Pitch Stabilization Of Vertical Takeoff & Landing Aircraft Using PID Controller
In this research we design a Vertical Takeoff & Landing (VTOL) Aircraft which can autonomously control its stable flight. In this paper, the stabilization of the Pitch of Vertical Takeoff & Landing (VTOL) Aircraft, i.e. the tail, is being discussed. Test bench isalso constructed to test the concept. Kalman Filter is used to estimate the angle from the redundant data of accelerometer and gyroscope and Digital Low Pass Filter is used to reduce the noise of the actuator. The PID control system is used for the stabilization of Pitch of VTOL Aircraft. The graphs for the angle estimation, noise reduction and PID controller with and without load are shown.
Introduction
In the past few decades, aerial transportation has grown rapidly in the entire world. Most of the countries in the world are using mainly aerial transportation for their travelling and trade purposes since it is fastest and cost effective. Variety of aerial vehicles are used for this purpose, such as helicopters, multirotors, fixed-wing airplanes and Vertical Takeoff & Landing (VTOL) Aircrafts. All of these have their own advantages and shortcomings. Helicopters and multirotors can take off and land vertically and additionally they get stable at a certain altitude and they can maintain their position accurately. But they cannot fly forward at high speed, and their payloads are very limited compared to fixed wing plane with the same gross weight. Conventional fixed-wing aircraft can fly forward at high speed and large payloads. However, they cannot take off and land vertically, and the appropriate runways are required. On the other hand, VTOL Aircrafts contains all the advantages of helicopters, multirotors and fixed-wing airplanes. They can take off and land vertically and they can get stable at the desired altitude. Moreover when in conventional flight mode it can fly forward at high speed and also they have large payloads. The final objective of this research is to develop stabilized Pitch model of a real life VTOL Aircraft that can take autonomous flight. There are several ways to perform the VTOL maneuver, we are doing this with tilting wing aircraft.
It is important to detect the attitude, i.e. the inclination with respect to the vertical, of the VTOL Aircraft’s tail in order to correct its position. An accelerometer cannot be used individually to detect attitude position correctly. The signal is noisy although the aircraft is still. The noisy signal from the accelerometer is common to all accelerometers. So, more sophisticated method to measure attitude position is needed. For this purpose, the system needs additional sensor, i.e. gyroscope. This sensor is used in airplane to detect the attitude position. Unfortunately, there is a drift in the gyroscope operation. This makes the gyroscope alone will not give the exact attitude position for a long period. To handle the noise from accelerometer and take advantage of stable signal from gyroscope Digital Low Pass Filter is used. Although this simple implementation is helpful to measure the attitude of an aircraft, it cannot handle the drift from the gyroscope. In order to give exact attitude position, the system needs a collaboration of accelerometer and gyroscope. To integrate these two sensors, a filter is used developed by Rudolf Kalman i.e. Kalman Filter.
The control system for the Pitch stabilization of VTOL Aircraft’s tail forms a large part of this research. The reason for this is the aircraft itself is unstable in fly and thus would be difficult to fly without any control system. Thus the PID controller is chosen as a control system due to its versatility and facile implementation.
Arduino UNO microcontroller is used for the implementation of the control system and filter algorithms. Arduino take sensor data from MPU-6050 apply Kalman Filter and PID controller and send it to Electronic Speed Controller to drive the Brushless DC motor. Additionally, it communicates to the personal computer through XBEE S1 Pro to transmitted and received, measurable data and commands, serially. GUI based environment is developed in Python to plot and display the data collected from the test bench of VTOL Aircraft’s tail to visualize the system performance.
Hardware description
Arduino UNO is decided to utilize as main microcontroller in this research. This microcontroller offered all the features we needed for this research, 1 PWM output pin, 1 analog input, single UART, for Universal Asynchronous Receiver Transmitter, and SPI, for Serial Peripheral Interface, communication protocols to connect sensors and actuators of this research. It is based on based on the ATmega328P microcontroller. The board comes with 14 digital input/output pins (of which 6 can be used as PWM outputs), 6 analog inputs, UART and SPI protocols pins, a 16 MHz crystal oscillator, a USB connector, and a power jack.
Brushless DC motor is used as a main actuator for controlling of tail. Brushless DC (BLDC) motor is a DC motor that uses an electrical commutation system instead of a mechanical commutation system such as a brush. In BLDC, relation between torque vs current and speed vs voltage are linearly equivalent. Here Golden Power A2212-10 1400KV Brushless Motor is used with 14 poles and minimum recommended ESC and Lithium Polymer battery of 20A and 2-3S respectively. Those poles will create a difference of polarity, so the stator could move from one pole to another and create a rotation.
To drive and current amplification of BLDC motor, Electronic speed controller (ESC), HobbyKing Red Brick 30A ESC, is used. The speed of the motor that it produces depends on receiving frequency at signal pin. Commercially, ESC classified with its maximum current that the motor can pull. Brushless ESC has 2 terminals for battery, 3 terminals connect ESC with brushless motor, additionally 3 pins to connect with 5 Vcc, ground, and input signal from the microcontroller of the receiver.
