INTRODUCTION
Inductively Coupled Power Transfer (ICPT) technology is a practical and flexible
technology developed to deliver power wirelessly from the stationary power source
to one or more loads. It is becoming increasingly popular in a variety of industrial
and commercial applications where high reliability and residuefree operation
within exacting or harsh environments may be necessary (Si
et al., 2008; Boys et al., 2007; Wu
et al., 2011; Villa et al., 2012).
Generally, the output of ICPT system is regulated by a DC/DC converter which
is located ahead of the inverter. This method is of high cost and low efficiency.
For traditional ICPT system, it uses single LC resonant network to maximize
the output energy (Tian et al., 2012; Wang
et al., 2004). There is a large current in primary coil which would
dramatically increase the losses of inverter and reduce the system efficiency.
At present, there are some difficulties in system controller: nonlinearity,
high orders and high frequency. Due to nonlinear switch network in system, switching
nonlinearity exists in system dynamic behaviors. At present, in addition to
the traditional PID control, robust control (Li et al.,
2011, 2012; Wang et al.,
2009) is used in ICPT system but there is certain ripple and it’s so
difficult in selecting the weighting functions. Because the inverter is just
periodic variable structure system, the sliding mode control is a better method
with strong adaptability (Zhang and Qiu, 2006; Xu
et al., 2007; Wan et al., 2011; Tang
et al., 2012; Kang and Jin, 2010; Zribi
and AlRifai, 2006; Xizheng and Yaonan, 2011; Rabi,
2006; Lasaad et al., 2007). However, in order
to eliminate the chattering problem in traditional sliding mode control, the
common method is the quasi sliding mode control (Slotine
and Sastry, 1983). As an improvement of traditional sliding mode control,
the quasi sliding mode control doesn’t require the control structure switching
on switching surface. It can vary the structure on the boundary layer so that
continuous feedback control can be occurred within the boundary layer. With
these differences it makes the quasi sliding mode control avoid or weaken the
chattering fundamentally. Besides, for ICPT system, there are many perturbation
actions (such as load disturbance, frequency disturbance (Li
et al., 2012), so the application of traditional control way is limited.
Based on the above analysis, this study presents quasi sliding mode control strategy with feed forward compensation in improved ICPT system. A high frequency transformer is set up which reduces loss and makes the impedance between inverter and resonant network match. Moreover, a phaseshift method is proposed to realize the rapid regulation of the output voltage.
IMPROVED ICPT SYSTEM
The circuit topology of improved ICPT system is shown in Fig. 1. Similar to the traditional ICPT system, it consists of two independent sections named primary part and secondary part.
In primary part, DC input voltage V_{d} is selected as energy input.
A high frequency transformer network is added between the full bridge inversion
networks, made up of S1, S2, S3 and S4 and resonant network comprising resonant
inductance L_{p} and capacitance C_{p}. In secondary part, energy
pickup coil (L_{s}) receives energy from primary part and produce resonance
in network comprising resonance inductance L_{s} and capacitance C_{s}.

Fig. 1: 
Improved circuit topology of ICPT system, V_{d}: DC
power supply, S1S4: Insulating gate bipolar transistor (IGBTs), u_{in}:
Output voltage of inverter, N: Winding turns ratio, u_{p}: Voltage
of the primary capacitor C_{p}, i_{p}: Current of the primary
inductor L_{p}, M: mutual inductance, i_{s}: Current of
the secondary inductor L_{s}, u_{s}: Voltage of the secondary
capacitor C_{s}, Cf: Filter capacitor, L_{f}: Filter inductor,
R: Load resistor, R_{L}: Equivalent resistance 
The rectifier and filter circuits and load can be simplified by an equivalent
resistance R_{L}. The high frequency transformer network not only realizes
the electric isolation between the full bridge inverter and resonant network
to protect Insulated Gate Bipolar Transistor (IGBT) but also changes the output
impedance of inverter to realize the impedance matching of system by changing
the winding turns ratio. According to the AC impedance model of system resonant
tank, the equivalent impedance Z_{s} of secondary parts is:
where, ω is the operating frequency.
The reflecting impedance Z_{r }is:
Hence, the system impedance Z_{t} is:
It can be concluded from Eq. 13 that the
impedance can be changed by the winding turns ratio N of the high frequency
transformer. An appropriate N can be designed to achieve the purpose of the
impedance matching.
PHASESHIFT REGULATION AND MODELING
One output regulating method which doesn’t need additional circuit, economizes
the cost and improves the efficiency is to shift the phase of the gate signals.
As shown in Fig. 1, the switches S1 and S2, S3 and S4 are
complementarily controlled. If both the upper switches S1 and S3 (or both the
lower switches S2 and S4) are “on”, the AC output voltage from the
inverting network is zero. Otherwise, the output voltage will be either positive
V_{d} or negative V_{d}, depending on the state of the switches.
Because of this, phaseshift duty cycle control can be utilized to regulate
the output voltage.

