The need to ease pressure from the depleting fossil fuel reserves coupled with the rising global energy demand has seen a drastic increase in research and uptake of renewable energy sources in recent decades. Of the commonly exploited renewable energy resources, hydropower is currently the most popular resource accounting for 17% of the world's total energy generation, a portion which translates to 85% of the renewable energy share. However, despite the huge potential, hydropower is dependent on the availability of water resource, which is affected by climate change. During wet seasons, hydropower system operators are faced with a deluge of floods which results in excess power generation and spillage. The situation reverses in dry seasons where system operators are compelled to curtail power generation because of low water levels in the hydro reservoirs. The later situation is more pronounced in drought prone regions such as Southern Africa where some hydropower plants are completely shut down in dry seasons due to water shortage. This dissertation focuses on the application of optimal control to hydropower plants with pumpback retrofits powered by on-site hydrokinetic and wind power systems. The first section of this work develops an optimal operation strategy for a high head hydropower plant retrofitted with hydrokinetic-powered cascaded pumpback system in dry season. The objective of pumpback operation is to recycle a part of the downstream discharged water back to the main dam to maintain a high water level required for optimal power generation. The problem is formulated as a discrete optimisation problem to simultaneously minimise the grid pumping energy demand, minimise the wear and tear associated with the switching frequency of the two pumps in cascade, maximise restoration of the reservoir volume through pumpback operation and maximise the use of on-site generated hydrokinetic power for pumping operation. Simulation results based on a practical case study show the pumping energy saving advantages of the cascaded pumping system as compared to a classical pumped storage (PS) system. The second section of this work develops an optimal control system for assessing the effects of ecological flow constraints to the operation of a hydropower plant with a hydrokinetic-wind powered pumpback retrofit. The aim of the control law in this case is to use the allocated water to optimally meet the contractual obligations of the power plant. The problem is formulated as a discrete optimisation problem to maximise the energy output of the reservoir subject to some defined technical and hydrological constraints. In this system, pumping power is met primarily by the wind power generator output supplemented by the on-site generated hydrokinetic power. The excess hydrokinetic power is exported to the grid to meet the committed demand. Three different optimisation scenarios are developed: The first scenario is the baseline operation of the hydropower plant without any intervention. The second scenario incorporates the hydrokinetic-wind-powered pumpback operation in the optimal control policy. The third scenario includes the downstream flow constraint to the optimal control policy of the second optimisation scenario. Simulation results based on a practical case study show that ecological flow constraints have negative effects to the economic performance of a hydropower plant. / Dissertation (MEng)--University of Pretoria, 2017. / MasterCard Foundation Scholars Program / Centre of New Energy Systems / University of Pretoria / Electrical, Electronic and Computer Engineering / MEng / Unrestricted

This dissertation is focused on the modeling and robust model-based control of high degree-of-freedom (DoF) systems. While most of the contributions are applicable to any difficult-to-model system, this dissertation focuses specifically on applications to large-scale soft robots because their many joints and pressures constitute a high-DoF system and their inherit softness makes them difficult to model accurately. First a joint-angle estimation and kinematic calibration method for soft robots is developed which is shown to decrease the pose prediction error at the end of a 1.5 m robot arm by about 85\%. A novel dynamic modelling approach which can be evaluated within microseconds is then formulated for continuum type soft robots. We show that deep neural networks (DNNs) can be used to approximate soft robot dynamics given training examples from physics-based models like the ones described above. We demonstrate how these machine-learning-based models can be evaluated quickly to perform a form of optimal control called model predictive control (MPC). We describe a method of control trajectory parameterization that enables MPC to be applied to systems with more DoF and with longer prediction horizons than previously possible. We show that this parameterization decreases MPC's sensitivity to model error and drastically reduces MPC solve times. A novel form of MPC is developed based on an evolutionary optimization algorithm that allows the optimization to be parallelized on a computer's graphics processing unit (GPU). We show that this evolutionary MPC (EMPC) can greatly decrease MPC solve times for high DoF systems without large performance losses, especially given a large GPU. We combine the ideas of machine learned DNN models of robot dynamics, with parameterized and parallelized MPC to obtain a nonlinear version of EMPC which can be run at higher rates and find better solutions than many state-of-the-art optimal control methods. Finally we demonstrate an adaptive form of MPC that can compensate for model error or changes in the system to be controlled. This adaptive form of MPC is shown to inherit MPC's robustness to completely unmodeled disturbances and adaptive control's ability to decrease trajectory tracking errors over time.

