 Open Access
 Total Downloads : 42
 Authors : Qingsong Jiao
 Paper ID : IJERTV7IS030079
 Volume & Issue : Volume 07, Issue 03 (March 2018)
 Published (First Online): 20032018
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Double Closed Loop Coordinated Control of Quadrotor Based on PID / LADRC
Qingsong Jiao
Tianjin University of Technology and Education Tianjin 300222, PR China
Abstract For control system of a quadrotor aircraft with underdriven, strong coupling and nonlinear characteristics. This paper presents a double closed loop collaborative control method of PID / LADRC to control the position and attitude of the control system. Among them, the attitude loop is the inner loop of the control system, and the linear automatic disturbance rejection control method is adopted. The position loop is the outer loop of the control system, and the PID control method is adopted. Due to the underdriven nature of the control system of quadrotors aircraft itself, the expected values of pitch and roll angle are given by the outer loop controller. Finally, through the MATLAB simulation of the control system, and then to verify the effectiveness of the control system of quadrotor using the PID / LADRC double closedloop coordinated control method.
Keywords: Quadrotors; Position Control; Attitude Control; Automatic Disturbance Rejection Control; PID Control

INTRODUCTION
In recent years, the continuous development and advancement in the field of control have promoted the development of the quadrotors aircraft. In terms with the traditional unmanned aerial vehicle, the quadrotors aircraft have the pros of small size, light weight and flexible maneuver performance. Therefore, a considerable number of domestic and foreign universities and researcher's attention. As the quadrotors aircraft can achieve translation and rotation during the movement, and then can do pitch, roll, yaw, hover and vertical movement, before and after the movement and lateral movement of the six basic movement states. Through the different combinations of the six basic movement states, it can make any trajectories and motions in any threedimensional space and is widely used in civil and military areas. For example, on the military side, the quadrotors aircraft can perform control tasks such as detecting battlefields, targeting and tracking targets, and delivering weapons as carriers; On the civilian side, the quadrotors aircraft can be used in aerial photography, environmental surveys and search and rescue after a major disaster [1], and can carry on scientific experiments by carrying a variety of devices.
Due to the typical features of underdriven, strong coupling and nonlinearity, the quadrotors aircraft bring tremendous difficulties to the control of quadrotor aircraft [2]. At the same time, the mass of quadrotors aircraft is lighter, so during the movement in the extremely vulnerable to external environment and other factors. Thus, we need to be strong antiinterference performance in the design of the controller.
The continuous development and advancement of control theory has given rise to an increasing number of control methods being applied to the analysis and design of the quadrotors control system. In the meantime, the control system can be controlled more optimally by using the above control methods. For example, PID control [34]adaptive control
[5], fuzzy control [6], sliding mode control [78]and ADRC [9]. Simple sliding mode control has the significant pros of strong robustness. When the control system is disturbed by the outside world, the steady state error will be generated, which will result in lower control accuracy. The adaptive control is generally used in conjunction with other methods, and through the integrated control technology to achieve the stability of its control system. In the case of model uncertainty and external disturbance, adaptive fuzzy control based on fuzzy CMAC is applied to the control system. At the same time, adaptive parameters are used to make the control system have good steady state performance.In this paper, based on a dual closedloop control method combining PID and LADRC to control the position and attitude of the quadrotors, the inner loop adopts the method of LADRC to control the attitude of the aircraft, while the outer loop adopts the method of PID control to control the position of the aircraft, the controller has strong antijamming performance and strong robustness.

