<p> The topic of study within includes the development and application of nonlinear control technologies on sampled systems. Discrete control structures are introduced that expand on existing differential geometric and predictive control methods. The differential geometric techniques are described from the error trajectory context, which are typically only derived for continuous application. The discrete error trajectory controllers introduced have one of two configurations. The first configuration requires satisfaction of the error trajectory objective at the next sampling interval through prediction of system behaviour over the controller sampling interval. This objective found limited success and it is observed that satisfaction of the error trajectory objective at discrete intervals does not generally result in the intended response. The second configuration minimizes the integrated distance from the error manifold defined by the error trajectory objective over the entire controller sampling interval. It is observed that this integrated error trajectory controller best emulates the intent of the continuous controller in the discrete domain. Techniques borrowed from predictive control are incorporated into the integrated error trajectory controller such as input move suppression and constraints to produce an optimal error trajectory controller, further improving performance.</p> <p> The predictive control method introduced utilizes a transformation of the input space. The differentiating property of input transformation predictive control (ITPC) from other methods is the prediction technique that is capable of estimating the future behaviour of nonlinear systems through elementary matrix operations similar to the dynamic matrix control (DMC) prediction technique. This is achieved by separation of the steady state and dynamic system properties and the introduction of an intermediate state prediction layer. This allows for the nonlinear prediction of system behaviour without the need to numerically integrate the system model.</p> <p> Two example systems are used to demonstrate application of the discrete error trajectory and ITPC on nonlinear controllers. Performance for these control structures is compared to technologies accepted within the control community for a broad range for characteristics including, computation efficiency, design effort and other nonlinear performance criteria, with favourable results.</p> / Thesis / Master of Engineering (MEngr)

The stability and safety of robotic systems are heavily impacted by delays and parametric uncertainties due to external disturbances, modeling inaccuracies, reaction forces, and variations in dynamics. This work addresses the effects of parametric uncertainties in the application of payload transportation by robotic systems that involve time delays and state constraints. The problem is split into two research questions: control of a quadrotor UAV in the presence of delays and control of robotic systems with state constraints. The first two papers explore the approaches for remotely operated quadrotors in the presence of delays and uncertainties. Specifically, the first paper surveys the existing methods for controlling a payload-carrying UAV and further presents a class of control techniques in theory that focus on time-delayed systems. The second paper proposes an adaptive control solution for the tracking control of a quadrotor UAV to transport various unknown payloads in the presence of unknown time-varying delays. The proposed controller is robust to modeling uncertainties and does not require knowledge of the uncertainties' bounds. The performance of the controller is verified on a MATLAB-SIMULINK simulated environment. The final three papers deal with enforcing state constraints on tracking control to ensure the safety of the robots in the presence of parametric uncertainties. The third paper exploits state constraints in the post-grasping scenario of the space debris disposal application. This work proposes a robust control for a space robot to follow the desired trajectory without any violation to safely grasp, carry, and release unknown payloads in their respective regions. The controller is tested in a MATLAB-SIMULINK environment with the dynamics of a planar space robot. The fourth paper introduces an adaptive control technique without any a priori knowledge of the system dynamics or the bounds of uncertainties to impose state constraints in control. The proposed controller is designed for a generic Euler-Lagrangian system in the presence of parametric uncertainties, where the state-dependent nature of the uncertainties introduces unboundedness in the overall uncertainty. The controller is validated in simulation using a robotic manipulator in a pick-and-place operation. The final paper proposes an adaptive controller for the tracking control of an experimental planar space robot. The proposed controller enforces constraints on the robot's states and their derivatives on the tracking control for transporting different payloads without any knowledge of the dynamics of the robot or the bounds of the uncertainties. The controller is validated on the experimental space robot. The stability of the proposed controllers is studied analytically using the Lyapunov theory. The results are presented with various plots and numerically analyzed on the metrics of root mean squared errors and peak errors.

