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Floating offshore wind farm control and optimization, control of an integrated solar thermal system
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Graduate Student Supervision
Doctoral Student Supervision (Jan 2008 - Nov 2019)
Linear parameter-varying (LPV) control is a systematic way for gain-scheduling control of a nonlinear or time-varying system that has parameter-dependent dynamics variations in its operating region. However, when the dynamics variations are large, LPV control may give the conservative performance. One way to reduce the conservatism is switching LPV (SLPV) control, in which we partition the operating region into sub-regions, design one local LPV controller for each sub-region, and switch among those local controllers according to some switching rules. On the one hand, this thesis makes three theoretical contributions to the SLPV control theory. Firstly, this thesis proposes a new approach to designing SLPV controllers with guaranteed stability and performance even when the scheduling parameters cannot be exactly measured. Secondly, this thesis presents two algorithms to optimize the switching surfaces (SSs) that can further improve the performance of an SLPV controller. One algorithm is based on sequentially optimizing the SSs and the SLPV controller for the state-feedback case. The other one is based on particle swarm optimization and can be used for both state-feedback and output-feedback cases. Finally, this thesis introduces a novel approach to designing SLPV controllers that could yield significantly improved local performance in some sub-regions without much sacrifice of the worst-case performance. This is different from the traditional approach that often leads to similar performance in all the sub-regions.On the other hand, this thesis addresses two practical problems using the theoretic approaches developed in this thesis. One is control of miniaturized optical image stabilizers with product variations. Specifically, multiple parameter-dependent robust (MPDR) controllers are designed to adapt to the product variations, while being robust against the uncertainties in measurement of the scheduling parameters that characterize the dynamics variation. Experimental results validate the advantages of the proposed MPDR controllers over a conventional robust mu-synthesis controller. The other application is control of a floating offshore wind turbine on a semi-submersible platform. SLPV controllers are designed for regulating the power and the generator speed and reducing the platform motion. The superior performance of the SLPV controllers is demonstrated in high-fidelity simulations.
This thesis presents new approaches to feed-drive control of computer numerical control (CNC) machine tools machine tools with a significant range of dynamic variations during machining operations. Several sources which can cause dynamic variations of feed-drive systems are considered, such as the change of table position, the reduction of workpiece mass, and the variations of tool-path orientation. Feed-drive systems having the dynamic variations are modeled as linear parameter varying (LPV) models. For the LPV models, three control methods are proposed to achieve satisfactory control performance of feed-drive systems.In the first method, we propose a parallel structure of an LPV gain-scheduled controller which aims at both tracking control and the vibration suppression by taking into account the resonant modes' variations which are peculiar to ball-screw drives. In the second method, instead of designing one LPV controller, a set of gain-scheduled controllers are designed to compensate for a wide range of dynamic variations. In this method, switching between two adjacent controllers may result in a transient jump of control signal at switching instants. In the third method, to ensure a smooth control signal, we present a novel method to design a smooth switching gain-scheduled LPV controller. The moving region of the gain-scheduling variables is divided into a specified number of local subregions as well as subregions for the smooth controller switching. Then, one gain-scheduled LPV controller is assigned to each of the local subregions, while for each switching subregion, a function interpolating local LPV controllers associated with its neighbourhood subregions is designed. This interpolating function imposes the constraint of smooth transition on controller system matrices.The smooth switching controller design problem amounts to solving a feasibility problem which involves non-linear matrix inequalities that are solvable by a proposed iterative descent algorithm. The developed smooth switching controller is applied to control problems in both parallel and serial CNC machine tool mechanisms. Finally, for the multi-axis CNC machine tools, a multi-input-multi-output (MIMO) LPV feedback controller is designed to directly minimize contouring error in the task coordinate frame system.
This thesis considers variations in the parameters of the dynamics of linear systems, and tackles modeling of Linear Time-Invariant (LTI) and Linear Parameter Varying (LPV) plants. The variations in the dynamics make the controller design challenging, and to successfully overcome this challenge, two methods are proposed in this thesis. One method generates a connected model set. The idea of the multidimensional principal curves methodology is employed to detect the nonlinear correlations between parameters of the given set of system dynamics. The connected model set is simple and tight, leading to both nonconservatism and reduced computational complexity in subsequent controller design, and hence, to improve the controller performance. The other method is developed to derive a family of discrete model sets for a given set of system response data. A relaxed version of the normalized cut methodology is developed and used in an algorithm to divide a given set of system responses into the smallest possible number of partitions in such a way that a desired performance objective is satisfied for all partitions by designing one controller for each partition. Using the proposed method, a tight uncertainty model is derived for Hard Disk Drive (HDD) systems, and an H∞ controller is synthesized. The dynamics of HDDs is studied from a controller design point of view. Especially, the variations in the dynamics due to the change in temperatures and limited precision in the production line are examined. Also, the variations in the dynamics of Ball Screw Drive (BSD) systems due to the structural flexibility, runout, and workpiece mass variation are studied. These three factors are explicitly incorporated in LPV models. To build the LPV models, it is determined how the system parameters are affected by two variables, namely, the measurable table position and the uncertain mass of the table. We design robust gain scheduling controllers which are scheduled by the table position and are robust over the table mass.
