A two-degree-of-freedom flight attitude simulator with variable load is used as an experimental platform to study the adaptive control of aircraft under variable load. According to the theory of relay feedback, the adaptive controller of flight attitude simulator is designed by using the method of PID control based on relay feedback, and the parameters of the controller and the experimental results are given.
Through theoretical analysis and experimental verification, the validity of the adaptive control algorithm in aircraft control and the adaptability under variable load are proved. At the same time, the flight attitude simulator is an ideal experimental platform for studying adaptive control and aircraft control. The micro-rotorcraft has very important application value in the military and civil fields. Because of its vertical takeoff and landing function, easy to manufacture, remote control and relatively low cost, small rotorcraft aircraft is widely used in entertainment, air surveillance, search and rescue, and control theory research. Some well-known high-tech enterprises at home and abroad have produced a series of micro-rotor aircraft with excellent performance. Since 2005, high-tech enterprises in many countries, including China, Germany, the United States and France, have developed their own small rotor products. Not only that, many research institutes at home and abroad have also carried out various studies around micro-rotor aircraft. In February, Professor Weger Kumar of the University of Pennsylvania demonstrated the flexible formation operation of the quadruple rotor. At the end of 2013, 3D Robotics launched Pixhawk hardware in conjunction with the PX4 Open Source Flight Control Development Team of Zurich Federal Institute of Technology. In recent years, domestic universities, such as Tsinghua University, Hong Kong University of Science and Technology and Beijing University of Aeronautics and Astronautics, have made some progress in the research of Rotor UAV. In order to effectively improve the efficiency and reduce the cost of research and development of attitude control system, the rotor flight simulator emerged as the times require, and became an indispensable experimental device in the development of flight control system and attitude control system. These devices will provide an efficient and low-cost research platform for autonomous control of aircraft. To this end, some companies and universities are designing and developing this flight simulation product. The typical helicopter model is the University of Toronto project. In this scheme, TSK Mystar 60 is used as a model helicopter, and the helicopter is fixed in a special structure frame to realize helicopter attitude simulation with two or three degrees of freedom [2]. In addition, in 2009, the University of Toronto and the Hong Kong University of Science and Technology developed a helicopter simulator [3-4]. In this scheme, the model helicopter is used as the main body and the support is assisted. At the same time, the attitude of the simulator is measured by using the MEMS components, and then the attitude control is realized. The helicopter simulator scheme of the School of Electrical Engineering of Sarajevo University in Sarajevo City, Bosnia and Herzegovina is relatively novel [5-6]. The helicopter model used by the team is a product of Humusoft, thermostatic element but the novelty is that they use the virtual reality toolbox in MATLAB to model the helicopter, and the experiment process is simpler and safer. In addition, the most famous companies for developing micro-flight simulators are Shenzhen Gugao Company, Quanser Company of Canada, Humusoft Company of Czech Republic and Feedback Company of UK. Shenzhen Gugao Company has developed a three-degree-of-freedom helicopter simulator. The system provides a control algorithm research platform based on MATLAB/Simulink. Quanser has developed a two-degree-of-freedom helicopter simulator that uses an information acquisition card as a sensor. Humusoft and Feedback have also developed their own hardware devices. In this paper, a small two-degree-of-freedom flight attitude simulator suitable for the study of attitude control of micro-rotorcraft in laboratory environment is presented. Compared with the existing schemes, the structure of the equipment is different, and the centroid position of the whole system can be changed conveniently, thus changing the parameters of the dynamic equation of the controlled object. This makes the dynamic characteristics of the simulator different in the vicinity of different pitch angles. This provides a good experimental platform for the study of robust, adaptive attitude stabilization and large angle attitude adjustment control. At the same time, the dynamic model of the pitch channel is established, the dynamic characteristics of the pitch channel are analyzed in detail, and the adaptive tuning control law of the parameters of the pitch channel is designed. Finally, the effectiveness of the adaptive tuning algorithm and the ability of the controller parameter self-tuning for the variable load system are verified by experiments. The configuration of the flight attitude simulator is shown in Figure 1. The mechanical structure consists of three parts: the base, the supporting rod and the swing arm. A motor is installed at both ends of the swing arm. The two motors are perpendicular to each other. A propeller is installed on the motor to provide driving force for the swing arm.
Fig: F1 is pitch propeller lift, vertical pendulum rod upward; F2 is yaw propeller lift, vertical direction outside the paper surface, L is counterweight copper block to fulcrum distance; L is pitch channel pendulum arm length; mg is counterweight block gravity. If only the dynamic model of pitch passage is considered, the spatial motion can be simplified to plane motion. See Fig. 2. The horizontal position is defined as 0 position point, and the counter-clockwise rotation (upward in the figure) is in the positive direction. Among them: the pitch angle of the swing arm is phi; the moment of inertia of the whole swing arm to O point is J; and the angular velocity damping coefficient is K. The mechanical parameters of the system are shown in Table 1. This system is a non-linear controlled system. If the non-linear part is linearized at a certain point, a second-order linear steady-state system can be obtained. The open-loop stability of the system varies with the linearization point. In theoretical modeling, the input of the system represented by the dynamic equation (1) is the lift provided by the propeller. But in the actual system, the propeller is driven by the motor, and there is a certain functional relationship between the motor speed and the propeller lift. Ideally, the lift is proportional to the square of the speed.
