1. Introduction
Unmanned aerial vehicles (UAVs) have the advantages of flexible control, simple structure, and low cost, and are widely used in monitoring, plant protection, inspection, disaster relief, etc. [
1,
2,
3]. The flight time of a UAV is an important indicator to measure its performance, and it is a key factor in determining the flight range, the amount of information obtained, and the quantity and quality of tasks performed by a UAV. Therefore, how to effectively extend the flight time of UAVs is a key issue restricting the development of UAVs in the context of no significant improvement in battery energy storage capacity.
There are two ways to prolong the flight time of drones. The first is to increase the capacity of lithium batteries, but the load capacity of drones is limited, and overweight lithium batteries will affect their performance. If the traditional wired plug-in charging method is used, it will consume a lot of manpower and reduce the flexibility of the drone. If the charging process does not require manual intervention, the efficiency of the drone’s mission will be greatly improved. Paper [
4] proposes that photovoltaic cells can be installed on the wings of UAVs, but this method is too dependent on solar radiation, which greatly limits the working time of UAVs. Paper [
5] proposes laser beam technology to charge UAVs, but the power source of this method must always be kept close to the UAV, which increases the cost of UAV operation, and the laser will cause serious harm to organisms.
Wireless power transmission (WPT) can realize the wireless transmission of energy through non-physical direct contact. It has the advantages of high security, strong reliability, and easy automation of the charging process. Therefore, wireless power transmission technology can be applied to the field of drones. Establishing an unattended charging base station wirelessly charges the UAV to make up for the limitation of its short-term operation. At present, there are a few types of research on the wireless power transmission technology of drones. In paper [
6], a small receiving coil is installed at the bottom of the landing gear of the UAV. The magnetic field of this coupling device has a small space and has little impact on the equipment of the UAV. However, the small receiving coil has a poor ability to capture magnetic flux and cannot perform high-power transmission. Paper [
7] installed a hollow planar, receiving coil on the abdomen of the UAV, so that the coil area of the fuselage was significantly smaller than the area of the transmitting end. However, in this coupling device, since the receiving coil of the system is directly installed on the abdomen of the UAV, it occupies the installation space of the UAV’s pan/tilt, which seriously affects the operation performance of the UAV. Paper [
8] developed a 51 W six-wing UAV wireless power transmission system with a maximum charging efficiency of 63.4%. And the external environment will easily make the six-wing UAV unbalanced and difficult to control. Paper [
9] designed a conical convex structure for the wireless charging of drones and the designed coupling device structure. In the process of UAV docking, by relying on the constraints of the physical shape of the coupling device, the UAV can directly stop at the designated transmission position, but this solution needs to modify the UAV style, and increases the design cost of the coupling device. Paper [
10] used the method of expanding the transmitting coil to realize WPT but did not optimize the parameters of the coupling mechanism, and the transmission efficiency was only 62%.
The WPT system for small UAVs is easily affected by various factors such as the environment during the working process. This will directly affect the stability of the UAV during the charging process and may even cause the system to stop working. In the wireless power transmission control system, the control strategy can be divided into primary side control and secondary side control according to the location of the control [
10]. Primary side control refers to controlling the output current by adjusting the parameters of the power input terminal [
11]. This method can generally be divided into two methods: adjusting the excitation current of the transmitter and adjusting the operating frequency of the transmitter. However, in actual use, it is often necessary to add an auxiliary wireless communication module. Otherwise, it is necessary to estimate the transmission state of the system by collecting the voltage and current information of the primary side, and the control accuracy of the system depends entirely on the accuracy of the estimation algorithm. When the estimation accuracy of the estimation algorithm is low, the effect of the primary side control is not ideal. Secondary side control is a method to realize output current regulation by controlling the receiving end, which can complete the control of system output without wireless communication [
12,
13]. Paper [
14] proposes to place the planar air-core receiving coil under the center plate of the frame, the system transmission power is 70 W, the efficiency is 89%, and the secondary side DC–DC circuit is used to charge the system with a constant current. However, the constant current effect is poor when the mutual inductance fluctuates due to environmental changes after the UAV docks. At present, although some scholars have proposed new methods to control the work of DC–DC circuits, they are not all applied to UAV-WPT systems [
15,
16,
17].
