Frontiers in Computing and Intelligent Systems 
ISSN: 2832-6024 | Vol. 11, No. 1, 2025 

 

46 

Full‐bridge	DC‐DC	Converter	based	on	Linear	Active	
Disturbance	Rejection	Control	
Xuequan Hua 

School of Information and Control Engineering, Jilin Institute of Chemical Technology, Jilin Jilin, 132000, China 

 

Abstract: Dual Active Bridge (DAB) converter has been a research hotspot in recent years. It is widely used in distributed 
power generation system, DC microgrid system and power management system. Traditional PI controllers do not perform well 
in the face of nonlinear loads and external disturbances, so a more advanced control method is needed to improve the stability 
and performance of the system. In this paper, a control strategy based on active disturbance rejection control (ADRC) is proposed 
to improve the control performance of full-bridge DC-DC converter. First of all, the small signal mathematical model of full-
bridge DC-DC converter is established, and the function relationship between input, output, control quantity and disturbance 
quantity in the system is obtained. Then, the extended state observer of ADRC core module is designed, and its parameters are 
adjusted and simulated, compared with the traditional PI controller. The simulation results show that the full-bridge DC-DC 
converter based on LADRC has faster dynamic response and better disturbance immunity, which can effectively improve the 
stability and robustness of the system. 

Keywords: Dual Active Bridge DC-DC Converter; Linear Active Disturbance Rejection Control; Robustness. 
 

1. Introduction 
The isolated dual active bridge DC-DC (DAB) converter 

has the advantages of bidirectional power flow, high power 
density, easy to realize zero voltage switching, convenient for 
cascade and parallel processing, etc. Therefore, DAB 
converter plays a connecting role in the system, and its control 
effect will directly affect all aspects of the energy conversion 
system. Therefore, DAB has gradually become the research 
hotspot of bidirectional DC converter, and its immunity and 
dynamic response control have also attracted the attention of 
many scholars[1]. 

There are two ways to improve the performance of 
switching converters, one is to propose a new circuit topology, 
the other is to find a better control strategy. The difficulty of 
improving the converter topology depends on the degree of 
functionality and performance enhancements required. 
Simple enhancements, such as efficiency improvements or 
adaptations of specific input and output voltages, may require 
only minor adjustments to existing topologies. However, 
implementing complex features, such as increased isolation, 
multi-port support, or reduced inductance, often requires in-
depth circuit design knowledge and system-level 
optimization, and can therefore involve greater engineering 
challenges and cost inputs. Therefore, it is more convenient 
to optimize the converter from the control strategy. It is very 
important to realize the immunity and robustness of DAB 
converter in the complex and dangerous environment such as 
input voltage fluctuation and output load disturbance. At 
present, the traditional closed-loop control strategy is PI 
control, whose control mode is relatively simple and the 
design is relatively concise. However, due to the defects of 
the algorithm itself, it is difficult for the DAB converter to 
quickly recover to the original state under harsh environment 
(such as large disturbance of input and output, etc.), and the 
dynamic response is slow, resulting in poor system 
performance. At present, in addition to the PI controller, the 
control methods to improve the stability of the system include 
fuzzy neural network prediction[2], synovium control[3], etc. 

Although these methods are better than the traditional PI 
control, their application is still limited because they rely too 
much on the parameters and natural frequencies of the control 
system model. 

There are many limitations in power transmission, 
including input voltage, output voltage, switching frequency 
of the system, equivalent inductance, shift ratio, etc. However, 
for a definite DAB converter, its system parameters are fixed, 
such as input and output voltage, switching frequency, 
equivalent inductance, etc. And its shift ratio D is a physical 
quantity that can be adjusted by control. In the traditional 
closed-loop control mode of DAB converter, PI controller is 
used to adjust the shift ratio and then control the transmission 
power of the system. The purpose of the controller designed 
in this paper is to control the voltage stability of the DC bus, 
and to achieve stability under various disturbances. In the case 
of large shift ratio, the initial value of energy will be very large, 
which is not conducive to the transmission speed of current, 
resulting in its rising speed too slow, which will limit the 
transmission power; In the case of small shift ratio, the current 
will rise rapidly at this time, which will lead to insufficient 
transmission power, resulting in a waste of energy. 