Fig. 2: 
Phaseshift control, GS1: Gate drive of S1, GS2: Gate drive
of S2, GS3: Gate drive of S3, GS4: Gate drive of S4 
Figure 2 shows a situation when the gate signals of S3 and
S4 are lagging S1 and S2 by t_{1}. In this case, the output voltage
is a PWM square wave with a duty cycle of (T2t_{1})/T. For inverter
side, the equivalent impedance of load also is changed.
The relationship between the inverter output voltage u_{in }and phaseshift
angle α is:
where, α is 2πt_{1}/T.
According to t he Kirchhoff’s voltage law and current law, the system
can be described as follows (Sun et al., 2005):
where, λ is 1/(L_{p}L_{s}M^{2}).
where, i_{p}, u_{p}, i_{s} and u_{s} represents the exciting current, the voltage of resonant capacitor C_{p}, the pickup current and pickup voltage. The Eq. 5 can be described as:
Where:
A and B as the constant matrixes denote the system matrix and control matrix.
QUASI SLIDING MODE CONTROLLER DESIGN
From the Eq. 5, the ICPT system is just a variable structure system, so the sliding mode control strategy has strong adaptability for this system. In sliding mode control strategy, the system dynamics is forced by the controller to stay confined in a subset of the state space denominated sliding surface. That is, one first constructs a Lyapunov function and then tries to and a control law to make the derivative of the Lyapunov function negative definite. As the method provides robustness characteristics, there is a major problem, the chattering phenomenon, usually encountered in the practical implementation. This phenomenon is highly undesirable because it may excite the highfrequency unmodeled dynamics.
According to the Eq. 5, the new state space description about errors of each state can be obtained as follows:
Where:
i_{p(ref)}, u_{p(ref)}, i_{s(ref)} and u_{s(ref)} represent the reference values of i_{p}, u_{p}, i_{s} and u_{s}.
The switching function (sliding surface) s can be described as:
where, k_{1}, k_{2} and k_{3} represent the control parameters termed as sliding coefficients.
So, it can be obtained:
Where:
According to the generalized sliding mode conditions s.<0, it can be obtained:
Here, the normal movement segment can be limited with exponential reaching rate to improve its dynamic quality. The exponential reaching rate can be described as:
Then, the control function can be worked out:
The chattering problem of traditional sliding mode control is caused by the
sign(s) of Eq. 12. In order to eliminate the chattering,
the saturation function sat(s) is used instead of sign(s):
where, Δ represents the boundary layer. The essence of saturation function
is that switching control is used beyond the boundary layer while linear feedback
control is used within the boundary layer. In this strategy, the system dynamics
is forced by the controller to limit in some Δ neighborhood of ideal sliding
mode. The quasi sliding mode doesn’t require meeting the condition of existence
condition within the boundary layer, so there is no switch on the switching
surface and the chattering is essentially eliminated. Besides, the quasi sliding
mode control has many advantages, such as fast response, insensitive to parametric
variable and external disturbance and excellent steady as well as dynamic response.
Substituting Eq. 1312 and the quasi
sliding control function u_{s} can be rewritten as:
Because the main factor of breakage system steady process is the frequent switching of system load in ICPT system, a load disturbance feedforward compensation controller is introduced to improve the control performance of system. This way could reduce the gain of switching term in the sliding mode controller; improve system dynamic performance by the feedforward compensation of external dynamic disturbance.
The feedforward compensation control function u_{c} can be expressed as:
where, d is the transfer function, f is the load disturbance.
Combining the quasi sliding mode controller and the feedforward compensation controller, the control system is shown in Fig. 3, the designed control function u is:
Actually, the system is disturbed by many uncertain factors which include the uncertain of system matrix and external load disturbance, so the system becomes unsteady. So the system can be described accurately as:
Let the switching function ds/dt = 0, so it can be obtained:

