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Novel Control Techniques for a Quadrotor Based on the Sliding Mode Controller

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Novel Control Techniques for a Quadrotor Based on the Sliding Mode Controller University of Cincinnati mechanical and materials engineering Novel control techniques for a quadrotor based on the Sliding Mode Controller A thesis submitted to the Graduate school of the University of Cincinnati in partial fulfillment of the requirements for the degree of Master of Science in the Department of Mechanical and Materials Engineering of the College of Engineering and Applied Science by Madhavan Sudakar M.S. University of Cincinnati Nov 11, 2020 Committee Chair: Manish Kumar, Ph.D. Abstract The thesis focuses on formulating novel mathematical control designs and implementing them on a quadrotor UAV (Unmanned Aerial Vehicle). The novel designs are based on the sliding mode control technique. The conventional sliding mode controller uses information from a sliding surface which comprises of a combination of state errors and a fixed set of stable coefficients. In this thesis, two different sets of objectives are achieved by modifying the conventional architecture. For the first objective, resistance to high external wind disturbance during outdoor quadrotor flight is attempted. This is achieved by incorporating information from not just the sliding surface but also the derivative of the sliding surface into the control input. The second objective involves using a sliding surface whose coefficients are not fixed but variable in nature. It is desired to generate a PD controller that stabilizes the quadrotor dur- ing flight by using this form of sliding surface. To achieve the second objective, two control architectures are presented. In the first, the process of adaptation of the sliding coefficients occurs to reduce the magnitude of state errors to zero. The second algorithm keeps adapting the sliding mode coefficients to the point where they converge at values which form a stable sliding surface. CASE - I Quadrotor belongs to the class of multi-rotor UAV (Unmanned Aerial Vehicle). Its increas- ing uses in the commercial world for image capturing, package delivery, and defense is making it an invaluable type of drone in today’s world. However, during these operations, fluctuation in the system parameters such as loss in motor thrust or natural disturbances like wind and gusts may occur. These may result in the quadrotor deviating from its desired trajectory which results in a loss of accuracy. These factors necessitate a robust controller which can resist varied sorts of disturbances. This study was chosen to be based on the sliding mode control since it has an inherent robustness to start off with. Sliding Mode Controller falls under the category of non-linear iii controllers. Its design makes it inherently robust and resistant to external disturbances. To achieve this, however, rapid switching of the control input is applied. This uses a lot of energy and is a cause for concern when implemented on hardware (rapid switching of the motor may result in its wear and tear). This novel control design aims to largely reduce the magnitude of the back and forth switching of the control input while attempting to ensure a similar degree of robustness to external disturbances. To achieve this, two sliding surfaces, as opposed to the conventional usage of just one, is considered. Firstly, the concept of multiple sliding surface is introduced. Its difference as compared to the conventional sliding mode is explained. Its theoretical implementation and stability when applied for quadrotor position and attitude control is shown mathematically using Lyapunov theory. Lastly, waypoint navigation is attempted in the presence of simulated wind and distur- bances in all 6 axis. The results are obtained, analyzed and bench marked against a PID and a conventional sliding mode controller. The motor control input behavior of the novel algorithm under the influence of wind gusts is also looked into. Possible drawbacks of the algorithm and the reasons for them are analyzed. Future work is also discussed. CASE - II The PD (Proportional Derivative) controller is basic in its structure and is the most widely used controller in UAV hardware. One major challenge in its implementation is the tuning of its gains for the 3 rotational and 3 translation degrees of freedom. For quadrotor waypoint navigation, a PD controller has shown to achieve good performance for waypoint navigation and trajectory tracking. However quadrotor’s complex, coupled, non-linear dynamics makes the tuning of its gains a time intensive and arduous process. We have tried to address the above mentioned issue in this study. In order to do so, the concept of sliding surface, similar to the one used in sliding mode control, has been considered. Only in this case, the coefficients of the sliding surface are not fixed but have the