Active Disturbance Rejection Control (ADRC) is a control 
strategy based on modern control theory, which does not 
depend on the internal information of the object, and has the 
advantages of simple structure and strong adaptability. It can 
solve the contradiction between fast response and overshoot 
of PI controller, and has the characteristics of good dynamic 
response and strong anti-interference ability. In 2018, 
Zhiqiang Gso proposed a linear active disturbance rejection 
control method (LADRC), which can greatly simplify the 
tuning of ADRC parameters and provide a good reference for 
other scholars to study ADRC[4]. Based on the above 
research, this paper designs a control strategy based on linear 
active disturbance rejection control (LADRC) for DAB 
converter and verifies its good control effect through 
simulation. 



 

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2. System Modeling of DAB Converter 

2.1. Circuit Topology of DAB Converter 
Figure 1 shows the circuit topology structure diagram of 

DAB converter. Although the number of power switching 
tubes (active semiconductor fully controlled type) is 
increased for DAB converter, its control modes are 
correspondingly increased and the degree of freedom is 
increased, which is more suitable for the scene with large 
fluctuation range on input side and load side[5]. When the 
input voltage changes and load change range is large, by 
adding the phase shift Angle control between the bridge arms, 
the return power can be reduced, so as to reduce the loss of 
the converter, which also does not have much influence on the 
zero-voltage switch of the switching tube. 

 
Figure 1. Topology structure of dual active DAB converter 

 
The DAB converter consists of a primary bridge H1 (S1-S4) 

and a secondary bridge H2 (M1-M4) connected by a high-
frequency transformer T. L is the transmission inductance; U1 

and U2 are the DC voltage of the primary side (input voltage) 
and the secondary side (output voltage) respectively. R2 is 
equivalent load of DAB converter; C1 is the protection 
capacitor on the input side, and C2 is the support capacitor on 
the output side. i1, i2 and i0 are the input current, output current 
and load current of the converter respectively, and iL is the 
current flowing through the equivalent inductance L. The 
ratio of the transformer is K=n:1. 

2.2. Power Analysis of Single Phase Shift 
Control 

 
Figure 2. Waveform diagram of steady-state controlled by single 

phase shift 
 

DAB converter commonly used Single Phase Shift control 
(SPS), this control mode is easy to achieve, can reduce the 
voltage and current stress of the power switch tube. The 
steady-state waveform diagram of single-phase shift control 
of DAB converter is shown in Figure 2. 

In the figure, S1-S4 and M1-M4 are the corresponding 
switch control signals with the same frequency and duty cycle 
of 0.5. The diagonal switch control signals are the same and 
complementary to the other diagonal signal. Th is half a 
switching period, Tf=1/2f (f is the switching frequency), Ts is 
a switching period; D represents the shift ratio between H1 
and H2 Bridges, i.e. D=φ/π; UL Indicates the voltage at both 
ends of the inductor. D>0 indicates that the power flows from 
the primary side to the secondary side, that is, the energy 
passes through positively. D<0 indicates that the power flows 
from the secondary side to the primary side, that is, the energy 
flows in reverse. Due to the symmetrical structure of DAB 
converter, the forward flow of energy and the reverse flow 
mechanism are the same. In this paper, the forward flow of 
energy is used as the basis for analysis. 

By analyzing the steady-state mechanism of DAB 
converter under single phase shift control, it is not difficult to 
conclude that the current iL flowing through the equivalent 
inductor L is centrosymmetric in one cycle, then the algebraic 
sum of the inductor current in one cycle is zero, and only the 
mathematical model of steady-state power in one cycle needs 
to be calculated. 

