Based on the Lyapunov stability theorem, a model reference adaptive sliding mode control scheme is proposed in this thesis for a class of multi-input multi-output (MIMO) dynamic systems with mismatched model uncertainties and external disturbances in order to solve robust tracking problems. In this method, the adaptive mechanism is employed both in sliding surface function and control effort so that once the dynamics of the controlled system enters the sliding surface, the state trajectories of system can achieve asymptotical stability even if the mismatched perturbations exist. In addition, with an adaptive mechanism embedded in the proposed control scheme, the controller will asymptotically adapt the unknown upper bound of perturbations so that the information of upper bound of perturbations is not required. A numerical example and a practical experiment are given for demonstrating the feasibility of the proposed control scheme.

No description available.

Based on Lyapunov theorem, two different types of control schemes for solving robust tracking problems are presented in this thesis. The first one is model reference adaptive sliding mode control, which is designed for a class of SISO LTI systems with relative degree one possessing additive and multiplicative unstructured uncertainties in the input and output channels. By introducing a perturbation estimation process embedded in the proposed control scheme, the chattering phenomenon can be reduced effectively since only the perturbation estimation error needs to be overcomed. The second one is optimal model reference adaptive control, which is designed for a class of multi-input systems with input non-linearity. These systems are subject to model uncertainties and time-varying delay.

A simple technique of designing a robust discrete-time variable structure output tracking controller for a class of perturbed MIMO linear and nonlinear systems is proposed in this thesis. For linear systems, a model reference scheme is employed. Both an adaptive mechanism and a perturbation estimation process are embedded in the proposed control scheme. The information of the upper bound of the perturbation estimation error is not required due to the usage of adaptive mechanism. It is shown that the dynamics of the controlled systems will be driven into the vicinity of the designed switching surface, therefore the tracking error will be constrained in a small bounded region. Furthermore, the stability of the overall controlled system is guaranteed, and one can increase the tracking accuracy by adjusting the controller's parameters or by employing the perturbation estimation process.

Based on the Lyapunov stability theorem, an optimal model reference adaptive control (OMRAC) scheme with perturbation estimation is presented in this thesis to solve robust tracking problems. The plant considered belongs to a class of MIMO perturbed dynamic systems with input nonlinearity and time varying delay in the state. The proposed control scheme contains three types of controllers. The first one is a linear feedback controller, which is an optimal controller if there is no perturbation. The second one is an adaptive controller, it is used for adapting the unknown upper bound of perturbation estimation error. The last one is the perturbation estimation mechanism. The property of uniformly ultimately boundness is proved under the proposed control scheme, and the effects of each design parameter on the dynamic performance is analyzed. Two numerical examples are given for demonstrating the feasibility of the proposed methodology.

Based on the Lyapunov stability theorem, a model reference adaptive variable structure control (MRAVSC) scheme with perturbation estimation is presented in this thesis for solving robust tracking problems. The plant considered belongs to a class of MIMO linear time invariant systems with arbitrary relative degree possessing additive and multiplicative unstructured uncertainties in the input and output channels. By introducing a perturbation estimation process embedded in the proposed control scheme, both the perturbations and differentials of tracking errors can be estimated. In addition, the proposed control scheme also contains an adaptive mechanism in order to automatically adapt the unknown upper bound of perturbation estimation error, and guarantee the property of uniformly ultimate boundedness for the closed-loop controlled system. Finally, two numerical examples are presented to demonstrate the feasibility of the proposed control scheme.

Based on the Lyapunov stability theorem, a methodology of designing robust discrete-time model reference variable structure state tracking controller is proposed in this thesis for a class of multi-input multi-output (MIMO) discrete-time systems. This variable structure controller is composed of three types of controllers. The first one is the feedback control law, which can eliminate the nominal term in the derivative of a Lyapunov function. The second one is the switching control law, which can determine the decreasing rate of the Lyapunov function. The third one is the adaptive control law, which is used to overcome the perturbations. The resultant robust variable structure controllers are capable of driving all the trajectories of tracking errors toward a small bounded region. The information of upper bound of the perturbation, which is not a constant and is dependent on the norm of state variable, is not required beforehand due to some adaptive mechanisms are embedded in the proposed control scheme, and the stability of the overall controlled system is guaranteed. A numerical example and a practical example are given to demonstrate the feasibility of the proposed control scheme.

Tailsitter UAVs (Unmanned Aerial Vehicles) are a type of VTOL (Vertical Take off and Landing) aircraft that combines the agility of a quadrotor drone with the endurance and speed of a fixed-wing aircraft. For this reason, they have become popular in a wide range of applications from tactical surveillance to parcel delivery. This thesis details a clean sheet design process for a tailsitter UAV that includes the dynamic modeling, control design, simulation, vehicle design, vehicle prototype fabrication, and testing of a tailsitter UAV. The goal of this process was to design a robust controller that is able to handle uncertainties in the system's parameters and external disturbances and subsequently can control the vehicle through the transition between vertical and horizontal flight regimes. It is evident in the literature that most researchers choose to model and control tailsitter UAVs using separate methods for the vertical and horizontal flight regimes and combine them into one control architecture. The novelty of this thesis is the use of a single dynamical model for all flight regimes and the robust control technique used. The control algorithm used for this vehicle is a MRAC (Model Reference Adaptive Control) law, which relies on reference models and gains that adapt according to the vehicle's response in all flight regimes. To validate this controller, numerical simulations in Matlab and flight tests were conducted. The combination of these validation methods confirms our adaptive controller's ability to control the transition between the vertical and horizontal flight regimes when faced with both parametric uncertainties and external disturbances. / Master of Science / Unmanned aircrafts have been a topic of constant research and development recently due to their wide range of applications and their ability to fly without directly involving pilots. More specifically, VTOL UAVs have the advantage of being able to take off without a runway while retaining the efficiency of a classical aircraft. A tailsitter UAV behaves as a traditional quadrotor drone when in its vertical configuration and can rotate to a horizontal configuration, where it takes advantage of its wings to fly as a conventional aircraft. Modeling the dynamics of the tailsitter UAV and designing an autopilot controller is the main focus of this thesis. An adaptive controller was chosen for the tailsitter UAV due to its ability to modify the gains of the system based on the behavior of the vehicle to adapt to the unknown vehicle properties. This controller was validated using both computer simulations and actual flight tests. It was found that the adaptive controller was able to successfully control the transition between the vertical and horizontal flight regimes despite the uncertainties in the parameters of the vehicle.

