3. Electronic Theses and Dissertations (ETDs) - All submissions
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Item Learning safe predictive control with gaussian processes(2019) Van Niekerk, BenjaminLearning-based methods have recently become popular in control engineering, achieving good performance on a number of challenging tasks. However, in complex environments where data efficiency and safety are critical, current methods remain unsatisfactory. As a step toward addressing these shortcomings, we propose a learning-based approach that combines Gaussian process regression with model predictive control. Using sparse spectrum Gaussian processes, we extend previous work by learning a model of the dynamics incrementally from a stream ofsensory data. Utilizinglearned dynamics and model uncertainty, we develop a controller that can learn and plan in real-time under non-linear constraints. We test our approach on pendulum and cartpole swing up problems and demonstrate the benefits of learning on a challenging autonomous racing task. Additionally, we show that learned dynamics models can be transferred to new tasks without any additional training.Item Friction compensation in the swing-up control of viscously damped underactuated robotics(2018) De Almeida, Ricardo GalhardoIn this research, we observed a torque-related limitation in the swing-up control of underactuated mechanical systems which had been integrated with viscous damping in the unactuated joint. The objective of this research project was thus to develop a practical work-around solution to this limitation. The nth order underactuated robotic system is represented in this research as a collection of compounded pendulums with n-1 actuators placed at each joint with the exception of the first joint. This system is referred to as the PAn-1 robot (Passive first joint, followed by n-1 Active joints), with the Acrobot (PA1 robot) and the PAA robot (or PA2 robot) being among the most well-known examples. A number of friction models exist in literature, which include, and are not exclusive to, the Coulomb and the Stribeck effect models, but the viscous damping model was selected for this research since it is more extensively covered in existing literature. The effectiveness of swing-up control using Lyapunov’s direct method when applied on the undamped PAn-1 robot has been vigorously demonstrated in existing literature, but there is no literature that discusses the swing-up control of viscously damped systems. We show, however, that the application of satisfactory swing-up control using Lyapunov’s direct method is constrained to underactuated systems that are either undamped or actively damped (viscous damping integrated into the actuated joints only). The violation of this constraint results in the derivation of a torque expression that cannot be solved for (invertibility problem, for systems described by n > 2) or a torque expression which contains a conditional singularity (singularity problem, for systems with n = 2). This constraint is formally summarised as the matched damping condition, and highlights a clear limitation in the Lyapunov-related swing-up control of underactuated mechanical systems. This condition has significant implications on the practical realisation of the swing-up control of underactuated mechanical systems, which justifies the investigation into the possibility of a work-around. We thus show that the limitation highlighted by the matched damping condition can be overcome through the implementation of the partial feedback linearisation (PFL) technique. Two key contributions are generated from this research as a result, which iii include the gain selection criterion (for Traditional Collocated PFL), and the convergence algorithm (for noncollocated PFL). The gain selection criterion is an analytical solution that is composed of a set of inequalities that map out a geometric region of appropriate gains in the swing-up gain space. Selecting a gain combination within this region will ensure that the fully-pendent equilibrium point (FPEP) is unstable, which is a necessary condition for swing-up control when the system is initialised near the FPEP. The convergence algorithm is an experimental solution that, once executed, will provide information about the distal pendulum’s angular initial condition that is required to swing-up a robot with a particular angular initial condition for the proximal pendulum, along with the minimum gain that is required to execute the swing-up control in this particular configuration. Significant future contributions on this topic may result from the inclusion of more complex friction models. Additionally, the degree of actuation of the system may be reduced through the implementation of energy storing components, such as torsional springs, at the joint. In summary, we present two contributions in the form of the gain selection criterion and the convergence algorithm which accommodate the circumnavigation of the limitation formalised as the matched damping condition. This condition pertains to the Lyapunov-related swing-up control of underactuated mechanical systems that have been integrated with viscous damping in the unactuated joint.Item An investigation of techniques for nonlinear state observation(2016) McBride, Dean Christian TaitAn investigation and analysis of a collection of different techniques, for estimating the states of nonlinear systems, was undertaken. It was found that most of the existing literature on the topic could be organized into several groups of nonlinear observer design techniques, of which each group follows a specific concept and slight variations thereof. From out of this investigation it was discovered that a variation of the adaptive observer could be successfully applied to numerous nonlinear systems, given only limited output information. This particular technique formed the foundation on which a design procedure was developed in order to asymptotically estimate the states of nonlinear systems of a certain form, using only partial state information available. Lyapunov stability theory was used to prove the validity of this technique, given that certain conditions and assumptions are satisfied. A heuristic procedure was then developed to get a linearized model of the error transient behaviour that could form the upper bounds of the transient times of the observer. The technique above, characterized by a design algorithm, was then applied to three well-known nonlinear systems; namely the Lorenz attractor, the Rössler attractor, and the Van Der Pol oscillator. The results, illustrated through numerical simulation, clearly indicate that the technique developed is successful, provided all assumptions and conditions are satisfied.Item Modelling, system identification and control of a fibre optic accelerometer(2015) Cornelius, Justin CalenControl of systems are important in most industrial sectors, they nd applications in electronics, machine design and navigation. These control systems often use sensors to work e ectively. One such sensor is an accelerometer, which is used to measure acceleration with one or more degrees of freedom. This research report investigates the modelling, system identi cation and controller design for an accelerometer, a Fibre Optic Accelerometer (FOA). Such a device may be applied in many applications such as anti-skid control, structural failure in buildings and bridges, as well as strategic missile guidance. This report presents a model of a FOA demonstrator which crudely models an industrially developed accelerometer, the demonstrator is made of a jig consisting of a guitar string and electromagnets. Such a model needs to account for a distributed parameter beam combined with a permanent magnet and four electromagnets. The guitar string is modelled using three beam models, namely a spring/damper model, an Assumed Modes Model (ASM) and a Transfer Function Model (TFM). The parameters for these beam models are identi ed using the Nelder-Mead simplex algorithm and the least squares method. The electromagnets within the jig, are modelled using a mathematical model obtained through curve tting of experimental data. The overall FOA sensor is optimised using a lead-lag controller. Five cost functions where investigated, these cost functions are H1, Integral Square Error (ISE), Integral Absolute Error (IAE), Integral Time Square Error (ITSE) and Integral Absolute Time Error (IATE). It was found that the guitar string may be modelled using a single degree of freedom beam model. This is based on a number of reasons, such as the aperture size - through which the tip Light Emitting Diode (LED) projects, the tip mass (permanent magnet) - acting as a natural damper and the fact that Position Sensing Device (PSD) only measures the tip position. It was found that a single degree of freedom model in two orthogonal axes, with a single link beam spring/damper model was the most suitable representation of the guitar string. And the IAE lead-lag controller was found to be the most e ective in controlling a guitar string, this e ectiveness was due to least settling time.