In one cycle, according to the DAB power definition, the 
transmitted power expression 1 of the DAB converter under 
SPS control can be obtained as follows: 

  1                (1) 

Since the conversion circuit of the DAB converter on both 
sides of the high-frequency transformer is symmetrical, the 
above analysis method can also obtain the power expression 
during DAB reverse transmission, so the total power 
expression of the DAB converter during power expression 2 
can be obtained: 

P |D| 1 |D|                     (2) 

D>0, indicates forward power transmission; D<0, reverse 
power transmission. 

According to power expression 2, the relationship between 
its own variable D and power P can be drawn, as shown in 
Figure 3. 

It can be seen from the figure that when the transmission 
power transmits energy in the reverse direction, D∈	(-1,0), the 
absolute value of the transmission power first increases and 
then decreases with the increase of the shift ratio. When 
D∈(0,1), the power is transmitted forward, and the change of 
the absolute value of the transmitted power is the same as in 
the reverse transmission. The transmission power has a 
maximum of nU1U2/8fL if and only if D=±0.5. 

In the process of energy transmission, if the energy loss of 
various devices is not considered, it can be considered that the 
input power of the system is equal to its output power, and the 
power on the output side can be expressed by the formula 
2P2=U2/R2, where R2 represents the load resistance on the 
output side. From Formula 1 and the power expression of the 
output side, the voltage expression 3 of the output side system 
can be obtained as follows: 

 

U D 1 D R                       (3) 

 



 

48 

 

 
Figure 3. Shift compared to the transmission power graph 

 
Similarly, when the power is transmitted in reverse, the 

expression 4 of U1 is: 

U D 1 D R                       (4) 

Where R1 is the equivalent load resistance on the U1 side. 
If the average value of input and output current is 

multiplied by the equivalent resistance of each side to 
represent the power of each side, the expression 5 of the 
average value of the current of each side can be obtained: 

I D 1 D

I D 1 D
                       (5) 

2.3. DAB Small Signal Modeling and its Design 
Accuracy 

The small-signal modeling of DAB converter is the basis 
for analyzing the closed-loop control and parameter design of 
the converter, because we can deduce the transfer function of 
DAB converter from the small-signal model, which is of great 
help to the parameter design of the control of DAB converter. 

According to expression 5, the average physical model of 
DAB can be obtained. By adding small disturbance signals to 
the steady-state model of DAB converter, and then separating 
the disturbance and ignoring the quadratic term, the first-
order small signal model of DAB converter can be obtained, 
and then the corresponding closed-loop control design can be 
carried out. In order to introduce low frequency small signal 
disturbance, perturbation U1→U1+ , U2→U2+ , I1→I1+ ̂ , 
I2→I2+ ̂  , D→D+d^ is added to the input current, output 
current and shift ratio expression obtained by equation 5, By 
eliminating the direct flow and high-order disturbance 
existing in the formula, the following expression 6 can be 
obtained: 

ı̂ b d b u
ı̂ b d b u

                        (6) 

In Formula 6, b1=nU2(1-2D)/2fL, b2=nD(1-D)/2fL, 
b3=nU1(1-2D)/2fL. 

Thus, DAB small signal model can be obtained, as shown 
in Figure 4: 

 
Figure 4. Small signal model of DAB 

 
From Figure 4, the transfer function formula 7 of DAB 

control quantity to output can be obtained: 

G |                    (7) 

Formula 7 represents the effect on the voltage on the load 
side when the shift ratio of the system is disturbed. 

Some parameters of the system in this paper are: U1=400V, 
U2=100V, L=150μF, C1=C2=500μF, R2=2Ω, f =20kHz. 
According to formula 3, the shift ratio D=1/4 of the system in 
the steady state can be obtained. According to Equation 7 and 
substituting relevant data, the initial open-loop transfer 
function 8 of the system without using PI controller can be 
obtained as follows: 

G
.

.
                          (8) 

The Bode diagram of the transfer function of the system 
can be made by MATLAB software, and the Bode diagram of 
the model can be obtained by small signal modeling method, 
as shown in Figure 5 below: 

It is proved that the establishment of the above physical 
model is relatively accurate, which is consistent with the 
previous theoretical analysis. It can be seen from the figure 
that the system is stable, but it can also be seen that the gain 
of the system in the low frequency band is low, and there is a 
certain steady-state error, so the system needs to be corrected. 

