In this research, nonlinear attitude controllers are designed for a low earth orbit satellite intended to be used in observatory missions. The attitude is represented by the Modified Rodriguez Parameters (MRP) which is a minimal representation providing a fully invertible kinematics. As a difference from the classical satellite models existent in the literature, the model of this work incorporates the dynamics of the reaction wheel (actuator) including a brushless dc motor which is armature controlled. The total model has four group of state vectors which are the attitude, body rates, actuator torque and velocity. The main control approach of this research is developed by utilizing integrator back - stepping which provides a recursive stabilization methodology to the designer. For performance comparison, a second controller based on input output feedback linearization (IOFL) is presented. Both of the approaches produce a torque demand law and this is used for generating a desired reaction wheel velocity command. A reaction wheel controller uses the motor as the actuator and produces the necessary amount of the torque according to the desired wheel velocity command. In addition for the back - stepping based approach, a stability analysis against the external disturbance torques is also provided. Simulations are presented for validating the performance and robustness of the proposed controllers.

Control algorithm is developed for a satellite with flexible appendages to achieve a good pointing performance. Detailed modeling activity was carried out that consists of sensor and actuator models, disturbances and system dynamics. Common hardware found in the spacecraft such as reaction wheels, gyroscopes, star trackers etc. were included in the model. Furthermore, the Newton-Euler method is employed for the derivation of multi-body equations of motion. Evaluation of the pointing accuracy with proper pointing performance metrics such as accuracy, jitter and stability during slew maneuvers are obtained through simulations. Control strategies are proposed to improve pointing performance.

In this dissertation the solutions of the dynamics and real-time optimal control of magnetic attitude control and formation flying systems are presented. In magnetic attitude control, magnetic actuators for the time-optimal rest-to-rest maneuver with a pseudospectral algorithm are examined. The time-optimal magnetic control is bang-bang and the optimal slew time is about 232.7 seconds. The start time occurs when the maneuver is symmetric about the maximum field strength. For real-time computations, all the tested samples converge to optimal solutions or feasible solutions. We find the average computation time is about 0.45 seconds with the warm start and 19 seconds with the cold start, which is a great potential for real-time computations. Three-axis magnetic attitude stabilization is achieved by using a pseudospectral control law via the receding horizon control for satellites in eccentric low Earth orbits. The solutions from the pseudospectral control law are in excellent agreement with those obtained from the Riccati equation, but the computation speed improves by one order of magnitude. Numerical solutions show state responses quickly tend to the region where the attitude motion is in the steady state. Approximate models are often used for the study of relative motion of formation flying satellites. A modeling error index is introduced for evaluating and comparing the accuracy of various theories of the relative motion of satellites in order to determine the effect of modeling errors on the various theories. The numerical results show the sequence of the index from high to low should be Hill's equation, non- J2, small eccentricity, Gim-Alfriend state transition matrix index, with the unit sphere approach and the Yan-Alfriend nonlinear method having the lowest index and equivalent performance. A higher order state transition matrix is developed using unit sphere approach in the mean elements space. Based on the state transition matrix analytical control laws for formation flying maintenance and reconfiguration are proposed using low-thrust and impulsive scheme. The control laws are easily derived with high accuracy. Numerical solutions show the control law works well in real-time computations.