Fig. 3: 
Block diagram of control system, H: Disturbance matrix, u_{1}(e)~u_{3}(e):
Quasi sliding mode control function, C: Output matrix, y: Output 
If the (KB') is nonsingular, the equivalent control function can be described as:
Substituting Eq. 1917, it can be obtained
the sliding mode motion equation:
According to the Eq. 20, it can be known that if it is satisfied the conditions of:
the sliding mode motion is not influenced by the external load disturbance. So the parameter of the controller should meet the conditions as far as possible. However, we can’t eliminate the disturbance completely. In this case, the feedforward compensation is built to counteract the varieties which result from the load disturbance. The condition of the feedforward controller is as follows:
where, G stands for the transfer function model of ICPT system.
The block diagram of control system is shown in Fig. 4. The control system consists of the state observer and control function. Based on detecting the output voltage of inverter u_{in} and reference u_{s(ref)}, the state observer is used to calculate the real time reference value of i_{p(ref)}, i_{s(ref)} and u_{p(ref)}. Then the control law is built by the errors of the four states.
When load varies result in the variety of output voltage, the controller can
calculate the control output to keep the output voltage stabilization.

Fig. 4: 
Structures of ICPT with quasi sliding control, V_{o}:
DC output voltage 

Fig. 5: 
Control flow chart 
The control flow chart is shown in Fig. 5. The voltage u_{s}
of C_{s} is detected for calculating the switching function. If the
sliding mode is out of the boundary layer, the switching control is used, while
if the sliding mode is within the boundary layer, linear feedback control is
used. However, when the disturbance appears, the feedforward compensation control
is used to eliminate the effect of load variation.
SIMULATION AND EXPERIMENT
In order to validate the feasibility of control strategy, the simulation model is built in MATLAB, the parameters are shown in Table 1.
In order to evaluate the performances of the proposed control strategy, the
traditional PI control result is compared. The simulation results in load perturbations
are shown in Fig. 6. It can be seen that with load resistance
changing from 20 to 5 Ω at the instants t = 0.04 sec, the output voltage
can faithfully follow the reference input (75 V) with the phaseshift angle
gradually decreasing from 61.212.6°. However, PI controller takes about
20 msec to adjust the output voltage to reaching the steady state again when
load variation occurs. And with a large overshoot about 28 V. It can be seen
that about 15 m sec^{1} is taken to reach the steady state almost without
overshoot and oscillation in quasi sliding mode control strategy with feedforward
compensation.
In order to verify the simulation results, an ICPT system experiment system
is set up as shown in Fig. 4, according to the parameters
in Table 1.

Fig. 6(ab): 
Simulation results with different control strategies, (a)
PI control and (b) Quasi sliding mode control with feedforward compensation 
Table 1: 
Parameters of ICPT system 

The experimental results using the quasi sliding mode control strategy with
feedforward compensation are shown in Fig. 7.
Figure 7a shows the steady state waveforms including the gate drives signals, input voltage of resonant network and DC output voltage. It can be seen that the DC output voltage is equal to 75 V with the phaseshift angle about 60° when the load resistance is 20 Ω. Due to parasitic parameters in circuit, there exists a certain difference between the experiment and simulation in the phaseshift angle.
From Fig. 7b, it can be known that the dynamic response process
just takes 15 m sec^{1} to successfully achieve tracking the reference
value when the load resistance changes from 205 Ω.

Fig. 7(ab): 
The waveforms of the proposed control system, (a) The steady
state waveforms of ICPT system and (b) The transient process of proposed
control strategy with load variations 
The overshoot and oscillation are also weakened in quasi sliding mode control
strategy. From these measured waveforms, it is evident that the quasi sliding
mode control system has achieved the fast and accurate dynamic tracking performance.
CONCLUSION
This study puts forward an improved ICPT system, which based on the principle of impedance matching. The output is regulated by shifting the phase of the gate signals with the quasi sliding mode control strategy. The feedforward controller is added into the system controller to overcome the voltage fluctuations caused by the variation of load disturbance. The controller is proposed in the paper and its performance is compared with that of a PI controller in order to show the necessary of using such a composite approach by simulation and experiment. The results have verified the feasibility of sliding mode control method on the field of ICPT.
ACKNOWLEDGMENTS
This research work is financially supported by National Natural Science Foundation of China (No. 51007100) and Fundamental Research Funds for the Central Universities (No. CDJXS10170002). Author also would like to give my special thanks to the reviewers of this paper for their contributions to this study.