3. Controller Design 
It can be seen from formula 7 that the system can be 

simplified into a first-order system, so a first-order active 
disturbance rejection controller is designed. According to 
Equation 7 and the small signal model in Figure 4DAB, the 
time-domain expression of DAB expression 9 can be written: 

C d                    (9) 

Formula 9 can be written as the general form 10 as follows: 
y a y w bu                       (10) 

The controller is designed to maintain the stability of the 



 

49 

output voltage. The control quantity is shifting ratio D, y 
represents the output voltage of the transformer, and the 
output U of the controller represents shift ratio D. w 
represents the disturbance in the internal and external parts of 

the system, and a1 is the internal parameter of the DAB 
converter (a1 and w are unknown). If b is the input control 
gain and part of it is known (known part is b0, b0=nU1(1-
2D)/2fL), then the above formula can be written as 11: 

 

 
Figure 5. Bode diagram of the open-loop transfer function of the system before adding the controller 

 
y a y w b b u b u f b u     (11) 

Choose state variables x1=y,x2=f, and let ,   to 
obtain the equation of state of the expression 12: 

x x b u
x h
y x

                          (12) 

Equation of expression 13 for establishing LESO is as 
follows: 

z z β z y b u
z β z y                   (13) 

In the formula, Z1 and Z2 are state variables of LESO; β1 
and β2 are observer gain parameters. z → x , z → x , where 
h is unknown, but can be estimated by LESO, so it can 
generally be ignored in LESO equation of state description. If 
the parameters are selected reasonably, the LESO state 
variables can track the system state variables in real time. 

The first-order linear error state feedback law (LESF) is 14 
because it does not need to observe the differential signal of 
the system state variable: 

u k ν z                    (14) 
In the formula, U0 represents the output item of LESF, and 

Kp represents the gain of the proportional controller. 
The traditional PI controller can eliminate the error of the 

system through integration, which will reduce the stability of 
the system. The first-order LADRC can make use of second-
order LESO to compensate the generalized disturbance in real 
time, which can effectively avoid the influence of the integral 
link [6]. The total disturbance of the system is estimated by 
expanding the state variables, and the input of the system is 
compensated. Formula 15: 

u                           (15) 

If the error of Z2's estimation of the total disturbance is 
ignored, then substituting equation 14 into equation 11 can be 
simplified to an integral component equation 16: 

y f y, w z u u                (16) 
According to equations 13 and 15, the closed-loop transfer 

function 17 of the DAB converter can be sorted out as follows: 

φ s
/ ⋅

                    (17) 

As can be seen from equation 17, the bandwidth of LSEF 
ω k , so in order to make the system eventually stable, to 
choose a better proportional gain value [7]. The detailed 
internal control structure diagram of LADRC of the system 
can be obtained according to formula 10, 13 and 14, as shown 
in Figure 6: 

 
Figure 6. Detailed internal structure of first-order LADRC 

 
In order to further simplify the parameter design of the state 

observer, the gain matrix of the observer is associated with 
the bandwidth of the observer through the method of pole 
parameter configuration, and the pole of equation 13 is 
assigned to the bandwidth w0 of LESO, namely, equations 18 
and 19: 

λ s s l s l s ω                (18) 
l 2ω
l ω

                          (19) 

After the above mathematical analysis, the parameters of 
the ladrc can be found to be properly configured with two 
parameters, and ω , ω 	 is able to make the control effect of 
the controller achieve the desired state [8]. 