My PhD thesis concentrates on the field of stochastic analysis, with focus on stochastic optimization and applications in finance. It is composed of two parts: the first part studies an optimal stopping problem, and the second part studies an optimal control problem. The first topic considers a one-dimensional transient and downwards drifting diffusion process X, and detects the optimal times of a random time(denoted as ρ). In particular, we consider two classes of random times: (1) the last time when the process exits a certain level l; (2) the time when the process reaches its maximum. For each random time, we solve the optimization problem infτ E[λ(τ- ρ)+ +(1-λ)(ρ - τ)+] overall all stopping times. For the last exit time, the process should stop optimally when it runs below some fixed level k the first time, where k is the solution of an explicit defined equation. For the ultimate maximum time, the process should stop optimally when it runs below a boundary which is the maximal positive solution (if exists) of a first-order ordinary differential equation which lies below the line λs for all s > 0 . The second topic solves an optimal consumption and investment problem for a risk-averse investor who is sensitive to declines than to increases of standard living (i.e., the investor is loss averse), and the investment opportunities are constant. We use the tools of stochastic control and duality methods to solve the resulting free-boundary problem in an infinite time horizon. Briefly, the investor consumes constantly when holding a moderate amount of wealth. In bliss time, the investor increases the consumption so that the consumption-wealth ratio reaches some fixed minimum level; in gloom time, the investor decreases the consumption gradually. Moreover, high loss aversion tends to raise the consumption-wealth ratio, but cut the investment-wealth ratio overall.

This thesis proposes new algorithms for a group of sensing robots to learn a para- metric model for a dynamic spatio-temporal field, then based on the learned model trajectories are planned for sensing robots to best estimate the field. In this thesis we call these two parts learning and monitoring, respectively. For the learning, we first introduce a parametric model for the spatio-temporal field. We then propose a family of motion strategies that can be used by a group of mobile sensing robots to collect point measurements about the field. Our motion strategies are designed to collect enough information from enough locations at enough different times for the robots to learn the dynamics of the field. In conjunction with these motion strategies, we propose a new learning algorithm based on subspace identification to learn the parameters of the dynamical model. We prove that as the number of data collected by the robots goes to infinity, the parameters learned by our algorithm will converge to the true parameters. For the monitoring, based on the model learned from the learning part, three new informative trajectory planning algorithms are proposed for the robots to collect the most informative measurements for estimating the field. Kalman filter is used to calculate the estimate, and to compute the error covariance of the estimate. The goal is to find trajectories for sensing robots that minimize a cost metric on the error covariance matrix. We propose three algorithms to deal with this problem. First, we propose a new randomized path planning algorithm called Rapidly-exploring Random Cycles (RRC) and its variant RRC* to find periodic trajectories for the sensing robots that try to minimize the largest eigenvalue of the error covariance matrix over an infinite horizon. The algorithm is proven to find the minimum infinite horizon cost cycle in a graph, which grows by successively adding random points. Secondly, we apply kinodynamic RRT* to plan continuous trajectories to estimate the field. We formulate the evolution of the estimation error covariance matrix as a differential constraint and propose extended state space and task space sampling to fit this problem into classical RRT* setup. Thirdly, Pontryagin’s Minimum Principle is used to find a set of necessary conditions that must be satisfied by the optimal trajectory to estimate the field. We then consider a real physical spatio-temporal field, the surface water temper- ature in the Caribbean Sea. We first apply the learning algorithm to learn a linear dynamical model for the temperature. Then based on the learned model, RRC and RRC* are used to plan trajectories to estimate the temperature. The estimation performance of RRC and RRC* trajectories significantly outperform the trajectories planned by random search, greedy and receding horizon algorithms.