THE QUADROTOR AIRCRAFT DYNAMICS MODEL AND ANALYSIS
As the quadrotor aircraft is a nonlinear, multivariable and strongly coupled underdriven system, in order to further control such underactuated control systems, such as the quadcopter, firstly,the dynamics model of the control system must be established. In order to establish the dynamics model of quadrotor control system, first and foremost,we must select the appropriate coordinate system, which is the ground coordinate system and the airframe coordinate system. When the quadrotor aircraft is flying, the constant change of the three Euler angles will directly result in the change of the flight state of the quadrotor aircraft in the airframe coordinate system, but the ground coordinate system will remain unchanged all the time. Fourrotor aircraft flying attitude in the air is usually reflected by three Euler angles. which is rolling angle , pitch angle and yaw angle .Euler angle is used to accurately determine the role of rigid body at a fixed point where the specific location. The selected fixed point is the origin of the airframe coordinate system, and the three attitude angles – roll
angle , pitch angle and yaw angle are used to determine
the coordinate of the axis of motion in the spatial direction. It can also indicate the rigid body around its corresponding rotation angle of the shaft. In order to describe the attitude of quadrotors aircraft more clearly, three Euler angles can be used to express the concrete conversion relationship between attitude matrix and Euler rotation, and then the concrete conversion relation between ground coordinate system and body coordinate system can be derived. Fig. 1 shows the relationship between the ground coordinate system and the airframe coordinate system.
xbThe horizontal plane 4
U1 Fi m
i 1
x' y
U 2 F1 F2 F3 F4 I1
(6)
g U F F F F I
3 1 2 3 4 2
x
g U 4 C F1 F2 F3 F4 I3
y'
O
yb
The vertical plane
zb
z'
Where U1 is the control input acting on the quadrotors in the zaxis direction; U 2 and U 3 denote the control inputs of the pitch angle and roll angle respectively; U 4 denotes
the yaw moment; C denotes the forcetotorque conversion factor .
Therefore, we can draw:
x U1 cos sin cos +sin sin K1 x m
z y U1 cos sin sin sin cos K2 y m
(7)
g
Figure 1 the relationship between the ground coordinate system and the
z U
1 cos cos g K3 z m
airframe coordinate system
The ground coordinate system to the airframe coordinate system conversion matrix as (1) shown, that is
The quadrotors body in rotation, the moment balance equation can be drawn:
I1 l F1 F2 F3 F4 K4
cos cos
R sin cos
cos sin sin sin sin
sin sin sin cos cos
cos sin cos sin sin
sin sin cos sin cos
(1)
I2 F1 F2 +F3 F4 K5
(8)
I3 C F1 F2 F3 F4 K6
sin
cos sin
cos cos
In orderto further simplify the dynamic model of the qu adrotors control system, according to Newton's second law, th e dynamic equations of the quadrotors can be expressed as:
Combined with equation(6) can be drawn:
=U2 lK5 I2
U3 lK4 I1
(9)
F m dv
(2)
U K I
dt
4 6 3
M dH
(3)
In conclusion, the nonlinear dynamics model of the
dt quadrotor obtained is:
In equation (2) and (3), F is the resultant force of
quadrotors aircraft flying in space , m is the mass of the quad
x U1 (cos sin cos sin sin ) K1 x / m
y U (sin sin cos sin cos ) K y / m
copter itself, v is the speed of the quadrotors in space motion,
1 2
z U1 (cos cos ) g K3 z / m
M is the external moment of rotation of the quadrotors, and H is the absolute moment of momentum of the quadrotors with respect to the ground coordinate system.
The fourrotor aircraft in flight during the specific force
U lK / I
2 5 2
U lK / I
3 4 1
(10)
situation is as follows: that the four rotor generated by the lift Fi i 1, 2,3, 4 , The body's own gravity mg and air resistance, quadrotors aircraft lift in the body coordinate
4
U4 K6 / I3
In the dynamics model of quadrotor aircraft,
x, y, z represents the position of the quadrotor aircraft;
, , represents the attitude of the aircraft, that is, roll
system as follows:
F Fi , The force components along
i1
angle, pitch angle and yaw angle; Ui i 1, 2,3, 4 indicates
the xaxis, yaxis and zaxis in three directions are:
the amount of control; Ki is the drag coefficient ; Ii represents
4 the moment of inertia of each axis; m is the mass of the
Fx cos sin cos + sin sin Fi
aircraft body itself; l is the distance between the center of
F cos sin sin sin cos
i1
4
F
(4)
mass of the aircraft body and the axis of rotation of the
y i
4
i1
Fz cos cos Fi
rotor; g
is the gravitational acceleration of the earth's surface.

