is to say, the overshoot is about 28%. These
two experiments demonstrate that when the system is under load disturbance,
its secondary output voltage can be stabilized by this neural network controller
with good control accuracy and robustness. Figure 10 and
11 also show that when the load becomes smaller, the primary
input voltage E_{dc} and the primary resonance current i_{lp}
become higher. However, when the load becomes bigger, the primary input voltage
E_{dc} and primary resonance current i_{lp} will step
down. These changes are caused by the variation of reflected impedance.
Moreover, as shown in Fig. 10 and 11, there are ripples in the waveforms of the secondary output voltage u_{o} and the control input voltage E_{dc}. These ripples are caused by the input current disturbance due to the high frequency switching of the primary Buck circuit and inverter. Some measures can be taken to minify these ripples, such as filtering inductor and/or capacitor optimization and switching frequency optimization.
CONCLUSIONS
This research studies the output voltagestabilizing strategy for the ICPT system. As it is difficult to accurately model and effectively control the ICPT system due to its higherorder switch nonlinear behaviors, a neural networkbased control strategy has been proposed. Compared with traditional models, the neural network has the feature of approximating complex nonlinear function. A feedforward neural network based on the BP algorithm has been designed. This neural network serves as the controller of the ICPT system to stabilize the output voltage. Based on the simulation analysis, it can be concluded that the proposed neural network controller can effectively and rapidly stabilize the output voltage which only shows small overshoot. This controller is not only accurate but also feasible. It can stabilize the output voltage even under parameter disturbance and load disturbance due to the selflearning ability and robustness. Furthermore, the load change experiments have verified that this neural networkbased control strategy has great control effect and strong flexibility.
ACKNOWLEDGMENTS
This research is financially supported by the National Natural Science Foundation of China (No. 51207173), the Chinese Research Fund for the Doctoral Program of Higher Education (No. 20100191120024) and the Postdoctoral Science Foundation of China (No. 20110490799). Authors also would like to give special thanks to the reviewers of this paper for their contributions to this study.