The turbocharger is an important component of competitive environmentally friendly vehicles. Mathematical models are needed for controlling turbochargers in modern vehicles. The models are parameterized using data, gathered from turbocharger testing ingas stands (a flow bench for turbocharger, where the engine is replaced with a combustion chamber, so that the exhaust gases going to the turbocharger can be controlled with high accuracy). Collecting the necessary time averaged data is a time-consuming process. It can take more than 24 hours per turbocharger. To achieve a sufficient level of accuracy in the measurements, it is required to let the turbocharger system reach steady state after a change of operating point. The turbocharger material temperatures are especially slow to reach steady state. A hypothesis is that modern methods in control theory, such as numeric optimal control, can drastically reduce the wait time when changing operating point. The purpose of this thesis is to provide a method of time optimal testing of turbo chargers.  Models for the turbine, bearing house and compressor are parameterized. Well known models for heat transfer is used to describe the heat flows to and from exhaust gas and charge air, and turbocharger material, as well as internal energy flows between the turbocharger components. The models, mechanical and thermodynamic, are joined to form a complete turbocharger model, which is validated against measured step responses. Numeric optimal control is used to calculate optimal trajectories for the turbo charger input signals, so that steady state is reached as quickly as possible, fora given operating point. Direct collocation is a method where the optimal control problem is discretized, and a non-linear program solver is used. The results show that the wait time between operating points can be reduced by a factor of 23. When optimal trajectories between operating points can be found, the possibility of further gains, if finding an optimal sequence of trajectories, are investigated. The problem is equivalent to the open traveling salesman, a well studied problem, where no optimal solution can be guaranteed. A near optimal solution is found using a genetic algorithm. The developed method requires a turbocharger model to calculate input trajectories. The testing is done to acquire data, so that a model can be created, which is a catch-22 situation. It can be avoided by using system identification techniques. When the gas stand is warming up, the necessary model parameters are estimated, using no prior knowledge of the turbocharger.

We are currently witnessing a rapid expansion of renewable power production, an increase dominated by wind and solar power. These intermittent energy sources, while having low production costs, increases the uncertainty on the electrical markets. Hydropower is a renewable source of electricity that is capable of controlled production. It is assumed that hydropower will take a more central role in terms of balancing deficiencies caused by intermittent sources. In this thesis, we present a detailed model of a single hydropower plant consisting of 𝑛 turbines. This model is then used as input of solving the optimisation problem of revenue maximisation for the hydro plant owner. The model used takes into account head effects as well as stochastic inflow of water and the stochastic fluctuations of electricity prices.

Freight transport demand has escalated and will continue to do so as economiesgrow. As the traffic intensity increases, the drivers are faced with increasinglycomplex tasks and traffic safety is a growing issue. Simultaneously, fossil fuel usageis escalating. Heavy duty vehicle (HDV) platooning is a plausible solution to theseissues. Even though there has been a need for introducing automated HDV platooningsystems for several years, they have only recently become possible to implement.Advancements in on-board and external technology have ushered in new possibilitiesto aid the driver and enhance the system performance. Each vehicle is able to serveas an information node through wireless communication; enabling a cooperativenetworked transportation system. Thereby, vehicles can semi-autonomously travel atshort intermediate spacings, effectively reducing congestion, relieving driver tension,improving fuel consumption and emissions without compromising safety. This thesis presents contributions to a framework for the design and implementation of HDV platooning. The focus lies mainly on establishing and validating realconstraints for fuel optimal control for platooning vehicles. Nonlinear and linearvehicle models are presented together with a system architecture, which dividesthe complex problem into manageable subsystems. The fuel reduction potentialis investigated through simulation models and experimental results derived fromstandard vehicles traveling on a Swedish highway. It is shown through analyticaland experimental results that it is favorable with respect to the fuel consumption tooperate the vehicles at a much shorter intermediate spacing than what is currentlydone in commercially available systems. The results show that a maximum fuelreduction of 4.7–7.7 % depending on the inter-vehicle time gap, at a set speedof 70 km/h, can be obtained without compromising safety. A systematic designmethodology for inter-vehicle distance control is presented based on linear quadraticregulators (LQRs). The structure of the controller feedback matrix can be tailoredto the locally available state information. The results show that a decentralizedcontroller gives good tracking performance, a robust system and lowers the controleffort downstream in the platoon. It is also shown that the design methodologyproduces a string stable system for an arbitrary number of vehicles in the platoon,if the vehicle configurations and the LQR weighting parameters are identical for theconsidered subsystems. With the results obtained in this thesis, it is argued that a vast fuel reductionpotential exists for HDV platooning. Present commercial systems can be enhancedsignificantly through the introduction of wireless communication and decentralizedoptimal control. / QC 20111012