THE DESIGN OF CONTROL SYSTEM
i1
And because the xaxis, yaxis, zaxis acceleration are:

The Structure of Control System
x Fx K1 x m
y 2
y F K y m
z F mg K z
m
(5)
Because the fourrotor aircraft dynamics model has four control inputs and six control outputs, the control system has a strong coupling, highly nonlinear.The rotation speed of the four rotors plays a decisive role in the three position
z 3
In reference [11], the control inputs of the quadrotors are defined as follows:
coordinates of the fourrotor and the three position coordinates of the centroid in the inertial coordinate system. The change of the three position coordinates of the quadruped's center of mass in the inertial coordinate system will give rise to the change of the three attitude angles, but the change of the three attitude angles will not cause the changes of the coordinates of the three positions. According to the strong coupling between
the three position coordinates of the quadrocopter's center of mass in the inertial coordinate system and the three attitude angles of the quadrotors, most of the control methods adopted by the quadrotors are the double closedloop coordinated control method. Double closedloop control system is
observation of the total disturbance, w is the disturbance and
u is the amount of control acting on the object.
According to the mathematical model of the control system of quadrotors, a LADRC is designed. Because its attitude angle satisfies the following relation:
composed of inner and outer loop, the outer ring is a position
control subsystem, the use of PID control method, and the
=U
2 lK5 I1
inner loop is the attitude control subsystem, the use of linear
U3 lK4 I2
(17)
automatic disturbance rejection control. Fig. 2 shows the block diagram of a double closedloop control system composed of
U
4 K6 I3
PID control and linear automatic disturbance rejection control.
Therefore, you can order
The output of (x, y, z)
=U3 lK4
I1 1
The command signal generator
(xd , yd , zd )
The PID U1
controller
The position control subsystem
position
U2 lK5
U K
I
2
2
I +
(18)
4 6 3 3
Linear automatic disturbance rejection controller
d U2 ,U3 ,U4
The output of
The attitude control subsystem
attitude (,,)
Among them, i i 1, 2,3
is the uncertainty of the
system internal disturbance, the actual flight process also need
Figure 2 The double closed loop control system structure
to consider the external disturbance.
di (i 1, 2, 3)
,let
fi i di ,
fi be the total perturbation of the control system,

The Design of Outer Loop Pid Controller
The position control loop of the quadrotors can be divided into two independent parts: height control and horizontal position control. Height control and horizontal position control
are shown in Equations. (11), (12) and (13), respectively
and
fi can lead, then
U3 lK4
U2 lK5
I1 f1 I2 f2
(19)
U K I f
z U1 cos cos g K3 z m
(11)
4 6 3 3
1 2
x U1 cos sin cos sin sin K1x m y U sin sin cos cos sin K y m
(12)
(13)
Take pitch channel as an example, design a LADRC,
Set x1 , x2 , x3 f1 . x3 is the expansion state
variable of pitch angle , so =U

lK
I f
can be
Supposing that the expected value of the position
coordinate x, y, z is xd , yd , zd , according to PID control algorithm can be obtained:
rewritten as
x1 x2
3 4 1 1
z K
z z K
z z dt K z z
(14)
pz d ix d dx d
x2 x3 lK4
I1 x2 U3
(20)
x K px xd x Kix xd xdt Kdx xd x
(15)
x f
3 1
y K py yd y Kiy yd y dt Kdy yd y (16)


The Design of Inner Loop Linear Automatic Disturbance Rejection Controller
Linear expansion of the pitch channel state observer design:
Let z1 x1 e , for its pitch channel linear expansion
Linear automatic disturbance controller LADRC is
state observer design, the process is as follows:
mainly composed of linear PD controller, linear expansion
z1 z2 1 e
2
2
3
state observer LESO and error compensation control
z z e a z