With regard to analyses conducted in previous research, wireless charging technology in the field of UAV-WPT application is not yet mature. The present UAV-WPT system faces several important problems that needs to be solved because of the unique shape, small size, and limited capacity, and so, the design needs to be improved to be able to adapt the system to the drone structure and have a good coupling mechanism. At the same time, due to the changeable working environment of the UAV, the UAV can still charge stably when small-range dislocation, resonance parameter deviation, and load change occur after the UAV lands, which is another important problem faced by the current UAV wireless charging system. In order to solve these problems, the research on UAV-WPT technology mainly focuses on the design scheme of magnetic coupling devices and the transmission performance control strategy.
The coupling mechanism of the primary and secondary sides of the UAV wireless charging system is prone to transverse and longitudinal bias during docking; the system coupling coefficient changes, and the transmission efficiency and output power of the system are significantly reduced. The existing research on system parameter optimization only considers the optimization of system transmission efficiency and output power when the primary- and secondary-side coils are aligned, and the optimization results cannot be obtained under the condition of bidirectional migration.
Aiming at solving the above problems, in this paper, we have designed a reliable and effective wireless charging system for UAVs. Based on the quadratic distribution of the offset of the UAV, an offset weight method is proposed to optimize the resonance parameters, and the coupling mechanism is designed to improve the efficiency of the UAV and the anti-offset ability of the aircraft wireless power transmission system. Secondly, the sub-side control technology is proposed to control the working time of the DC–DC MOS tube on the output side by using a model prediction control algorithm to achieve an accurate constant current for charging UAVs. Finally, we have also designed a WPT system that works at 85 kHz and has an output power of 45 W, and have verified the reliability of the coupling mechanism and control method through experiments.
3. Design of Constant Current Control Strategy for UAV-WPT
3.1. Secondary Side Constant Current Control Strategy Based on Model Predictive Control
To realize the control of the wireless charging system for small UAVs, it is first necessary to establish a mathematical model of the control object. Since the input voltage is provided by the wireless charging side, the power input end of the buck circuit can be simplified as a power supply during the modeling process. The control of the buck circuit facilitates the control of the output current. The simplified model is shown in
Figure 13. For this model, the state-space averaging method is used to describe the dynamic characteristics of the circuit. Based on ignoring the state transition time of the switch tube, i
L, and V
c are used to represent the current flowing through the inductor and the voltage across the capacitor, respectively.
At
, the switch tube is in the conduction state, the diode is in the cut-off state at this time, the inductor stores energy through the power supply terminal, and the load R is supplied with energy by the capacitor C. The system state equation at this time is:
At
, the switch tube is in the off state, and the inductance supplies power to the load R and the capacitor C at this time. The state equation of the system at this time is:
The state variable
,
is selected at this time through Formulas (11) and (12) at the k switching cycle of the switching tube
, whose on and off state equations are shown in Formula (13):
where G
1, H
1, G
2 and H
2 are:
In the case of ensuring that the sampling period and the switching period do not change, the discrete-time state equation can be obtained by discretizing Formula (14):
Assuming that the turn-on and turn-off times of the switch tube is D, the state space averaging method can be used to obtain:
Among them, , , .
3.2. Model Predictive Controller Design
According to the principle of the model predictive control algorithm [
22], the augmented matrix is established based on Formula (16), as shown in Formula (17).
where
is a zero vector.
To enhance the controller’s ability to track system state changes and target physical quantities, as well as improve the robustness to system changes, it is possible to expand the dimension of the state vector by establishing an augmented matrix; and thus, the error of the model parameter drift is improved. Using the augmented matrix, the prediction equation of the system in the future N
P sampling moments can be extended to better reflect the changing trend of the system state. That is, the augmented matrix can expand the state vector of the system so that the controller can understand the state changes of the system more comprehensively and make more accurate control decisions. The prediction equation of the system in N
P sampling time in the future is:
NC is the length of the control sequence, and NP is the step size of the prediction time domain. Among them, the prediction time-domain step size directly affects the stability and robustness of the system. Generally, the stability of the control system can be enhanced by increasing the prediction time-domain step size, but too large a prediction time-domain step size will lead to rapid system failure performance deterioration, affecting the dynamic response speed of the system. In a general predictive control system, it is necessary to ensure that the length of the control sequence is greater than the predicted time domain step size. To ensure the stability and robustness of the system, the time domain step size NP is set to 5, and the control sequence prediction step size NC is 3.
Therefore, the cost function J can be established according to the above parameters, as shown in Formula (19):
Formula (18), when applied to a quadratic programming problem, can be expressed as:
In the formula, Rr(k) = [0, …,0, ref(k)]T is a column vector with the same dimension as X(k); ref(k) represents the target reference value at time k; Q and R, respectively, are a weight matrix composed of weight constants and . Increased values in the weight matrices Q and R. can speed up the dynamic response of the system but lead to a decrease in system stability, and vice versa. In this design, the weight constant = 1 and = 10−5 is chosen to achieve higher control precision.
