Design, analysis and development of optimal satellite attitude control system

Abstract

Satellite attitude control is an essential part of satellite missions, as it provides the orientation of the satellite from one point of view to another one. In this thesis, a comprehensive investigation on design, analysis and optimization of a satellite attitude controller are presented, by mostly focusing on enhancing controller performance and robustness. Two primary controllers are investigated as Linear Quadratic Regulator (LQR) and Model Predictive Controller (MPC) and their disturbance rejection capabilities are compared. Initial chapter provides the fundamental concepts and definitions such as reference frames, Euler angles, quaternions and so on. Conversion between quaternions and Euler angles are also presented. Additionally, nonlinear mathematical model is constructed as dynamics and kinematics subsystems. Disturbance model acting on satellite is also presented as gravity gradient and aerodynamic torque. The total nonlinear model is presented as state space equations. Dimension reduction of the nonlinear model is executed by decreasing the number of quaternion elements. Then, the linearization of nonlinear model is performed. Both analytical and numerical linearization methods are explained. It is shown and validated that the linearized state space system model presents the nonlinear model for small angle deviations. The controller design focuses on optimal control methods, that are used in many areas as well as satellite attitude control systems. Two primary controller approaches are presented as LQR and MPC. The LQR controller is introduced as a optimal controller algorithm. LQR is based on the minimization of a cost function that is constructed by states and inputs of the system. Weight parameters, Q and R, affecting the performance of the LQR controller are investigated and fine tuning of these parameters is performed. It is observed that the appropriate selection of cost function parameters significantly affects the controller performance, especially in terms of steady state error. LQR controller shows the capability of optimal control on stabilizing and attitude tracking performance of the satellites. Additionally, Model Predictive Control approach is explored in detail. As distinct from classical control methods, in MPC, a prediction model is utilized; states and outputs are "predicted" by using this model. Construction of prediction equations in state space is explained in detail. MPC control also is an optimal control approach. However, the MPC updates the solution of the optimization problem in each time step and produces updated predictions to be applied on calculation of control input. The MPC has also constraint handling capability, meaning that one can limit the control signals, states and outputs of the system as a part of optimization problem. In this case, the optimization problem becomes a constrained quadratic programming problem in which the problem can be solved numerically. A comparative analysis has been executed between LQR and MPC controllers. Their disturbance rejection capabilities are analyzed by utilizing a simulation experiment. A constant disturbance was applied to the system after a specific simulation time. It is observed that the MPC controller outperforms the LQR controller by successfully compensating the error between disturbed signal and the reference where the LQR controller fails to do so. Disturbance rejection performances of two controllers are also compared with the calculation of root mean square error values between disturbed and reference signals. It is found that the root mean square error value for LQR controller is 0.01 whereas this value is 0.0029 for MPC controller, which is significantly lower than LQR controller. Based on the outcomes of this thesis, further recommendations for future research are proposed. As an ongoing study, more advanced satellite attitude control methods can be utilized such as Linear Quadratic Integrator and Linear Quadratic Gaussian controllers. These advanced control methods offer improved performance since they also account the integral action on control, system uncertainties, noise and so on. Additionally, nonlinear control methods such as sliding mode control and adaptive control can provide robustness to the system as they account for nonlinearities and uncertainties in the system. Development of estimators such as Kalman Filter and Particle Filter can also be utilized to model the measurement noise and including this noise into the system model to enhance the control performance of the system under the presence of disturbance. Model-based design techniques such as processor-in-the-loop and hardware-in-the-loop simulations may assist to improve the system's control performance as they allow for the evaluation of control algorithms in real-time. Implementation of proposed control algorithms into the embedded hardware will also enable the testing of hardware and software constraints, as well as actual implementation on real satellites.