No description available.

Constrained optimization is used to derive human postures and movements. In the first study a static 3D model with 30 muscle groups is used to analyse postures. The activation levels of these muscles are minimized in order to represent the individual's choice of posture. Subject specific data in terms of anthropometry, strength and orthopedic aids serve as input. The aim is to study effects from orthopedic treatment and altered abilities of the subject. Initial validation shows qualitative agreement of posture strategies but further details about passive stiffness and anthropometry are needed, especially to predict pelvis orientation. In the second application, the athletic long jump, a problem formulation is developed to find optimal movements of a multibody system when subjected to contact. The model was based on rigid links, joint actuators and a wobbling mass. The contact to the ground was modelled as a spring-damper system with tuned properties. The movement in the degrees of freedom representing physical joints was described over contact time through two fifth-order polynomials, with a variable transition time, while the motion in the degrees of freedom of contact and wobbling mass was integrated forwards in time, as a consequence. Muscle activation variables were then optimized in order to maximize ballistic flight distance. The optimization determined contact time, end configuration, activation and interaction with the ground from an initial configuration. The results from optimization show a reasonable agreement with experimentally recorded jumps, but individual recordings and measurements are needed for more precise conclusions.

This Thesis presents an optimal framework with dynamic perceptibility and chaos compensation for the control of robot manipulators. The fundamental objective of this framework is to obtain a variety of control laws for implementing dynamic visual servoing systems. In addition, this Thesis presents different contributions like the concept of dynamic perceptibility that is used to avoid image and robot singularities, the framework itself, that implements a delayed feedback controller for chaos compensation, and the extension of the framework for space robotic systems. Most of the image-based visual servoing systems implemented to date are indirect visual controllers in which the control action is joint or end-effector velocities to be applied to the robot in order to achieve a given desired location with respect to an observed object. The direct control of the motors for each joint of the robot is performed by the internal controller of the robot, which translates these velocities into joint torques. This Thesis mainly addresses the direct image-based visual servoing systems for trajectory tracking. In this case, in order to follow a given trajectory previously specified in the image space, the control action is defined as a vector of joint torques. The framework detailed in the Thesis allows for obtaining different kind of control laws for direct image-based visual servoing systems. It also integrates the dynamic perceptibility concept into the framework for avoiding image and robot singularities. Furthermore, a delayed feedback controller is also integrated so the chaotic behavior of redundant systems is compensated and thus, obtaining a smoother and efficient movement of the system. As an extension of the framework, the dynamics of free-based space systems is considered when determining the control laws, being able to determine trajectories for systems that do not have the base attached to anything. All these different steps are described throughout the Thesis. This Thesis describes in detail all the calculations for developing the visual servoing framework and the integration of the described optimization techniques. Simulation and experimental results are shown for each step, developing the controllers in an FPGA for further optimization, since this architecture allows to reduce latency and can be easily adapted for controlling of any joint robot by simply modifying certain modules that are hardware dependents. This architecture is modular and can be adapted to possible changes that may occur as a consequence of the incorporation or modification of a control driver, or even changes in the configuration of the data acquisition system or its control. This implementation, however, is not a contribution of this Thesis, but is necessary to briefly describe the architecture to understand the framework’s potential. These are the main objectives of the Thesis, and two robots where used for experimental results. A commercial industrial seven-degrees-of-freedom robot: Mitsubishi PA10, and another three-degrees-of-freedom robot. This last one’s design and implementation has been developed in the research group where the Thesis is written.