The following is a study of an attitude control system (ACS) for a low earth orbit nanosatellite. Control actuation is applied using three reaction wheels and three mutually orthogonal current-driven magnetorquers which produce torques by interacting with the earth’s magnetic field. Control torques are distributed amongst the actuators allowing them to work together in concert. This type of control is referred to as hybrid magnetic attitude control. To account for the nearly periodic behavior of the earth’s magnetic field, control torques are assigned using periodic and optimal control theory. The primary focus is to apply the time-varying Linear Quadratic Regulator controller to test the stability and energy consumption of the ACS when reaction wheels are removed from the control law, or are simulated to be missing. Other situations studied include the effects of control saturation, introducing uncertainty in the orbital inclination, and observing performance as the number of magnetic coils is increased.

The following is a study of an attitude control system (ACS) for a low earth orbit nanosatellite. Control actuation is applied using three reaction wheels and three mutually orthogonal current-driven magnetorquers which produce torques by interacting with the earth’s magnetic field. Control torques are distributed amongst the actuators allowing them to work together in concert. This type of control is referred to as hybrid magnetic attitude control. To account for the nearly periodic behavior of the earth’s magnetic field, control torques are assigned using periodic and optimal control theory. The primary focus is to apply the time-varying Linear Quadratic Regulator controller to test the stability and energy consumption of the ACS when reaction wheels are removed from the control law, or are simulated to be missing. Other situations studied include the effects of control saturation, introducing uncertainty in the orbital inclination, and observing performance as the number of magnetic coils is increased.

The vertical take-off and landing capabilities of quadrotors, and their maneuverability has contributed towards their recent popularity. They are widely used for indoors applications, where robust control strategies and automation of mission planning is necessary. In this thesis, a mathematical model for a quadrotor is derived using Newton's and Euler's laws. The model is linearized around hover and optimal control theory is used to derive a standard linear quadratic regulator controller for trajectory following. A feedorward of the tracking error is introduced to the standard LQR to improve its transient response. The performance of the proposed controller is compared with a conventional PID controller and the standard LQR controller for a variety of trajectories. The proposed controller produced a faster transient response with better disturbance rejection. A* algorithm is used to generate collisionree paths for the quadrotor where the proposed LQR is used to follow the trajectory.

In the last decades, the quadrotor has been used in many areas, and deigning an effective flight control algorithm for the quadrotor has attracted great interests in both control and robotics communities. This thesis focuses on the flight control of the quadrotor by using different methods: The extend Kalman filter (EKF) based linear quadratic regulator (LQR) method and learning-based model predictive control (LBMPC) method. Chapter 4 investigates the flight control of a quadrotor subject to the model uncertainties and external disturbances. We propose a LQR based tracking algorithm. However, the designed LQR controller is hard to be implemented because of the existing noises in the measured states. A modified EKF is then designed for the online estimation of the position, velocity and motor dynamics by using the measured outputs. From the experimental testing results, it is shown that the proposed EKF-based LQR control method solves the tracking problem of the quadrotor with less tracking errors than only using the LQR method. In Chapter 5, the tracking control problem of the quadrotor subject to external disturbances and physical constraints is studied. A model predictive control (MPC) based algorithm is proposed. To reduce the computational load, a modified prior barrier interior-point method is used to solve the quadratic programming (QP) problem. Nevertheless, the achievable flight performance by using the standard MPC algorithm is affected by external disturbances. A LBMPC algorithm is proposed for the disturbance rejection. From the simulation results, it is shown that using the proposed LBMPC algorithm have less tracking errors than applying the standard MPC algorithm. / Graduate

Data centers operations are notoriously energy-hungry, with the computing and cooling infrastructures drawing comparable amount of electrical power to operate. A direction to improve their efciency is to optimizethe cooling, in the sense of implementing cooling infrastructures controlschemes that avoid performing over-cooling of the servers.Towards this direction, this work investigates minimum cost linearquadratic control strategies for the problem of managing air cooled datacenters. We derive a physical and a black box model for a general datacenter, identify this model from real data, and then derive, present andtest in the eld a model based Linear-Quadratic Regulator (LQR) strategy that sets the optimal coolant temperature for each individual coolingunit. To validate the approach we compare the eld tests from the LQR strategy against classical Proportional-Integral-Derivative (PID) controlstrategies, and show through our experiments that it is possible to reducethe energy consumption with respect to the existing practices by severalpoints percent without harming the servers within the data center fromthermal perspectives.

