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Micro air vehicles (MAVs) have a wide application such as the military reconnaissance, meteorological survey, environmental monitoring, and other aspects. In this paper, attitude and altitude control for Quad-Rotor type MAVs is discussed and analyzed. For the attitude control, a new method by using three gyroscopes and one triaxial accelerometer is proposed to estimate the attitude angle information. Then with the approximate linear model obtained by system identification, Model Reference Sliding Mode Control (MRSMC) technique is applied to enhance the robustness. In consideration of the relatively constant altitude model, a Linear Quadratic Gaussian (LQG) controller is adopted. The outdoor experimental results demonstrate the superior stability and robustness of the controllers.

Recently, a new class of flight vehicles called micro air vehicles (MAVs) which have a great potential for military, industrial as well as civilian applications, has been gaining tremendous attention.

Since 1990s, with the development of the Micro Electro Mechanical Systems (MEMS) technology, the single rotor helicopter has been the favorable platform for MAVs research. However, the limitations such as complexity, instability, and payload limitation slowed the trend down. Meanwhile, the multirotor vehicle especially the Quad-Rotor type MAVs become more attractive. The Quad-Rotor, compared with single rotor helicopter and dual-rotor vehicle, has excellent capabilities of superior payload, low cost, and simple construction. As a result, it can be widely used in military reconnaissance, meteorological survey, environmental monitoring, delivering light goods in emergency, and other aspects [

In this paper, system dynamics for attitude and altitude control as well as the control algorithms of a typically Quad-Rotor type MAV are discussed. With the historical flight data of the vehicle obtained by experiments, the mathematical model is determined by system identification tools in Matlab. For the attitude control, instead of using the IMU unit or the extended Kalman filter (EKF), we select three gyroscopes and a triaxial accelerometer to estimate the attitude angle by Kalman flitre. The main advantages of this method are the low price and less computation which will promote the industrialization process. In consideration of the parameter uncertainties, model errors, and other interference, we apply the MRSMC to pursue good robustness. As to altitude control, we propose to use barometer and accelerometer instead of the widely used GPS to improve the precision. Then a model-based controller by optimal control methodology is designed.

Our research platform is a 4-channel radio controlled Quad-Rotor type MAV designed by our research group. The vehicle airframe is constructed by carbon fiber which can provide significant stiffness and rigidity while keeping the weight down. The lift results from four AKE brushless motors. In order to drive these brushless motors, Pentium-18A Ultra-PWM brushless controllers which support 50 Hz–500 Hz PWM signal communication are selected. By using the brushless controllers, the maximum rotational speed can reach about 8000 rpm and acquire about 1 Kg payload with four APC1245 propellers. The flight time is about 20 minutes with a three-cell-2100 mAh LiPo battery without payload. Figure

Specification of Quad-Rotor type MAV.

Parameter | Value | Unit |
---|---|---|

Maximum Diameter | 500 | mm |

Height | 250 | mm |

Total mass | 1.1 | kg |

Maximum lift | 1 | kg |

Quad-Rotor type MAV.

The embedded control system consists of three gyroscopes, one triaxial accelerometer, one barometer, one 12 bit ADC chip MCP3204, and one Arm7 micro controller. The gyroscope ADXRS610 and triaxial accelerometer ADXL335 from Analog Devices Corporation are used to stabilize the attitude of the vehicle. The MPX5100Ap barometer together with the accelerometer is used for altitude control.

The running process of the embedded control system is as follows. Firstly, the Arm7 receives digital sensor data from ADC chip and control instruction from a 72 MHz PPM receiver. Then run the control program to draw a control output for each axis, respectively. At last, the summarized rotational control instructions are sent to the motor drivers to complete the specified movement. All the processing is done at a frequency of 400 Hz. The configuration of the overall system can be seen in Figure

Configuration of 4 rotors type MAV system.

For the

The tuning of rotational speed of every rotor leads to one degree of freedom of the MAV; coupled motion and nonlinearity are very obvious. Therefore, it is quite difficult to analyze such system. In this research, we neglect the coupled motion and gain an approximate linear attitude model. Plus, the Roll attitude model is the same as Pitch owing to the symmetry structure, and the modeling is conducted aiming at roll angle only.

As an assumption, no coupling exists and the variation range of attitude angle is small. The following relationship between the torque around the center and the obtained roll angle can be described as [

Here,

In general, the angular is estimated by the IMU sensor. In this research, we propose one accelerometer and three gyroscopes to estimate the angle. In particular, the accelerometer measures not only dynamic acceleration but also gravity. The relationship can be represented as

Considering that the air resistance exits and the coefficient is

Thereby, the transfer function from the attitude angle to the dynamic acceleration is derived as

The following block diagram in Figure

Block diagram of the transfer function.

