Modelling and control of coupled infinite-dimensional systems

First, we consider two classes of coupled systems consisting of an infinite-dimensional part [sigma]d and a finite-dimensional part [sigma]f connected in feedback. In the first class of coupled systems, we assume that the feedthrough matrix of [sigma]f is 0 and that [sigma]d is such that it becomes well-posed and strictly proper when connected in cascade with an integrator. Under several assumptions, we derive well-posedness, regularity and exact (or approximate) controllability results for such systems on a subspace of the natural product state space. In the second class of coupled systems, [sigma]f has an invertible first component in its feedthrough matrix while [sigma]d is well-posed and strictly proper. Under similar assumptions, we obtain well-posedness, regularity and exact (or approximate) controllability results as well as exact (or approximate) observability results for this class of coupled systems on the natural state space. Second, we investigate the exact controllability of the SCOLE (NASA Spacecraft Control Laboratory Experiment) model. Using our theory for the first class of coupled systems, we show that the uniform SCOLE model is well-posed, regular and exactly controllable in arbitrarily short time when using a certain smoother state space. Third, we investigate the suppression of the vibrations of a wind turbine tower using colocated feedback to achieve strong stability. We decompose the system into a non-uniform SCOLE model describing the vibrations in the plane of the turbine axis, and another model consisting of a non-uniform SCOLE system coupled with a two-mass drive-train model (with gearbox), in the plane of the turbine blades. We show the strong stabilizability of the first tower model by colocated static output feedback. We also prove the generic exact controllability of the second tower model on a smoother state space using our theory for the second class of coupled systems, and show its generic strong stabilizability on the energy state space by colocated feedback

Stability properties of coupled impedance passive LTI systems

We study the stability of the feedback interconnection of two impedance passive linear time-invariant systems, of which one is finite-dimensional. The closed-loop system is well known to be impedance passive, but no stability properties follow from this alone. We are interested in two main issues: (1) the strong stability of the operator semigroup associated with the closed-loop system, (2) the input-output stability (meaning transfer function in H∞) of the closed-loop system. Our results are illustrated with the system obtained from the non-uniform SCOLE (NASA Spacecraft Control Laboratory Experiment) model representing a vertical beam clamped at the bottom, with a rigid body having a large mass on top, connected with a trolley mounted on top of the rigid body, via a spring and a damper. Such an arrangement called a tuned mass damper (TMD), is used to stabilize tall buildings. We show that the SCOLE-TMD system is strongly stable on the energy state space and that the system is input-output stable from the horizontal force input to the horizontal velocity output

Strong stabilization of a wind turbine tower model in the plane of the turbine blades

We investigate the strong stabilization of a wind turbine tower model in the plane of the turbine blades, which comprises a nonuniform SCOLE system and a two-mass drive-train model (with gearbox). The control input is the torque created by the electrical generator. Using a strong stabilization theorem for a class of impedance passive linear systems with bounded control and observation operators, we show that the wind turbine tower model can be strongly stabilized. The control is by static output feedback from the angular velocities of the nacelle and the generator rotor

Load reduction of a monopile wind turbine tower using optimal tuned mass dampers

We investigate to apply tuned mass dampers (TMDs) (one in the fore–aft direction, one in the side– side direction) to suppress the vibration of a monopile wind turbine tower. Using the spectral element method, we derive a finite-dimensional state-space model d from an infinite-dimensional model d of a monopile wind turbine tower stabilised by a TMD located in the nacelle. and d can be used to represent the dynamics of the tower and TMD in either the fore–aft direction or the side– side direction. The wind turbine tower subsystem of is modelled as a non-uniform SCOLE (NASA Spacecraft Control Laboratory Experiment) system consisting of an Euler–Bernoulli beam equation describing the dynamics of the flexible tower and the Newton–Euler rigid body equations describing the dynamics of the heavy rotor-nacelle assembly (RNA) by neglecting any coupling with blade motions. d can be used for fast and accurate simulation for the dynamics of the wind turbine tower as well as for optimal TMD designs. We show that d agrees very well with the FAST (fatigue, aerodynamics, structures and turbulence) simulation of the NREL 5-MW wind turbine model. We optimise the parameters of the TMD by minimising the frequency-limited H2-norm of the transfer function matrix of d which has input of force and torque acting on the RNA, and output of tower-top displacement. The performances of the optimal TMDs in the fore–aft and side–side directions are tested through FAST simulations, which achieve substantial fatigue load reductions. This research also demonstrates how to optimally tune TMDs to reduce vibrations of flexible structures described by partial differential equations