4. Control Effect Verification 
In order to verify the superiority of the proposed LADRC 



 

50 

control strategy, the control simulation model of DAB 
converter is built based on MATLAB/Simulink simulation 
software. It is compared with the traditional PI single closed 
loop control. The internal parameters of DAB converter are 
shown in Table 1, and the controller parameters are shown in 
Table 2: 

 
Table 1. Detailed parameters of DAB converter 

Argument Numerical value Unit 

Supply voltage 400 U1/V 

Output voltage 100 U2/V 

Ratio of transformer 4:1 n 

Switching frequency 20 f/kHz 

Series inductance 150 L/μH 

Input capacitance 500 C1/μF 

Output capacitance 500 C1/μF 
 

Table 2. Controller parameters 
Argument Numerical value 

Observer bandwidth ω0 1200 
Controller bandwidthωc 10000 

Control gain b0 100000
 
In the process of parameter setting in this paper, the size of 

b0 is first determined, wc remains unchanged, and w0 is 
gradually increased until the impact of noise meets the 
requirements of the system. Then gradually increase wc, 
reduce w0 when the system cannot withstand the noise, and 
then increase wc, when the ideal waveform curve is basically 
reached, then fine-tune ω0 and ωc until the expected effect is 
better. 

The simulation model of the system was built in simulink 
simulation software. When the system reached a steady state, 
the main working waveform was shown in Figure 7. 

 

 
(a) Inductive current waveform 

 

 
(b) inductance voltage waveform 

Figure 7. Working waveform of stable working system 
 

According to (a) and (b) in FIG. 7, it can be seen that the 
voltage and current at both ends of the inductor are consistent 
with the final result of phase shift control analyzed above. 
Therefore, the final control effect of the LADRC strategy 
proposed in this paper is consistent with the results of the 
previous mathematical analysis, which can realize the control 
of DAB converter. 

In order to verify the good immunity of LADRC compared 
with PIDE, this paper tests the superiority of the control 
strategy by adding disturbance on the load side and power 
supply. 

(1) Load mutation 
Figure 8 compares the dynamic response of the two control 

schemes with a step change in load (2Ω-4Ω-2Ω). It can be 
seen from FIG. 8 (a) that when the load of the DAB converter 
suddenly increases at 0.02s, the output voltage returns 
increases to a certain extent, and then returns to the initial 
state after a short process. In FIG. 8 (b), when the load of the 
system suddenly decreases at 0.05s, the output voltage return 
of the DAB converter decreases instantaneously and also 
returns to the original state. This shows that the closed-loop 
design of the two control schemes of DAB transformation 

meets the dynamic response requirements of the system and 
has a certain anti-disturbance ability. As can be seen from 
Figure 8, the dynamic response of LADRC strategy is much 
better than that of PI control scheme no matter the load 
increases or the load decreases. In LADRC control scheme, 
when the load increases, the adjustment time is shortened by 
2ms compared with PI control, and the overshoot is reduced 
to 3V compared with PI control, and the overshoot time and 
overshoot also change significantly when the load decreases. 
Therefore, the LADRC control scheme can significantly 
improve the dynamic response and robustness of the system. 

(2) Input voltage mutation 
Figure 9 (a) shows the output voltage waveform when the 

input voltage suddenly decreases from 400V to 350V, and 
Figure 9 (b) shows the voltage waveform when it recovers to 
400V. It can be clearly seen from Figure 9 that the overshoot 
of LADRC during the transition process of restoring to the 
initial value when the input voltage suddenly increases or 
decreases, is about twice the overshoot of PI control strategy. 
The transition time is significantly faster than PI control. 
Therefore, the anti-input voltage disturbance capability of 
LADRC is better than that of PI control strategy. 



 

51 

 

 
(a) Sudden increase in load 

 
(b) Sudden load reduction 
Figure 8. Load mutation 

 

 
(a) Sudden decrease in input voltage 

 
(b) The input voltage is restored to 400V 

Figure 9. Input voltage 
 

5. Summary 
In order to improve the dynamic response and immunity of 

DAB converter, the working principle of DAB converter is 
analyzed first, and then small signal modeling is carried out. 
On this basis, an active disturbance rejection controller based 
on LESO is designed. The anti-interference ability of this 

control strategy is significantly better than that of PI control 
in the face of load side disturbance and power side 
disturbance. Therefore, the control strategy proposed in this 
paper has a good application prospect in the control of DC/DC 
converter. 



 

52 

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