Robust Optimal Controller Designs for Attitude and Altitude Control of a Quadrotor
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The Unmanned Aerial Vehicle (UAV) industry has seen a huge growth in the past couple of decades, driven mainly by availability of faster and affordable microcontrollers and sensors. The commercial and hobbyist sectors have been increasingly using rotorcraft UAVs for new and varied applications, all the way from asset inspection to bait deployment in long-line fishing. This has required control engineers to come up with systems that are extremely robust, and optimal so that the varying nature of payloads and the craft parameters itself does not affect the overall performance of the drone, while the best flight quality and maximum flight times are achieved. In this research the overall aim was to develop tracking attitude/altitude robust, and optimal controllers for a quadrotor UAV where non-trivial model uncertainty is present. To achieve this goal, a comprehensive framework that would develop optimal weight designs along with the robust controller was developed. This was achieved by enclosing the H-infinity problem inside a constrained non-linear optimization problem. Separate algorithms were proposed for Single Input Single Output (SISO) and Multi Input Multi Output (MIMO) systems for all three main variants of robust controller design strategies; namely the Mixed Sensitivity Optimization (MSO), Loop Shaping Design Procedure (LSDP) 1 and 2 degree of freedoms, and mu-synthesis. A detailed linearized model of the multivariable plant and a decoupled version of it was developed in addition to which, worst-case plant models with significant model uncertainty were constructed. In the SISO case, MSO, LSDP 1 and 2 DOF, and mu- synthesis based robust controllers were developed using the proposed algorithms for the decoupled plant. Satisfactory performances were obtained in all the cases with the controller achieving robust stability consistently. Performance comparisons were conducted among the developed controllers and benchmarked against a PID controlled system. For the systems containing model uncertainty the robust controllers performed better than that of the PID controlled, in terms of meeting the designs specifications, and the LSDP based controller performed the best among the robust controllers. Similarly for the multivariable case, MSO, LSDP 1 DOF and mu-synthesis based controllers were developed using the proposed algorithms. While the controllers assured robust stability, however, it was found that uncertainty in mass of the craft, and that of the thrust coefficient caused systems to fall short of providing guaranteed robust performances. The controllers were compared against one another, and it was once again found that LSDP based systems provided the best performance in terms of reference tracking, and achieving the required design specifications, while the mu controller was found to be the most conservative, with the MSO controller occupying a position between the two other controllers. A simulation based case study was performed inspired by the quadrotor being used in long-line fishing application with its unique time varying nature of the payload mass and slung load length. Two controllers, a PID based and a MSO robust controller based system were put to test on a quadrotor model carrying a slug load. It was observed that the PID based controller performed better than the robust controller for systems that are close to the nominal model. But performance deteriorated rapidly as the plant moved away from the nominal model with several models with uncertainty becoming unstable. The robust controller maintained stability even when tested over extreme plants with the performance deterioration taking a less steeper path than its PID counterpart. The proposed algorithms enabled an efficient design process of the optimal controller weights and significantly quickened the process of developing robust controllers for rotorcraft drones. The MATLAB framework involved in developing the algorithms are provided in this work. The controller comparison studies shed new insights into the overall process of selecting robust control strategies for varied and challenging UAV applications.