A quadrotor is a type of small unmanned aerial vehicle (UAV) with four rotors. Various control techniques have been successfully applied to the quadrotor. In this thesis, two control methods, including linear quadratic regulator (LQR) and H2-optimal control, are applied to the autonomous navigation and control of a quadorotor named QBall-X4 that is developed by Quanser. The continuous-time dynamic model is established using the Euler-Lagrange approach. Due to the nonlinearities in the quadrotor dynamics, we propose a simplified linear model, which is further used for the controller design in this thesis. According to the simplified quadrotor dynamics, we design an LQR controller to regulate the quadrotor system from its initial position to the desired position. The effectiveness of the controller is verified by simulation studies. However, the LQR control system is operated in the nominal model, and it can not present guaranteed performance when system uncertainties exist. The main emphasis is placed on designing an H2-optimal controller that minimizes the H2-norm of the transfer function. The solution is obtained by using the state-space approach and linear matrix inequality (LMI) method, respectively. In contrast to LQR control method, which is normally applied to a system with no disturbance, the H2-optimal controller takes the form of an observer together with a state feedback control gain to deal with the system uncertainties and disturbances. The simulation results and experimental study verify that the proposed H2-optimal controller is an effective option for the quadrotor with the attendance of uncertainties and disturbances. / Graduate

In this paper we develop a mathematical model of a two-dimensional aeroelastic airfoil. This model is used to design a flutter suppression controller. Flutter is a vibration in a wing caused by airstream energy being absorbed by the lifting surface. Flutter increases with increasing speed. For simplicity, we consider a flat plate in a two-dimensional flow. The model is developed in the frequency domain and then transformed into the time domain. The uncontrolled model is numerically simulated using MATLAB. Linear Quadratic Regulator (LQR) theory is used to design a state feedback controller. The LQR control scheme consists of using a full state feedback controller of the form u=-Kx, where K is a control gain matrix. The goal is to use LQR theory to supress flutter and to maintain stability of the closed loop system. / Master of Science

The diploma thesis deals with putting the pendulum into upright position and its stabilization on a real system. The opening chapter describes the limiting various implementation inverse pendulums, the use of major laboratory tasks in industry, and the selection of appropriate methods for stabilization. The real system was properly identified and parameterized. The mathematical model of the inverse pendulum was derived using the Lagrange method of the second type, the nonlinear system was converted into a status description and linearized for the needs of the state controller design. The system was simulated in the Matlab Simulink environment. The LQR controller was chosen as the regulator stabilizing in upright cases. A Kalman controller in discrete form was prepared for the filter signal and estimation of residual states. The energy method was chosen for the upright pendulums. The proposed methods were tested and implemented in simulation and on a real system.

The use of rotary winged unmanned aerial vehicles in military and civilian applications is rapidly increasing. The primary objective of this study is to develop an automatic flight control system for a radio controlled (RC) helicopter. There is a need for a simple, easy to use methodology to develop automatic flight controllers for first-flight. In order to make the work accessible to new research groups without physical helicopter platforms, a simulation environment is created for validation. The size 30 RC helicopter in AeroSIMRC is treated as the final target platform. A grey box, timedomain system identification method is used to estimate a linear state space model that operates around hover. Identifying the unknown parameters in the model is highly dependent on the initial guess values and the input data. The model is divided into subsystems to make estimation possible. A cascaded controller approach is followed. The helicopter’s fast angular dynamics are separated from the slower translational dynamics. A linear quadratic regulator is used to control the helicopter’s attitude dynamics. An optimised PID outer-loop generates attitude commands from a given inertial position trajectory. The PID controllers are optimised using a simplex search method. An observer estimates the unmeasured states such as blade flapping. The controller is developed in Simulink®, and a plug-in written for AeroSIMRC enables Simulink® to control the simulator through a UDP interface to validate the model and controller. The identified state space model is able to accurately model the flight data from the simulator. The controllers perform well, keeping the helicopter stable even in the presence of considerable disturbances. The attitude controller’s performance is validated using an aeronautical design standard (ADS-33E-PRF) for handling qualities. The trajectory tracking is validated in a series of simulator flight tests. The linear controller is able to sustain stable flight in constant winds of up to 60% of the helicopter’s maximum airspeed. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2014

The use of rotary winged unmanned aerial vehicles in military and civilian applications is rapidly increasing. The primary objective of this study is to develop an automatic flight control system for a radio controlled (RC) helicopter. There is a need for a simple, easy to use methodology to develop automatic flight controllers for first-flight. In order to make the work accessible to new research groups without physical helicopter platforms, a simulation environment is created for validation. The size 30 RC helicopter in AeroSIMRC is treated as the final target platform. A grey box, timedomain system identification method is used to estimate a linear state space model that operates around hover. Identifying the unknown parameters in the model is highly dependent on the initial guess values and the input data. The model is divided into subsystems to make estimation possible. A cascaded controller approach is followed. The helicopter’s fast angular dynamics are separated from the slower translational dynamics. A linear quadratic regulator is used to control the helicopter’s attitude dynamics. An optimised PID outer-loop generates attitude commands from a given inertial position trajectory. The PID controllers are optimised using a simplex search method. An observer estimates the unmeasured states such as blade flapping. The controller is developed in Simulink®, and a plug-in written for AeroSIMRC enables Simulink® to control the simulator through a UDP interface to validate the model and controller. The identified state space model is able to accurately model the flight data from the simulator. The controllers perform well, keeping the helicopter stable even in the presence of considerable disturbances. The attitude controller’s performance is validated using an aeronautical design standard (ADS-33E-PRF) for handling qualities. The trajectory tracking is validated in a series of simulator flight tests. The linear controller is able to sustain stable flight in constant winds of up to 60% of the helicopter’s maximum airspeed. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2014