b U
(21)
law LNESEF . Secondorder linear automatic disturbance
z e
3
2
3 3
rejection controller schematic diagram shown in Fig. 3.
Where
zi i 1, 2,3
is the observed value of
PD
W
V0
The disturbance
xi
i 1, 2,3, i
i 1, 2,3 is the observer gain, and the
The disturbance
u0 u ypoles of the extended state observer are all configured to
w , where a is the observer bandwidth, and 3w
0 1 0
1/b0
3w2
w3
a lK I
0.00192 ,
2 0
3 0
4 1
LESO
z
z3 b b0 1 .
1
2 The design of linear state error feedback controller for
Figure 3 The schematic of secondorder linear automatic disturbance rejection
pitch channel NLSEF
controller
Based on the feedback error signal, the design of a
U3
y z3 b
(22)
LADRC is independent of the exact math model of the control
system. The input signal is V0 , which is given as a state
y KP (d z1 ) Kd z2
reference.
z1 and
z2 are the observations of the linear
dilatometer, z3 is the dilatational state variable, that is, the
Where d
represents the expected value of pitch
angle, K P and Kd both represent the gain of the pitch channel
controller, and let
K p
2
w
c
, Kd
2wc ,
where
wc represents the bandwidth of the controller
and y represents the amount of feedback control.
By the same token, the design of the LADRC for the roll path and the yaw path can be performed.



SIMULATION RESULTS
The body parameters of a quadrotor aircraft are given by reference [10], and the body parameters of a quadrotor aircraft
Figure 5 The response curve of position coordinates
are set as:
K1 K2 K3 0.010
K4 K5 K6 0.012
I1 I2 1.25 I3 2.5 m 2kg l 0.2m g 9.8m / s2
Proportional coefficient K p , integral coefficient Ki
and
differential coefficient Kd values of PID controller can be
obtained by trial and error method, while the design of the main parameters of the LADRC, so that the LADRC bandwidth: w0 28 ,the pitch, yaw and roll the observer gain of
these three channel
1 1 1 3w0 84
1 , 2
, 3
respectively,the value is
Figure 6 The response curve of attitude angle
Through the simulation of quadruped rotor dualloop
3w2 2352 ,
w3 21952 . Let
2 2 2 0
3 3 3 0
coordinated control system by MATLAB/ simulink.As you
controller bandwidth
wc 2.8 , the parameters of PD
can see, the response curve of the position coordinate x, y, z
controller are configured as kd kd kd 2wc 5.6
k k k w2 7.84 b b b b 1 .
can reach the expected value in about 8 seconds and remains unchanged at all times, at the same time, the response curve of
p p p c
0 0 0 0
its yaw angle can reach a constant value in about 3 seconds
According to the above derivation process, a block diagram of the PID / LADRC double closedloop coordinated control system of the quadrotor aircraft control system can be set up, as shown in Fig. 4.
Figure 4 PID / LADRC double closedloop coordinated control simulation module diagram
By running the control system simulation block diagram in Fig. 4, we can get the curve of the position coordinates and attitude angle of the quadrotor, as shown in Fig.5 and Fig.6.
and remains unchanged, The response curve is almost no overshoot, while the pitch angle and roll angle can be restored to the desired value of 0 degrees after a period of time, which can make the quadrotors aircraft operating conditions remain stable, It is demonstrated that the coordinated control of quadrotors with PID and linear automatic disturbance rejection control can make the position response and attitude response have good dynamic performance with fast performance and stable performance. The experimental results show the effectiveness of the dual closedloop control which combines the PID control of quadrotor with the linear automatic disturbance rejection control.

CONCLUSION
In this paper, a quadrotor aircraft of fourinput and six output is proposed, which is based on PID and LADRC. The inner loop is designed with a linear automatic disturbance rejection controller control the attitude of the quadrotors aircraft, and the outer loop is designed PID controller to control the position of the quadrotors aircraft. For the linear automatic disturbance rejection controller, the linear state of
expansion observer is a core part of the system, which can estimate and compensate the total disturbance generated by the quadcopter in real time, according to the simulation results in this paper, we can know that the designed PID / LADRC double closedloop cooperative controller can make sure the control system of quadrotors aircraft can track and control the position and attitude better, and the control system has strong robustness.

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