Master's Student Supervision (2010 - 2018)
The full abstract for this thesis is available in the body of the thesis, and will be available when the embargo expires.
The full abstract for this thesis is available in the body of the thesis, and will be available when the embargo expires.
As offshore wind technology advances, floating wind turbines are becoming larger and moving further offshore, where wind is stronger and more consistent. Despite the increased potential for energy capture, wind turbines in these environments are susceptible to large platform motions, which in turn can lead to fatigue loading and shortened life, as well as harmful power fluctuations. To minimize these ill effects, it is possible to use advanced, multi-objective control schemes to minimize harmful motions, reject disturbances, and maximize power capture. Synthesis of such controllers requires simple but accurate models that reflect all of the pertinent dynamics of the system, while maintaining a reasonably low degree of complexity.In this thesis, we present a simplified, control-oriented model for floating offshore wind turbines that contains as many as six platform degrees of freedom, and two drivetrain degrees of freedom. The model is derived from first principles and, as such, can be manipulated by its real physical parameters while maintaining accuracy across the highly non-linear operating range of floating wind turbine systems. We validate the proposed model against advanced simulation software FAST, and show that it is extremely accurate at predicting major dynamics of the floating wind turbine system.Furthermore, the proposed model can be used to generate equilibrium points and linear state-space models at any operating point. Included in the linear model is the wave disturbance matrix, which can be used to accommodate for wave disturbance in advanced control schemes either through disturbance rejection or feedforward techniques. The linear model is compared to other available linear models and shows drastically improved accuracy, due to the presence of the wave disturbance matrix.Finally, using the linear model, we develop four different controllers of increasing complexity, including a multi-objective PID controller, an LQR controller, a disturbance-rejecting H∞ controller, and a feedforward H∞ controller. We show through simulation that the controllers that use the wave disturbance information reduce harmful motions and regulate power better than those that do not, and reinforce the notion that multi-objective control is necessary for the success of floating offshore wind turbines.
This thesis proposes an algorithm to designswitching surfaces for the switching linear parameter-varying(LPV) controller with hysteresis switching. The switching surfacesare sought for to optimize the bound of the closed-loopL2-gain performance. An optimization problem is formulatedwith respect to parameters characterizing Lyapunov matrixvariables, local controller matrix variables, and locations ofthe switching surfaces. Since the problem turns out to benon-convex in terms of these characterizing parameters, anumerical algorithm is given to guarantee the decrease of thecost function value after each iteration, which consists of two steps: direction selection and line search. A hybrid method whichis a combination of the steepest descent method and Newton'smethod is employed in the direction selection step to decide the orientation of proceeding. A numerical algorithm is used to compute the most appropriate length of the proceeding along the selected direction which generates the most decrease in the cost function. To demonstrate the efficiency and usefulness of the proposed algorithm, it will be applied to three examples in control applications: a tracking problem for a mass-spring-damper system, a vibration suppression problem for a magnetically-actuated optical image stabilizer, and an air-fuel-ratio control problem for automotive engines. In these examples, it will be shown that the proposed optimization approach to the design of the switching surfaces and the switching LPV controller is superior to heuristic approaches in closed-loop performances, at the price of higher computational costs. Additionally, it will be shown that the algorithm can be applied to the general n-parameters case.
The Three-Way Catalytic Converter (TWC) is a critical component for the mitigation of tailpipe emissions of modern Internal Combustion (IC) engines. Because the TWC operates effectively only when a stoichiometric ratio of air and fuel is combusted in the engine, accurate control of the air-fuel ratio is required. To track the desired ratio, a switching Linear Parameter Varying (LPV) air-fuel ratio feedback controller, scheduled based on engine speed and air flow, and providing guaranteed L2 performance, is introduced. The controller measures the air-fuel ratio in the exhaust flow using a Universal Exhaust Gas Oxygen (UEGO) sensor and adjusts the amount of fuel injected accordingly. A detailed model of the air-fuel ratio control problem is developed to demonstrate the non-linear and parameter-dependent nature of the plant, as well as the presence of pure delays. The model’s dynamics vary considerably with engine speed and air flow. A simplified model, widely used in literature and known as a First Order Plus Dead Time (FOPDT) model, is then derived. It effectively captures the control problem using a model which is linear but parameter-varying with engine speed and air flow. Large variation of the FOPDT model across the engine’s operating range has led to conservative LPV controllers in previous literature. For this reason, the operating range is divided into smaller subregions, and an individual LPV controller is designed for each subregion. The LPV controllers are then switched based on the current engine speed and air flow and are collectively referred to as a switching LPV controller. The controller design problem is expressed as a Linear Matrix Inequality (LMI ) convex optimization problem which can be efficiently solved using available LMI techniques. Simulations are performed and the air-fuel ratio tracking performance of the switching LPV controller is compared with that of conventional controllers including, H∞ and LPV, as well as a novel adaptive controller. The switching LPV controller achieves improved performance over the complete operating range of the engine.