ability to vary. iv The coefficients are made to relate with the gains of a PD controller. The study proposes two designs to determine the method by which these coefficients are made to vary. In the first case, the study adapts the gains in a manner so that the value of the sliding surface as well as all state errors converge to zero in the process of quadrotor flight. The second adapts the gains in a manner so that their combined form creates a stable sliding surface at the end of the quadrotor flight. The study presents these two adaptations occur successfully irrespective of the value of the coefficients that we begin with. Therefore, even when started off with a random set of coefficients (or gains) manual tuning is not required. In the thesis, firstly the theoretical formulation for the first of the two controller is pre- sented. This is mathematically derived from Lyapunov stability analysis. Next, to test its va- lidity, the algorithm has been applied in three cases presented. In these scenarios, the quadrotor has been assigned a random set of gains initially before its flight. Without adaptation some of them lead to an oscillatory response while in other cases, the quadrotor goes unstable. On applying the algorithm formulated in the thesis, good system stabilization is achieved. Per- formance before and after application of the algorithm is compared. Conclusions and future works are discussed. v Acknowledgements Firstly my heartfelt thanks to the person who guided me through the process, head of mechanical engineering department, Professor Manish Kumar. It was first in his class of decision engineering that I had him as a teacher. I took a liking to his remarkable patience during his lectures and his intuitive way of explaining concepts. Accordingly, I wished to take up my research under him and was glad to be accepted into his lab group. The process was far from what I consider the ideally ”smooth” case. An undecided final target and a hurried literature review were a few things that I did not clearly do from the very beginning. These resulted in the research process stretching for a long period of time. I am really grateful to Professor Manish Kumar for giving me the time and space to perform. It was due to his patience that I feel I have been able to finish off on a strong note. His consistent support during my research helped me face the ups and downs during the course. Continuous insistence by him to structurally document everything regularly, a habit I had to de- velop, still rings in my head. I gradually inculcated this trait towards the later half of my research, and it has helped a lot. His guidance provided direction to my research. Being a student in a couple of his classes was also an enjoyable experience. I thank you Professor for the patience and the faith you have shown in me throughout. I am grateful to Professor Rajnikant Rajsharma for his support. It was his teaching in some of the courses like modern control and non-linear controls that helped me build a strong foundation in the domain of controls. Also thank you Professor for guiding me like a friend and mentor. You provided valuable suggestions and inputs when I really needed them. Regards to my lab mates in the CDS lab who helped by suggesting different approaches through the course of my research. Rumits help, Siddarths dedication and interest, Gaurangs insistent effort to stuff concepts in my head and Shraddhas calmness helped a lot along the way. Thank you all ! My time with Fly UC provided me some interesting insights into the commercial real world applications of what I was learning. I am glad to have got an opportunity to work alongside Hayden vii and an enthusiastic Heath. Being in Fly UC taught me a portion of organizational side of a project along with the technical details. A thanks to the CEAS department for giving the opportunity as a MATLAB grader for a semester. It provided me the opportunity to understand a section of the course and education system for undergrads. I am grateful to all my roommates for the fun times when things got rough. They helped pro- vide me the support to go about the process with more calm. Special thanks to Ajith, Ananth, Abhishek, Vijay, Mehul, Subbu and Ketan for putting up with my complaining and trying to cheer me up whenever things went downhill. Lastly, I am thankful to my parents. Their encouraging words even so far off from India helped boost confidence and morale during challenging times. My sisters philosophical lectures on how to remain cheerful and not stress myself even during uncertain times did have a good steadying effect on me. All their persistent encouragement and motivation that things would go well are certain aspects to be grateful for. viii Contents Abstract iii Acknowledgements vii List of figures xii List of tables xiii 1 Introduction 1 1.1 Motivation and objectives of this thesis . .1 1.2 Contributions . .3 1.3 Thesis Organization .
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