Modelling and hyperbolic tangent adaptive lqr+pid control of a quadrotor

In recent years, unmanned aerial vehicles found wide range of application areas. With the developed technologies, decreased manufacturing and material costs unmanned aerial vehicles became affordable and popular for daily civil usage. As a vertical take-off and landing vehicle, quadrotor has four identical, symmetrically distributed and independently controlled rotos. Unlike conventional helicopter's one and big rotor quadrotor's four relatively smaller rotos provides safer civil usage. The mechanical design is simpler and easier because the rotor rotation axes are fixed, and no moving aerodynamic control surface is needed. Because of this simplicity, use is spread over a wider area than single-rotor systems. Small volume coverage, high maneuverability at low transient speeds and high load carrying capacity are other advantages of quadrotors. Because of these characteristics quadrotors usage areas expanded widely as movie making, surveillance, mapping, agriculture, hobby, racing, inspection, military and many more complex missions. To complete these missions safely and with high accuracy fast and robust controller must be designed. Researchers designed various controllers for quadrotors. Each control methods have its own advantages and disadvantages. One should choose appropriate controller according to mission to be accomplished. Controllers mainly divided in to two categories as linear and non-linear. As a linear controller PID is the most widely used controller. Ease of design and resistance to uncertainties are the main advantages of PID controllers. However, non-linearities in kinematic model or inability to model uncertainties correctly application of PID controller limits quadrotor's performance. Tuning controller gains correctly is not straightforward. These gains are adjusted around some trim conditions like hovering in some altitude and this causes design restrictions. Another widely used linear controlling method is Linear Quadratic Regulator. LQR has a similar structure to PID. Controller gains are calculated by minimizing cost function. To calculate gain matrix, the system needs to be linearized. In this work quadrotor, an unmanned aerial vehicle with four rotors, has been modelled, controller has been designed and simulated in Matlab Simulink software. Literature review about controller methods has been made and some explained in detail. After sharing definition, general properties and working principles, mathematical model with kinematic equations, force and moment balance model with dynamic equations and translation between body frame and earth frame model with Newton-Euler equations has been proposed. With these models simulation platform in Matlab Simulink software has been created and reference inputs has been supplied to non-linear quadrotor model. To increase accuracy of model and to obtain more realistic system outputs rotors has been modelled separately. Aim of this work is to form an adaptive controller which uses these two controllers together efficiently. PID and LQR controller has been designed and modelled separately for attitude and altitude controllers. Third controller has been designed with use of these two controllers together with variable weights. Controller weights were adjusted with hyperbolic tangent trigonometric function of error between reference input and actual output. This third controller was named as hyperbolic tangent adaptive controller. PID controller was designed for fast response and LQR controller was designed for reference trajectory following with possible lowest error. When error is high it means system is in transient state so weight of PID controller increases. In contrast when error is low system is in steady state, to use precise tracking advantage weight of LQR controller increases. This newly formed HTAC controller performance is compared with LQR and PID controllers in several aspects. Step input was given for all controllers and rise time, overshoot, settling time and steady state error values were inspected. Several trajectory inputs as a pitch, yaw, roll angles and altitude references were given and errors were measured to compare trajectory tracking performances of these 3 controllers. Energy consumption of this 3 controlling methods related directly with rotors energy consumption values. Four rotor's energy consumptions added and integrated over time to find overall energy consumption of quadrotor on the predefined maneuvers. Finally, wind forces on the quadrotor was calculated and was fed to system as a disturbance. Disturbance rejection performance was compared for both altitude and attitude controllers. With combining advantageous points of PID and LQR linear controllers, it has been analyzed that proposed hyperbolic tangent adaptive controller has better performance than PID and LQR controllers in many aspects. While using advantages of PID and LQR controllers it was analyzed that settling time performance of HTAC controller outperforms both controllers. HTAC consumes slightly less energy than other two controllers. Despite LQR controller less effected from disturbances HTAC controller rejects disturbances and reaches back its steady state value faster than the other controllers. Although analyses show HTAC controller performs very good in simulation environment experiments on a real quadrotor must be done. At the same time, it should be considered that the use of more than one controller will increase the system costs. The work to be done after this phase can be concentrated on realizing the system on the real quadrotor. Instead of the hyperbolic tangent function, intelligent algorithms can be used to calculate weights or nonlinear controllers can be used instead of linear controllers.