A Suitable Structure to Control the System of Quad-rotor Miniature Aerial Vehicles

Received Mar 7, 2018 Revised Aug 22, 2018 Accepted Sep 10, 2018 Miniature Aerial Vehicles with four rotors is called Quad-rotor MAV, popularly used in aspects of life such military, civilian products, processes and remote sensor, etc. In this paper, the authors present the suitable structure of control system for the Quad-rotor MAV. The first, the Six Degrees of Freedom (6 DOF) of the Quad-rotor MAV dynamic model is built. After, the control structure with the single loop is built. But in the single-loop system, only four control signals of Quad-rotor MAV can be controlled, so the Quadrotor MAV can be reached the height only and keep the stability. However, it is important to note that we have to well-known the orbit of the Quad-rotor MAV flight; the Quad-rotor MAV must fly point-to-point exactly, so the six coordinate variables must be controlled. So, the double loop control structure system is proposed to do that. Finally, the simulation results analysis and the experimental results of the real model are explored to prove the effectiveness of the proposed structure. Keyword:


INTRODUCTION
There is a wide range of Unmanned Aerial Vehicles (UAV) technology and satellite which under The overall force is the sum of four the rotors forces. The Pitch movement is controlled by reducing the front motor speed or increasing the rear motor speed. The Roll movement is controlled by reducing the left motor speed or increasing and the right motor speed. The Yaw movement is controlled by decreasing the front motor speed or increasing the rear motor speed combined with increasing or decreasing the speed of the side motors [13]- [16].

The Quad-rotor dynamic equations
The Quad-rotor is a multi-variable and nonlinear object with 4 input signal controls but with 6 degrees of freedom. In order to control the coordinates of Quad-rotor from a point to the other point in the space, it is very important to know the equations of Quad-rotor dynamic model, which is shown as follows [17]- [20].  U  x  m  U  y  m  U  zg  m  II  JU  p  qr  q  I  I  I  I I  J  U  q  pr  p  I  I  I  II  U  r pq with g is the gravitational acceleration, m is the weight of Quad-rotor, J TP is the inertia moment of the rotor. U 1 ,

The equations of controller and other stages
The PID controller has the equation in Laplace as follows: where: e is the error which is equal to the set value minus the real value. Kp is the gain coefficient, Ki is the integral coefficient, Kd is derivative coefficient, u is the output value of the controller.
In this paper, we introduce two control structures for Quad-rotor. The first is the control structure with the single loop [21], shown in Figure 2. The second is the control structure with the double loop [22], shown in Figure 3. Both structures are included of three main parts.
The first part is the controller. In the single loop control structure, the controller is the control algorithm block. In the double loop control structure, the controller includes two parts, which are the position control block and the attitude block connected to each other. The second part is the inverse transformation block. This block is built by the equations shown as follows: After the inverse transformation block, we received the signals shown as follows: The third part is the convert block of rotor speed. The equations of this block are as follows:   In Figure 4, the input block is the set values of the system. The control block is presented in detail as Figure 5. The Motor block is built according to the equation (2) with the role is converting the output value of controller into the value of motor speed  1 ,  2 ,  3 ,  4 . The dynamic block is built by the equations of Quadrotor aircraft (1). The selector block is presented in detail as figure 6, with the role is selecting the signals such as height (z), roll (ϕ), pitch (θ) and yaw (ψ) from the dynamic block into the IMU block. The IMU block is the measurement system which measures height (z), roll (ϕ), pitch (θ) and yaw (ψ) signals send to the controller. In Figure 5, the input 1 (In1) is the desired value of the height coordinate (z), the input 2 (In2) is the real value of the height coordinate which is measured by the height sensor. The role of the z PID controller is controlling the height coordinate (z), with input value is the error between In1 and In2. The input 3 (In3) is the desired value of the angle coordinate (roll (ϕ), pitch (θ) and yaw (ψ)). The input 4 (In4) is the real value of the angle coordinate which is measured by the angle sensor. There are three angle controllers which are the PID controllers for the roll (ϕ), pitch (θ) and yaw (ψ) angle. The output signals of the control block (U 1 , U 2 , U 3 , U 4 ) are through the inverse transform block to convert into the control signals as  1 ,  2 ,  3 and  4 . The inverse transform block is built according to the equation (6). Figure 6 shows the Quad-rotor dynamic block which is built according to the equation (1).