This thesis involves the modeling, validation, and control studies of a Control-Oriented, Reconfigurable, and Acausal Floating Turbine Simulator (CRAFTS), that is currently under development. CRAFTS uses Modelica®, an object-oriented, declarative, multi-domain modeling language for physical system modeling in the Dymola environment. The CRAFTS simulator facilitates rapid dynamic simulation of wind turbines with various model variants and enables control co-design. A major emphasis of this thesis is in the validation of the CRAFTS simulator for a 15-MW land-based wind turbine through several test cases. These test cases were collaboratively developed in conjunction with other participating research entities. CRAFTS has undergone rigorous testing, with a particular emphasis on comparison against the industry standard OpenFAST platform (developed by the National Renewable Energy Lab (NREL)) as well as experimental data. Open loop testing scenarios scrutinize the wind turbine dynamic conditions such as varying rotor speed and pitching angle maneuvers. Diverse combinations of ramp and step commands have been employed to modulate rotor speeds and pitching angles. Validation results indicate very good agreement between CRAFTS and baseline results. CRAFTS was also tested under various types of closed-loop control scenarios, such as different types of wind profiles and various wind velocities. Wind types encompass stepped winds, wind gusts, steady winds, and sinusoidal wind patterns. In closed loop testing, firstly an industry standard controller ROSCO (also developed by NREL) was used. Thereafter, a nonlinear controller developed in our prior research was implemented and investigated. The closed loop performance of the CRAFTS model was compared with OpenFAST. The tests confirmed the validity of the CRAFTS model under closed-loop and also validated the nonlinear controller. The work was a critical element in the development of the CRAFTS simulator. Validation tests provided valuable insight into the accuracy of the underlying physics and often provided valuable feedback that led to model improvements. The work has laid the foundations for more advanced research, especially in the area of multivariable control design for floating offshore wind turbines.

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Power converters are electronic circuits for conversion, control and regulation of electric power for various applications, such as from tablet computers in milliwatts to electric power systems at megawatts range. There are three basic types of power converters: buck (output voltage less than the input voltage), boost (output voltage higher than the input voltage) and buck-boost converters. The reliability of the power converters has become an essential focus of industrial applications. This research presents modeling and control of DC/DC boost converter using several control methods, such as Proportional-Integral (PI), Linear Quadratic Regulator (LQR) control, and nonlinear control concepts. Based on standard circuit laws, a mathematical model of the boost converter is derived which is expressed as a bilinear system. First a small signal model of the converter is derived to analyze the small deviations around the steady-state operating point which is used to develop closed loop control using the PI and the LQR methods. Simulation results show that the performance of the converter is good for operation around the operating state, however is unacceptable if there are large variations in the load or the reference input. To improve the performance of the closed loop system, the nonlinear control concept is used which shows excellent closed loop performance under large variations of load or setpoint. Comparative simulation results are presented for closed loop performance under various types of disturbances including random variations in load. / Electrical and Computer Engineering

High performance current control is critical to the success of the switched reluctance motor (SRM). Yet high motor phase nonlinearities in the SRM place extra burden on the current controller, rendering it the weakest link in SRM control. In contrast to linear motor control techniques that respond to current error, the deadbeat controller calculates the control voltage by the current command, phase current, rotor position and applied phase voltage. The deadbeat controller has demonstrated superior response in three-phase inverter current control, PM motor current control, and other relatively linear control applications. This study will investigate the viability and performance of a deadbeat controller for the highly nonlinear SRM. The need for an accurate deadbeat control model first motivates the investigation of experimental inductance measurement techniques. A deadbeat control law is then proposed through multiple revisions to demonstrate the benefit of the numerical method chosen to derive the controller and a current predictor that accounts for processor latency and PWM delay. The practical problems of loop delay, feedback noise, feedback filtering, and deadbeat controller parameter sensitivity are investigated by linear analysis, simulation, experimental implementation and nonlinear model analysis. Simulation and implementation verify deadbeat performance and various measures of transient performance are presented. To address the problem of SRM model error the study ends with a brief discussion of adaptive deadbeat control modifications for possible future research. / Master of Science