To power up our system for the recommendation of BLDC motors and ESC Lithium Polymer (LiPo) battery is used. TURNIGY nano-tech LiPo battery pack with a capacity, discharge rate and number of cells of 3000mAh, 25C and 3S respectively is used. LiPo cells maintain a more consistent voltage, over the discharge curve when compared to NiCd or NiMH cells.For the wireless communication purpose up to 1mile XBEE Pro S1 module is used due to its ability to easily program and use. This module is programmed with XCTU software. It operates at 3.3 volts, 215mA current 60mW output power which leads to the range of 1 mile (1500 meters). A sensor is used to calculate attitude of the VTOL Aircraft. The InvenSense MPU-6050 sensor contains a 3 axis MEMS accelerometer and a MEMS gyroscope on a single chip. The readings of the accelerometer and gyroscope are not accurate, so Kalman Filter is used to estimate the attitude. A wooden frame is made of the same length as of the VTOL Aircraft’s tail. To implement this research and avoid any mistake during implementation on VTOL Aircraft directly.
Implementation
Accelerometer Model
The accelerometer measures the difference between any linear acceleration in the reference frame of accelerometer aligned with VTOL Aircraft’s tail and inertial frame i.e. the earth's gravitational field vector. The roll, pitch and yaw rotation matrices, which transform a vector (such as the earth's gravitational field vector g), about the x, y and z axes respectively, are: Rx ( = Ry ( = Rz ( = The orientation angles are dependent on the order in which the rotations are applied. The rotation matrix for the conventional sequence of roll-pitch-yaw can be expressed as: Rxyz= After multiplying the above rotation matrix with the earth’s gravitational field vector the roll and pitch angles for the accelerometer data [Ax Ay Az]T are given below.
Due to the singularities that the Euler angles lead and creates gimbal lock issue a quaternion based representation can solve this inconvenient, however, the VTOL Aircraft usually do not require to perform acrobatic maneuvers. Therefore, roll and pitch angles are valid in this research. The main problem in using accelerometer is that its noise, which is shown in figure 3 even when the system is at steady state.
Gyro Model
A gyroscope is used to measure the angular rate, i.e. degrees per second it is rotating. The rotation is typically measured in reference to one of three axes: roll, pitch, or yaw. Since gyroscope provides angular rate it has to be converted in terms of roll, pitch, and yaw shown below: gyroXrate = gyroX / 131.0 gyroYrate = gyroY / 131.0gyroZrate = gyroZ / 131.0Where 131.0 is constant === The Gyroscope is also not convenient to use because it has bias, i.e. drift in its reading.
Gyros are accurate over short time scales, but have drifted errors over larger times and require an accelerometer or magnetometer to correct this drift. Whereas accelerometers are also not precise over short durations of time and require averaging functions to output. The Kalman Filter is used to resolve these issues to calculate precise angles.
Kalman Filter
There are two types of equations for the Kalman Filter, i.e. prediction equations and correction equations for time update and measurement update respectively. The prediction equations predict in time the current state and error covariance estimates to obtain the a priori estimates for the next time step. The correction equations are responsible for the final optimal states estimating in that they take a new timely measurement into consideration combining with the a priori estimates to obtain a corrected, or a posteriori, state estimate.
Noise reduction
The vibration of this system due to the actuators produces large amount of noise which can be seen in the figure. To remove this disturbing noise from the signal to get meaningful data for the correct angle measurement. This is done by filtering out signals from sensors with a high frequency. The MPU-6050 provides a configurable Digital Low Pass Filter (DLPF) on board. This is especially convenient because it’s not trivial to implement in software, as the math behind is not that easy. But main problem in using DLPF is the delay it produces. DPLF configurable table helps us to select bandwidth frequencies [8]. Figures 6 to 12 illustrate the noise reduction phenomena using DLPF for this system.
Setting the DLPF to the highest values removes most of the noise compared to the other settings. As the setting 6 works very well. But it has a significant delay for accelerometer and gyroscope equals to 19ms and 18.6ms respectively. Secondly, everything will be a cutoff whose number of changes is less than 5Hz.
Control system
The control performs a key role in the VTOL Aircraft’s stability, making possible to control precisely the Pitch of the aircraft. Here, it's main goal is to make the tail moves to a new desired position (called setpoint) and also react to external disturbances quickly and in a controlled way. Attitude control is the key element to maintain stability during flight. In this research the Proportional Integral Derivative, i.e. PID controller is used. The PID controller was chosen because it is widely used in the industry on practical applications with good results, and also has an easy implementation.
P is proportional which controls the present, the output will be proportional to the error when multiplied by a positive constant kp. I stand for integral which controls the past, the error in the past period of time multiplied by a positive constant ki. D is a derivative which controls the future with positive constant kd.
Results
Experiments are performed using test bench to verify the performance of the Kalman Filter and the PID controller. The bandwidth frequency of 44Hz is selected for DLPF of the accelerometer. So, despite vibration of the acceleration sensor due to motor operation and drift of the gyro sensor, the result of the Kalman Filter passes between the values measured by the acceleration sensor. The PID controller is so tuned that we end up with Kp, Ki and Kd values of table 1.
Conclusion
This research provides an excellent platform to develop skills to construct hardware as well as algorithms for stabilizing the Pitch of VTOL Aircraft. The results of this paper showed that the attitude of VTOL Aircraft can be stably controlled by solving the problems of the vibration occurring in the acceleration sensor and the drift and cumulative error of the gyro sensor, and applying the PID controller. Also, the experimental results showed that the application of the PID control technique that is commonly used in the attitude control of aerial vehicle can contribute to stable control of attitude by reducing unwanted vibrations that occur in the attitude control of the aerial vehicle. For future work, a further study on the attitude control of VTOL Aircraft and stabilization will be conducted based on the attitude values obtained stably.