Adaptive control has long focused on establishing stable adaptive control methods for various nonlinear systems. Existing methods are mostly based on the certainty equivalence principle which states that the controller structure developed in the deterministic case (without uncertain system parameters) can be used for controlling the uncertain system along by adopting a carefully determined parameter estimator. Thus, the overall performance of the regulating/tracking control depends on the performance of the parameter estimator, which often results in the poor closed-loop performance compared with the deterministic control because the parameter estimate can exhibit wide variations compared to their true values in general. In this dissertation we introduce a new adaptive control method for nonlinear systems where unknown parameters are estimated to within an attracting manifold and the proposed control method always asymptotically recovers the closed-loop error dynamics of the deterministic case control system. Thus, the overall performance of this new adaptive control method is comparable to that of the deterministic control method, something that is usually impossible to obtain with the certainty equivalent control method. We apply the noncertainty equivalent adaptive control to study application arising in the n degree of freedom (DOF) robot control problem and spacecraft attitude control. Especially, in the context of the spacecraft attitude control problem, we developed a new attitude observer that also utilizes an attracting manifold, while ensuring that the estimated attitude matrix confirms at all instants to the special group of rotation matrices SO(3). As a result, we demonstrate for the first time a separation property of the nonlinear attitude control problem in terms of the observer/controller based closed-loop system. For both the robotic and spacecraft attitude control problems, detailed derivations for the controller design and accompanying stability proofs are shown. The attitude estimator construction and its stability proof are presented separately. Numerical simulations are extensively performed to highlight closed-loop performance improvement vis-a-vis adaptive control design obtained through classical certainty equivalence based approaches. / text

M. Tech. Electrical Engineering / Deals with nonlinear methods for magnetic attitude control and reaction wheel attitude control. The work is divided into a number of parts. The first part, deals with the satellite attitude control basic information and development of a mathematical model of a low Earth orbit satellite. The second part introduces the controllers used in this dissertation. The third part deals with the dimension between the output of controller and input of reaction wheel. The fourth part solves the problem of the magnetic torque calculation. The last part carries out the simulation tests of those controllers for small satellite and cube satellite.

M. Tech. Electrical Engineering / The topic of this dissertation is the attitude control of a CubeSat in an elliptic orbit using nonlinear control. The attitude control system (ACS) is a subsystem of a CubeSat. Its principal goal is to stabilise the orientation of the satellite after launch and during the orbital motion of the satellite. Although several methods have been applied to achieve this objective, this still remains a challenging objective and hence plays an integral role in many modern technologies. CubeSat "Cube Satellite" is a miniaturised satellite which, due to its low cost and application potential is often used by academic institutions for research purposes. However, due to its physical size and weight of 1 kilogram, CubeSat have comparatively limited power supply and computational resources; hence the need for an uncomplicated and reliable control system is critical.

The design of controllers subject to the nonlinear H-infinity criterion is explored. The plants to be controlled are the attitude motion of spacecraft, subject to some disturbance torque. Two cases are considered: the regulation about an inertially-fixed direction, and an Earth-pointing spacecraft in a circular orbit, subject to the gravity-gradient torque. The spacecraft attitude is described using the modified Rodrigues parameters. A series of controllers are designed using the nonlinear H-infinity control criterion, and are subsequently generated using a Taylor series expansion to approximate solutions of the relevant Hamilton-Jacobi equations. The controllers are compared, using both input-output and initial condition simulations. A proof is used to demonstrate that the linearized controller solves the H-infinity control problem for the inertial pointing problem when describing the plant using the modified Rodrigues parameters.

The design of controllers subject to the nonlinear H-infinity criterion is explored. The plants to be controlled are the attitude motion of spacecraft, subject to some disturbance torque. Two cases are considered: the regulation about an inertially-fixed direction, and an Earth-pointing spacecraft in a circular orbit, subject to the gravity-gradient torque. The spacecraft attitude is described using the modified Rodrigues parameters. A series of controllers are designed using the nonlinear H-infinity control criterion, and are subsequently generated using a Taylor series expansion to approximate solutions of the relevant Hamilton-Jacobi equations. The controllers are compared, using both input-output and initial condition simulations. A proof is used to demonstrate that the linearized controller solves the H-infinity control problem for the inertial pointing problem when describing the plant using the modified Rodrigues parameters.