By solving a quadratic programming problem,
The optimal duty ratio control signal at the current moment can be obtained
. To cope with the interference brought by various external environments and device parameter changes to the system, the process will be executed in each sampling period in a rolling optimization manner. If the rated power output needs to be achieved, it can be achieved by changing the current reference value. The constant current control method program based on model prediction is written on the MATLAB platform, and the algorithm flow is shown in
Figure 14.
3.3. Simulation Verification
To verify the effectiveness of the secondary side power control combined with the model prediction control, the LCC-S topology simulation model was built in the MATLAB/Simulink environment. The values of the WPT system for small UAVs are as mentioned above, whereby buck circuit parameters take the filter inductance 22 and capacitance 5.2 . In the simulation, the reference current, mutual inductance, and load values are set as periodic jumps to simulate the impact of transmission distance changes, load mutations, and coil offsets on the system output in actual applications.
The response results of the model predictive controller and PI controller to the step reference signal are shown in
Figure 15.
The initial reference value of the load current is set to 3 A, and a step change occurs at 0.1 s. It can be seen that both sets of controllers can accurately track the step change of the reference value, and there is no significant difference in tracking accuracy, but there are significant differences in tracking speed and overshoot. When the reference voltage jumps from 3 A to 2 A, the MPC controller essentially has no overshoot, and it only takes 0.6 ms to complete the reference value tracking; the PI controller has a significant overshoot, and the response speed is still slower than MPC, and the excessive overshoot has the potential risk of affecting the safety of system components. It can be seen that the MPC control has obvious advantages over the PI control in terms of the speed of tracking the reference value, and it is more in line with the needs of the small UAV-WPT system for fast response.
In addition to fast response, the controller also needs to deal with the impact of dynamic disturbances in the mutual inductance coefficient and load value in the small UAV-WPT system. The response waveforms of the MPC and PI controllers when the mutual inductance jumps are shown in
Figure 16.
When jumps occur from 5
to 7
at 0.1 s, the input voltage amplitude will change abruptly. This process simulates the change of mutual inductance when the charging area is switched and the coil is offset in the small UAV-WPT system, and the controller needs to keep the load current as stable as possible under this condition. It can be seen from
Figure 14 that the PI controller needs a certain adjustment time to stabilize the load current, but there is an obvious overshoot in the adjustment process. Therefore, the load current fluctuates obviously during charging under the action of the PI controller, while the fluctuation of the load current under the control of the MPC is always less than 0.5%. It can be seen that, compared with the PI controller, the MPC controller is more robust to changes in mutual inductance.
Figure 17 shows the response waveforms of the MPC and PI controllers when the load jumps.
The load resistance value jumps from 20 Ω to 10 Ω at 0.1 s. It can be seen that both controllers produce obvious current spikes at the moment of the jump in the load resistance value. This is because the reference current value is set to 3 A before the jump, so that when the first jump occurs, the current change at both ends of the load. The voltage is still 20 V, so the current will change instantaneously, which is the reason for the current peak. During load switching, the regulation time of the MPC controller is 1.0 ms, while that of the PI controller is 3.9 ms, respectively. Therefore, when the load resistance changes, MPC control has obvious advantages in response speed compared with PI control. Combining
Figure 15 and
Figure 16, it can be seen that MPC has a strong robustness to the dynamic changes of mutual inductance and load, and can better meet the robustness requirements of the small UAV-WPT system.
5. Conclusions
In this paper, the equivalent circuit model of the LCC-S topology is first established. Based on the new orthogonal coupling device, according to the influence of the coupling coefficient change on the transmission efficiency caused by the coil offset, a probability model based on normal distribution is proposed. The offset weight method is used to complete the design of the system resonance parameters and improve the anti-offset capability of the UAV-WPT device; secondly, a constant current control strategy based on model prediction is proposed, and the duty cycle of the buck circuit is controlled through the model prediction algorithm, so that the system can still maintain a constant current output when the coupling coefficient, the load, and the reference current change, making the system more practical. The experiment results show that the coupling device designed this time can improve the anti-offset capability of the system, and the proposed control strategy can improve the system parameter efficiency based on realizing constant current output.
However, only the load was used instead of the battery in the experiment this time, which is the limitation of the current research. On the basis of this study, future research can study the control method for constant current and constant voltage charging to meet the actual needs of wireless charging for drones.