In addition, the motor used in this system is brushless DC motor, and the speed regulation mode is PWM speed regulation. In theory, the relationship between PWM duty cycle and speed is linear. However, the relationship between PWM duty cycle and speed in practical system is not ideal linear relationship. Therefore, there is a non-linear functional relationship between duty cycle and propeller lift. Among them, P is dimensionless duty cycle, and f (.) represents the static non-linear function relationship between duty cycle and propeller lift. The static non-linear function relationship of equation (2) is obtained by experiment and data fitting. Firstly, the relationship between duty cycle and rotational speed is obtained. On this basis, the relationship between rotational speed and propeller lift is obtained through experimental tests. In the experiment, because the motor’s forward and reverse characteristics of the pitch channel are different, two fitting curves of the pitch motor’s forward and reverse are obtained. The scatter plot and fitting plot are shown in Figure 3. Among them: N represents the speed of the motor, in units of rotation per minute (r/min).
In formula (3), the duty cycle P is negative; in formula (4), the duty cycle P is positive. The symbol of duty cycle represents the direction of motor rotation.
The principle of measuring the relationship between motor speed and lift is shown in Fig. 4. In the experiment, the position of counterweight is adjusted at a certain speed. After stabilization, the lift of propeller is calculated according to formula (5) and measured many times. Then the duty cycle is increased by 5%. Repeat the above operation. Finally, the lifting scatter plot and curve fitting plot of propeller with duty cycle of 5% and corresponding speed of 20% to 100% are obtained. See Fig. 5.
In the absence of other disturbances, the lift provided by the propeller is proportional to the first to third power of the rotational speed. Through experiments, it is found that quadratic function fitting has the best effect. The function relation corresponding to the curve is shown in equation (6). Furthermore, the relationship between duty cycle P of PWM and lift F can be obtained. For scatter plots and curve fitting figures, see Figure 6. For the corresponding analytical expressions of functions, see Formula (7) and Formula (8). For the flight attitude simulator described in this paper, in order to achieve attitude stabilization control, an easy engineering method is PID control. In practical use, only three coefficients, namely, proportion, differential and integral, need to be adjusted. Generally speaking, three proportional coefficients need to be set artificially. In this paper, a self-tuning PID algorithm is designed and implemented for specific controlled objects. In this paper, the relay feedback method is used to realize the self-tuning of the PID controller [7]. The characteristic of relay link is that it can make the system oscillate. By describing function method, if the Nyquist diagram of the controlled object and the negative inverse describing function of the non-linear link have intersection points, and the intersection points correspond to a stable limit cycle, the system will produce equal amplitude oscillation. In order to reduce the influence of noise, the relay feedback characteristic with a certain hysteresis width is used. The corresponding Nessler diagram and the schematic diagram of the relay negative inverse description function are shown in Figure 7. According to the description function analysis method, point A in the graph corresponds to a stable limit cycle.
The magnitude of the describing function of the relay link at this point corresponds to the critical gain of the controlled object, and the period of the limit cycle oscillation corresponds to the period of the controlled object oscillation. After these two key parameters are obtained, the strm relay tuning method can be used to tune the PID parameters. Relay feedback tuning methods are mostly used in industrial control. The most ideal model is FOPDT (First Order Plus Delay Time) model. The characteristics of the two-DOF flight attitude simulator linearized in horizontal position are quite different from those of FOPDT model. In order to realize the self-tuning control law smoothly, it is necessary to design an inner-loop controller to improve the dynamic response characteristics of the controlled object. It can be seen that no matter what the parameters of the original object are, the appropriate Kd and Kp can be selected to configure the feature roots of the system to the desired position.
At this time, the closed-loop step response curve of the controlled object with 0 degree setting point is shown in Fig. 8. The system block diagram of the self-tuning PID controller is shown in Fig. 9.
According to the strm setting rule, the hysteresis width of relay link can be selected as 0.164 8 and the upper saturation output D as 0.5. At this time, the Nyquist diagram of the controlled object and the negative reciprocal description function curve of the relay link are shown in Figure 10. As can be seen in the figure, the two curves do not intersect. At this time, although the dynamic characteristics of Gin (s) meet the requirements, the phase angle condition is still not satisfied, and an integral link is needed before the inner ring link. The system block diagram of the improved self-tuning PID controller is shown in Fig.
11.
At this time, the Nyquist diagram of the controlled object and the negative reciprocal description function curve of the relay link are shown in Figure 12. The numerical simulation analysis shows that the system will have self-sustaining oscillation at this time. When equal amplitude oscillation is achieved, the parameters of the PID controller can be tuned by using peak-valley search algorithm combined with strm relay setting formula. The system tuning-regulation response curve is shown in Fig. 13. In the figure, the first three oscillations are equal amplitude oscillations caused by relay links. Then the control algorithm automatically calculates the PID parameters, and then controls the controlled objects with these parameters. After completing the theoretical analysis and controller design, the control algorithm is transplanted to the controller of the actual system, and then the above self-tuning control law is realized physically on the helicopter simulator in the laboratory. The control frequency used in the actual system is 100 Hz. The physical diagram of the helicopter simulator is shown in Fig. 14. In each experiment, the self-tuning algorithm is used to realize the self-tuning of the PID parameters. When the system is stable, a disturbance is artificially given to the pitch channel, so that the system can stabilize itself to the desired position again. The response diagram of the above process is shown in Fig. 15. It can be seen that the test curve of the physical system is basically consistent with the theoretical analysis, and the parameter adaptive tuning control law of the two-degree-of-freedom flight attitude simulator is successfully realized. The model parameters of the controlled object are changed by changing the position of the swing arm counterweight. The parameters of the pitch channel are successfully realized by using the same self-tuning algorithm.