This thesis focuses on decentralized deadbeat output regulation of discrete-time nonlinear plants that are composed of multiple agents. These agents interact, via scalar-valued signals, in a known structured way represented with a graph. This work is motivated by applications where it is infeasible and/or undesirable to introduce control action within each plant agent; instead, control agents are introduced to interact with certain plant agents, where each control agent focuses on regulating a specific plant agent, called its target. Then, two analyses are carried out to determine if regulation is achieved: targeting analysis is used to determine if control laws can be found to regulate all target agents, then growing analysis is used to determine the effect of those control laws on non-target plant agents. The strength of this novel approach is the intuitively-appealing notion of each control agent focusing on the regulation of just one plant agent. This work goes beyond previous research by generalizing the class of allowable plant dynamics, considering not only arbitrary propagation times through plant agents, but also allowing for non-symmetrical influence between the agents. Moreover, new necessary and sufficient algebraic conditions are derived to determine when targeting succeeds. The main contribution of this work, however, is the development of new easily-verifiable conditions necessary for targeting and/or growing to succeed. These new conditions are valuable due to their simplicity and scalability to large systems. They concern the positioning of control agents and targets as well as the propagation time of signals through the plant, and they help significantly with design decisions. Various graph structures (such as queues, grids, spiders, rings, etc.) are considered and for each, these conditions are used to develop a control scheme with the minimum number of control agents needed.

The author develops a nonlinear longitudinal model of an aircraft modeled by rigid fuselage, tail, and wing, where the wing is attached to the fuselage with a torsional spring. The main focus of this research is to retain the full nonlinearities associated with the system and to perform gust load alleviation for the model by comparing the impact of a proportional-integral- lter nonzero setpoint linear controller with control rate weighting and a nonlinear Lyapunov-based controller. The four degree of freedom longitudinal system under consideration includes the traditional longitudinal three degree of freedom aircraft model and one additional degree of freedom due to the torsion from the wing attachment. Computational simulations are performed to show the aeroelastic response of the aircraft due to a gust load disturbance with and without control. Results presented in this thesis show that the linear model fails to capture the true nonlinear response of the system and the linear controller based on the linear model does not stabilize the nonlinear system. The results from the Lyapunov-based control demonstrate the ability to stabilize the nonlinear response, including the presence of an LCO, and emphasize the importance of examining the fully nonlinear system with a nonlinear controller.

Stability is a critical issue in gain-scheduled control problems in that the closed loop system may not be stable during the transitions between operating conditions despite guarantees that the gain-scheduled controller stabilizes the plant model at fixed values of the scheduling variable. For Linear Parameter Varying (LPV) model representations, a controller interpolation method using Youla parameterization that guarantees stability despite fast transitions in scheduling variables is proposed. By interconnecting an LPV plant model with a Local Controller Network (LCN), the proposed Youla parameterization based controller interpolation method allows the interpolation of controllers of different size and structure, and guarantees stability at fixed points over the entire operating region. Moreover, quadratic stability despite fast scheduling is also guaranteed by construction of a common Lyapunov function, while the characteristics of individual controllers designed a priori at fixed operating condition are recovered at the design points. The efficacy of the proposed approach is verified with both an illustrative simulation case study on variation of a classical MIMO control problem and an experimental implementation on a multi-evaporator vapor compression cycle system. The dynamics of vapor compression systems are highly nonlinear, thus the gain-scheduled control is the potential to achieve the desired stability and performance of the system. The proposed controller interpolation/switching method guarantees the nonlinear stability of the closed loop system during the arbitrarily fast transition and achieves the desired performance to subsequently improve thermal efficiency of the vapor compression system.

<p>For a successful design of an engineering system it is essential to pay careful attention to its dynamic response. This is particularly true, in the case of nonlinear systems, since they can exhibit very complex dynamic behaviour, including multiple co-existing stable solutions and chaotic motions, characterized by large sensitivity to initial conditions. In some systems nonlinear characteristics are desired and designed for, but in other cases they are unwanted and can cause fatigue and failure. A type of dynamical system which is highly nonlinear is discontinuous or non-smooth systems. In this work, systems with impacts are primarily investigated, and this is a typical example of a discontinuous system. To enhance or optimize the performance of dynamical systems, some kind of control can be implemented. This thesis concerns implementation of low-cost control strategies for discontinuous systems. Low-cost control means that a minimum amount of energy is used when performing the control actions, which is a desirable situation regardless of the application. The disadvantage of such a method is that the performance might be limited as compared with a control strategy with no restrictions on energy consumption. In this work, the control objective is to enforce a continuous or discontinuous grazing bifurcation of the system, whichever is desirable. In Paper A, the dynamic response and bifurcation behaviour of an impactoscillator with dry friction is investigated. For a one-degree-of-freedom model of the system, analytical solutions are found in separate regions of state space. These are then used to perform a perturbation analysis around a grazing trajectory. Through the analysis, a condition on the parameters of the system is derived, which assures a continuous grazing bifurcation. It is also shown that the result has bearing on the dynamic response of a two-degree-of-freedom model of the system. A low-cost active control strategy for a class of impact oscillators is proposed in Paper B. The idea of the control method is to introduce small adjustments in the position of the impact surface, at discrete moments in time, to assure a continuous bifurcation. A proof is given for what control parameters assures the stabilization. In Paper C, the proposed low-cost control method is implemented in a quarter-car model of a vehicle suspension, in order to minimize impact velocities with the bumpstop in case of high amplitude excitation. It is shown that the control method is effective for harmonic road excitation.</p>

Thesis--Auburn University, 2009. / Abstract. Vita. Includes MatLab code. Includes bibliography (p.43-44).

Thesis (Ph. D.)--Missouri University of Science and Technology, 2009. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed January 13, 2009) Includes bibliographical references.

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. / Discusses the process of standing from a chair is the first movement to be affected by physical impairment or ageing. That justified the increase of researches around sit-to-stand movements nowadays.This thesis presents the design of a four links wearable device that can assist disable people to stand from a sitting position. The four links are joined at the ankle, the knee and the HAT (Head, Arm and Trunk) where actuators are mounted. The system is built around three controllers. The Goal Controller drives the links along their reference trajectories, the Stability Controller makes sure that the system does not collapse as it is rising, and the last controller combines the signal from the 2 first ones.The reference trajectories are obtained from data recorded from healthy people performing the movement. The main idea behind the present design is that from seat off, the floor projection of the body centre of pressure is evaluated and compared to the most stable position. The stability controller generates the torque necessary to compensate the deviation, while the third controller adjusts the level of participation of that torque to satisfy both the trajectory and the stability objectives. Similar idea was previously found in Prinz (2010).

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.