A escolha do modelo de referência é a principal tarefa a ser executada pelo projetista em um projeto de controle por modelo de referência. Uma má escolha do modelo de referência pode resultar em um desempenho de malha fechada que tem pouca semelhança com o especificado e a malha fechada pode até ser instável. Neste trabalho, esse problema será discutido no controle de plantas multivariáveis. O resultado experimental em uma planta de controle de nível de três tanques mostra uma aparentemente correta, ainda que ingênua, escolha do modelo de referência levando a um desempenho muito pobre em malha fechada. O problema é, então, analisado, expondo a ingenuidade do exemplo. Começa-se por reconhecer as restrições fundamentais impostas pelo sistema e, em seguida, deriva-se diretrizes gerais que respeitam essas restrições, para uma escolha eficaz do modelo de referência em sistemas multivariáveis. Também é proporcionada uma nova formulação para calcular o grau relativo mínimo de cada elemento do modelo de referência sem a necessidade de um modelo completo da planta. A aplicação destas orientações em simulações e na planta de três tanques ilustra sua eficácia. / The choice of the reference model is the main task to be performed by the designer in a model reference control design. A poor choice of the reference model may result in a closed-loop performance that bears no resemblance to the specifications and the closedloop may even be unstable. In this work we discuss this issue in the control of multivariable plants. Experimental results in a three tank level control plant show a seemingly correct, yet naive, choice of reference model leading to very poor closed-loop performance. The problem is then analyzed, exposing the naivete of the design example. We start by recognizing the fundamental constraints imposed by the system and then deriving general guidelines respecting these contraints for the effective choice of the reference model in multivariable systems. We also provide a novel formulation to compute the minimal relative degree of each element of the reference model without needing a complete model of the plant. The application of these guidelines to simulations and the three tank plant illustrates their effectiveness.

In this dissertation, new model reference adaptive control architectures are presented with stability, performance, and robustness considerations, to address challenges related to the verification of adaptive control systems. The challenges associated with the transient performance of adaptive control systems is first addressed using two new approaches that improve the transient performance. Specifically, the first approach is predicated on a novel controller architecture, which involves added terms in the update law entitled artificial basis functions. These terms are constructed through a gradient optimization procedure to minimize the system error between an uncertain dynamical system and a given reference model during the learning phase of an adaptive controller. The second approach is an extension of the first one and minimizes the effect of the system uncertainties more directly in the transient phase. In addition, this approach uses a varying gain to enforce performance bounds on the system error and is further generalized to adaptive control laws with nonlinear reference models. Another challenge in adaptive control systems is to achieve system stability and a prescribed level performance in the presence of actuator dynamics. It is well-known that if the actuator dynamics do not have sufficiently high bandwidth, their presence cannot be practically neglected in the design since they limit the achievable stability of adaptive control laws. Another major contribution of this dissertation is to address this challenge. In particular, first a linear matrix inequalities-based hedging approach is proposed, where this approach modifies the ideal reference model dynamics to allow for correct adaptation that is not affected by the presence of actuator dynamics. The stability limits of this approach are computed using linear matrix inequalities revealing the fundamental stability interplay between the parameters of the actuator dynamics and the allowable system uncertainties. In addition, these computations are used to provide a depiction of the feasible region of the actuator parameters such that the robustness to variation in the parameters is addressed. Furthermore, the convergence properties of the modified reference model to the ideal reference model are analyzed. Generalizations and applications of the proposed approach are then provided. Finally, to improve upon this linear matrix inequalities-based hedging approach a new adaptive control architecture using expanded reference models is proposed. It is shown that the expanded reference model trajectories more closely follow the trajectories of the ideal reference model as compared to the hedging approach and through the augmentation of a command governor architecture, asymptotic convergence to the ideal reference model can be guaranteed. To provide additional robustness against possible uncertainties in the actuator bandwidths an estimation of the actuator bandwidths is incorporated. Lastly, the challenge presented by the unknown physical interconnection of large-scale modular systems is addressed. First a decentralized adaptive architecture is proposed in an active-passive modular framework. Specifically, this architecture is based on a set-theoretic model reference adaptive control approach that allows for command following of the active module in the presence of module-level system uncertainties and unknown physical interconnections between both active and passive modules. The key feature of this framework allows the system error trajectories of the active modules to be contained within apriori, user-defined compact sets, thereby enforcing strict performance guarantees. This architecture is then extended such that performance guarantees are enforced on not only the actuated portion (active module) of the interconnected dynamics but also the unactuated portion (passive module). For each proposed adaptive control architecture, a system theoretic approach is included to analyze the closed-loop stability properties using tools from Lyapunov stability, linear matrix inequalities, and matrix mathematics. Finally, illustrative numerical examples are included to elucidate the proposed approaches.