The model of double loop control structure
The structure of single loop control has only four control signals, so Quad-rotor MAV only can be reached the height and stability. However, it is important to note that we have to well-known the orbit of the Quad-rotor MAV flight, and in order that Quad-rotor MAV can fly point-to-point, six coordinate variables must be controlled. So the double loop control structure system is proposed to do that.
The control structure with the double loop is presented as Figure 7, the internal function blocks in this control structure are built according to the equations (1)-(6). There are similarities between the double loop structure control and the single loop structure control relatively. However, there are some differences as: the input block in the double loop structure includes six desired values, which are the x, y, z position coordinates and the Roll (ϕ), Pitch (θ), Yaw (ψ) angle coordinates of the Quad-rotor. The selector block is used to select signals from the dynamic block into the IMU block, those selection signals after crossing IMU is the input of the control block. The difference of the selector block in the double loop control structure is that there are 6 signals (x, y, z position coordinates and Roll (ϕ), Pitch (θ), Yaw (ψ) angle coordinates) instead of 4 signals in the single loop control structure. The role of the display block is displaying the response of position coordinates (x, y, z) and angles coordinates (ϕ, θ, ψ) of the control system.
The control block is shown in detail as Figure 8. The role of the position control block is controlling the x,y,z coordinates, with the input signals are In1 and In2. In1 is the desired values of x, y, z coordinates and In2 are the real values of x, y, z coordinates from the sensor. The role of the transition block is calculating the angles coordinates (ϕ, θ, ψ). The role of the attitude control block is controlling the angles coordinates, with In1 is the desired value of angles coordinates (ϕ, θ, ψ) from the transition block, In2 is the real values of angle coordinates from the sensor. The role of the inversion block is converting the output values of the control block into the rotor speed value of four rotors Ω 1 , Ω 2 , Ω 3 , Ω 4 .

THE SIMULATION RESULTS AND ANALYSIS
We execute the simulation in two cases. The first case is the single loop structure control, the control signals are the height (z), roll (ϕ), pitch (θ) and yaw (ψ) coordinates. The second case is the double

In the case of single loop structure
After many experimental studies, the parameter values of the PID controller for the height (z), roll (ϕ), pitch (θ) and yaw (ψ) coordinates are shown in Table 1. Then, we test the ability of Quad-rotor to fly in space with the initial angles (ϕ, θ, ψ) is (0.2, 0.2, 0.5) rad. The simulation results are shown in Figure 9.  The simulation results show that the initial angles are not balanced, after controlling (after the 3rd second), the angle coordinates (ϕ, θ, ψ) are balanced with the values (0, 0, 0). The height coordinate (z) reaches equilibrium at the height of 0.5 m. After the transition time, all coordinates have good equilibrium, it is confirmed that the control structure works well and efficiently.

In the case of double loop structure
In the double loop structure control, we set the parameter values of the PID controller for the position coordinates (x,y,z) and roll (ϕ), pitch (θ), yaw (ψ) coordinates as in Table 2. Running the Quad-rotor fly from the position coordinates (x,y,z)=(0, 0, 0) to (0.1, 0.1, 1) m, and the angular coordinates (ϕ,θ,ψ) change the desired value from (0, 0, 0) to (0.1, 0.1, 1) rad, the simulation results are shown in the Figure 10.   The simulation results in Figure 10 show that the roll (ϕ), pitch (θ), yaw (ψ) coordinates attain the desired coordinates after about 4 seconds, the position coordinates (x,y,z) attain the desired coordinates after about 10 seconds. After the transition time, all coordinates are stable, it is confirmed that the double loop control structure can control the Quad-rotor fly point-to-point well and efficiently.

THE EXPERIMENTAL RESULTS
After constructing the control structure for Quad-rotor and defining the control parameters, we install on the real device, the Quad-rotor MAV model is shown as Figure 11.   The experiment results show that the responses of Roll, Pitch, Yaw coordinates (ϕ,θ,ψ) and the x, y and z coordinates are good, all coordinates attain the desired value after about 4 seconds. However, the angular coordinates have the fluctuation about ±5 degrees. The amplitudes of this fluctuation are small and acceptable. So it is confirmed that the system control worked well and efficiently.

CONCLUSION
In this research, the authors have proposed two control structures for the Quad-rotor, particularly in the control system structure with the double loop. The simulation results are presented to prove that six coordinates (x,y,z,ϕ,θ,ψ) can be controlled by four rotors, so the Quad-rotor can fly point-to-point exactly in the space. Then, the experimental results make certain that the Quad-rotor can go to the desired position and the desired direction with the short transition time, so the proposed control structure can be applied in practice with the low cost and the high-efficiency.