The attitude determination and control subsystem (ADCS) is a critical part of any satellite conducting scientific experiments that require accurate positioning (such as Earth observation and solar spectroscopy). The engineering design process of this subsystem has a long heritage; yet, it is surrounded by several limitations due to the stringent physical constraints imposed on small satellites. These limitations (e.g., limited computational capabilities, power, and volume) require an improved approach for the purpose of attitude determination (AD) and control. Previous space missions relied mostly on the extended Kalman filter (EKF) to estimate the relative orientation of the spacecraft because it yields an optimal estimator under the assumption that the measurement and process models are white Gaussian processes. However, this filter suffers from several limitations such as a high computational cost. This thesis addresses all the limitations found in small satellites by introducing a computationally efficient algorithm for AD based on a fuzzy inference system with a gradient decent optimization technique to calculate and optimize the bounds of the membership functions. Also, an optimal controller based on a fractional proportional-integral-derivative controller has been implemented to provide an energy-efficient control scheme. The AD algorithm presented in this thesis relies on the residual information of the Earth magnetic field. In contrast to current approaches, the new algorithm is immune to several limitations such as sensitivity to initial conditions and divergence problems. Additionally, its computational cost has been reduced. Simulation results illustrate a higher pointing stability, while maintaining satisfying levels of pointing accuracy and increasing reliability. Moreover, the optimal controller designed provides a shorter time delay, settling time, and steady-state error. This demonstrates that accurate attitude determination and control can be conducted in small spacecraft.

A multirotor is a type of aerial vehicle that has attracted a lot of attention in recent years. Multirotors have found applications in a variety of different fields and they are used by scientists and researchers, commercial UAV companies and radio control enthusiasts alike. In this thesis a multirotor with eight rotors, also called an octorotor, is used. A physical model of the octorotor has been developed using theory from rigid body mechanics and aerodynamics. The unknown parameters in this model have been found using several identification experiments. The model has been used for controller design and comparison in a simulation environment. An attitude estimation algorithm has been designed and implemented on the target hardware. The algorithm is referred to as a nonlinear complementary filter and it uses a quaternion rotation representation and onboard measurements to compute an estimate of the current aircraft attitude. Two different attitude controllers have been designed and evaluated. The first controller is based on PID techniques which are commonly used in multirotor flight stabilization systems. The second controller uses a novel control structure based on L1 adaptive control techniques. A baseline attitude PD controller is augmented with an L1 adaptive controller in the rate feedback loop. The two controller structures are compared using a simulation environment based on the developed model of the octorotor. The results show that the proposed structure gives a notable performance increase with respect to robustness against modeling errors and input disturbance rejection compared to the PID controller. However, the L1 adaptive controller is more complex to implement and gives less noise attenuation. The PID controller has been implemented on the platform's hardware and initial flight tests have been performed with promising results. / En multirotor är en typ av flygande farkost som har fått mycket uppmärksamhet under senare år. Multirotorer tillämpas inom flertalet områden och de används av bland annat forskare och vetenskapsmän, kommersiella UAV- företag samt hobbyentusiaster. I detta examensarbete används en multirotor med åtta rotorer, en så kallad oktakopter. En fysikalisk modell av oktakoptern har tagits fram med hjälp av teori från stelkroppsmekanik och aerodynamik. De okända parametrarna i modellen har skattats med hjälp av ett flertal identifieringsexperiment. Modellen har använts för att designa och jämföra regulatorer i en simuleringsmiljö. En algoritm för att skatta farkostens attityd har designats och implementerats på oktakopterns hårdvara. Algoritmen är en variant av ett olinjärt komplementärt filter och använder en kvaternionrepresentation av attitydvinklar och uppmätt sensordata för att skatta farkostens nuvarande attityd. Två olika attitydregulatorer har designats och utvärderats. Den första regulatorn är baserad på PID-teknik vilket är vanligt för stabilisering av multirotorsystem. Den andra regulatorn använder en ny regulatorstruktur baserad på L1-adaptiv teknik. En grundregulator av PD-typ utökas med en L1-adaptiv regulator i vinkelhastighetsloopen. De två regulatorstrukturerna jämförs i en simuleringsmiljö baserad på den framtagna modellen av oktakoptern. Resultaten visar att den föreslagna regulatorstrukturen ger en betydande prestandaökning gällande robusthet mot modellfel och undertryckning av ingångsstörningar jämfört med PID-regulatorn. Dock är L1-regulatorn mer komplex att implementera och den ger mindre brusundertryckning. PID-regulatorn har implementerats på plattformens hårdvara och inledande flygtester har genomförts med lovande resultat.