Consequently, the complete dynamic state model which governs the MAVs is formed by selecting angular acceleration, angular velocity, angle, dynamic acceleration as the state variables and angular velocity, measured acceleration as the output

The unknown parameters mentioned previously are determined by the system identification tool in Matlab with the historical flight data supplied. To verify the model accuracy, a comparison of the real plant model and the simulated model output for the same control instruction is conducted in Figure

Cross-validation result of angular velocity and acceleration output.

Considering the nonlinearity and the strong coupling of the real Quad-Rotor model, it is of great importance to design the controller with good robustness in both stability and performance. Hence, the MRSMC technique is adopted to enhance the robustness.

The basic idea of MRSMC is to minimize the tracking error of state variables between the vehicle and the reference model in sliding mode. The block diagram of MRSMC is shown in Figure

Block diagram of MRSMC.

To generate the reference signals, a specified reference model whose states variables correspond directly to the identified model is built

Here

Making the system satisfies the following conditions:

Then

To ensure the output

The output

So

In this work, the parameters are chosen as

Step response of the reference model.

To design the feedback controller, the sliding mode control technique is proposed because of its high robustness to exogenous disturbances and parametric uncertainties.

Considering that the control goal is to make the real plant output angle to track the angle of the reference model. Thus, a novel state

And the expansion system can be given as

The switching function

When the state variables are subject to the sliding surface,

Substituting

The previous system described by (

The nonlinear term of SMC is selected as

Then the control input can be acquired:

Because only part of the state variables can be measured, a Kalman filter is introduced to estimate the attitude angle and unobservable state variables. The Kalman filter has three main functions: provide the state variables for controller, estimate the attitude angle information, filter the sensor noise. Therefore, the calculation is greatly reduced and makes the attitude controller running at the 400 Hz frequency become possible. The simulation result of MRSMC is shown in Figure

Simulation result of MRSMC.

The altitude results from the lift of four rotors, so the model can be easily obtained. Then the LQG controller based on optimal control is designed.

The altitude of the vehicle is controlled by the rotational speed of four rotors. The control input

The relations of power

From (

As stated in earlier chapters, the unknown parameters are determined by identification and the system’s time history response is analyzed in Figure

Cross-validation result of altitude model.

The altitude model is insensitive to the outer interference, so it is not difficult to obtain a relative stable model and the LQG control method is applied. LQG is a preferable design method for servo system based on the optimal control technique.

To strengthen the controller performance in tracing, a new state variable

The quadratic form criterion function is defined:

The optimal control goal is to determine control input

In view of (

Then the adjoint equation and boundary condition can be obtained:

With condition

Assuming the relationship between

When the time variable

The feedback gain

Since the controller is designed based on state feedback, it is necessary to obtain all the state conditions. In the altitude model obtained previously, the acceleration and the altitude variable can be observed by the onboard sensors, and there is still one state variable that is unavailable. Then a Kalman filter is designed to estimate the unavailable state variable, and it can also filter the noise in the meanwhile. Therefore, the control performance is improved.

In order to verify the performance of our platform as well as the properties of attitude and altitude controller, outdoor flight experiments are carried out. The operator sends the reference instruction to the Quad-Rotor by using a 72 Mhz PPM Propo. The flight data is transmitted to the ground station by the XBee-pro wireless model.

Firstly, a flight test of letting the MAV keep hovering and high-speed moving is performed. Figures

Attitude experimental result.

Estimate result of roll angle and acceleration.

As to the system’s robustness, a comparison experiment is conducted between LQG and MRSMC technology for attitude control with a 300 g payload. But when the LQG controller is installed, the flight performance degrades badly and the operation of the vehicle becomes a difficulty. Therefore, only the MRSMC robust experiment is carried out successfully. The corresponding plots can be seen in Figure

Robust experimental result.

In the altitude test, a step signal of 5 m is given to the MAV after hovering stably for some time in a fixed altitude. Result from the flight test is shown in Figure

Altitude experimental result.

In this research, a brief introduction is given to the Quad-Rotor, which is selected as our controlled object. Then the attitude and altitude control is discussed. For the attitude, MRSMC is proposed due to its insensitiveness to parametric uncertainties, model errors, and outer disturbances. Whereas in altitude control, the model-based optimal controller is designed. To verify the performance of the controllers, the hovering control and guidance control are conducted in flight experiments. By using MRSMC, the attitude controller also obtains good robustness. In the future, we will focus on velocity and position control, so that the fully autonomous flight will be accomplished.

This work was supported by the scientific research fund of Nanjing University of Information Science & Technology.