Robust Output Regulation of Euler-Bernoulli Beam Models

In this thesis, we consider control and dynamical behaviour of flexible beam models which have potential applications in robotic arms, satellite panel arrays and wind turbine blades. We study mathematical models that include flexible beams described by Euler-Bernoulli beam equations. These models consist of partial differential equations or combination of partial and ordinary differential equations depending on the loads and supports in the model. Our goal is to influence the models by control inputs such as external applied forces so that measured deflection profiles of the beams in the models behave as desired. We propose dynamic controllers for the output regulation, where the measurements from the models track desired reference signals in the given time, of flexible beam models. The controller designs are based on the so-called internal model principle and they utilize difference between measurement and desired reference trajectory. Moreover, the controllers are robust in the sense that they can achieve output regulation despite external disturbances and model uncertainties. We also study the output regulation problem when there are certain limitations on the control input. In particular, we generalize the theory of output regulation for dynamical systems described by ordinary differential equations subject to input constraints to a particular class of systems described by partial differential equations. We present set of solvability conditions and a linear output feedback controller for the output regulation

Control of large offshore wind turbines.

Several control strategies are proposed to improve overall performances of conventional (geared equipped) and hydrostatic offshore wind turbines. Firstly, to maximise energy capture of a conventional turbine, an adaptive torque control technique is proposed through simplifying the conventional extremum seeking control algorithm. Simulations are conducted on the popular National Renewable Energy Laboratory (NREL) monopile 5-MW baseline turbine. The results demonstrate that the simplified ESC algorithms are quite effective in maximising power generation. Secondly, a TMD (tuned mass damper) system is configured to mitigate loads on a monopile turbine tower whose vibrations are typically dominated by its first mode. TMD parameters are obtained via H2 optimisation based on a spatially discretised tower-TMD model. The optimal TMDs are assessed through simulations using the NREL monopile 5-MW baseline model and achieve substantial tower load reductions. In some cases it is necessary to damp tower vibrations induced by multiple modes and it is well-known that a single TMD is lack of robustness. Thus a control strategy is developed to suppress wind turbine’s vibrations (due to multiple modes) using multiple groups of TMDs. The simulation studies demonstrate the superiority of the proposed methods over traditional ones. Thirdly, the NREL 5-MW baseline turbine model is transformed into a hydrostatic wind turbine (HWT). An H∞ loop-shaping torque controller and a light detection and ranging-based linear-parameter-varying anti-windup pitch controller are designed for the HWT. The tests on a monopile HWT model indicate good tracking behaviours of the torque controller and much improved performances of the linear-parameter-varying pitch controller over a gain-scheduled PI pitch controller. Finally, the hydraulic reservoir of a barge HWT is made into a bidirectional-tuned- liquid-column-damper (BTLCD) to suppress barge pitch and roll motions. The simulation results validate the effectiveness of the optimal BTLCD reservoir in reducing the tower loads and power fluctuations

Nonlinear constrained and saturated control of power electronics and electromechanical systems

Power electronic converters are extensively adopted for the solution of timely issues, such as power quality improvement in industrial plants, energy management in hybrid electrical systems, and control of electrical generators for renewables. Beside nonlinearity, this systems are typically characterized by hard constraints on the control inputs, and sometimes the state variables. In this respect, control laws able to handle input saturation are crucial to formally characterize the systems stability and performance properties. From a practical viewpoint, a proper saturation management allows to extend the systems transient and steady-state operating ranges, improving their reliability and availability. The main topic of this thesis concern saturated control methodologies, based on modern approaches, applied to power electronics and electromechanical systems. The pursued objective is to provide formal results under any saturation scenario, overcoming the drawbacks of the classic solution commonly applied to cope with saturation of power converters, and enhancing performance. For this purpose two main approaches are exploited and extended to deal with power electronic applications: modern anti-windup strategies, providing formal results and systematic design rules for the anti-windup compensator, devoted to handle control saturation, and “one step” saturated feedback design techniques, relying on a suitable characterization of the saturation nonlinearity and less conservative extensions of standard absolute stability theory results. The first part of the thesis is devoted to present and develop a novel general anti-windup scheme, which is then specifically applied to a class of power converters adopted for power quality enhancement in industrial plants. In the second part a polytopic differential inclusion representation of saturation nonlinearity is presented and extended to deal with a class of multiple input power converters, used to manage hybrid electrical energy sources. The third part regards adaptive observers design for robust estimation of the parameters required for high performance control of power systems

Identification of unknown structural loads from dynamic measurements using robust observers

The global trends in the construction of complex structures e.g. high buildings, wind turbines or airplanes\u27 tend to make the structures more intelligent by integrating sensing units together with evaluation algorithms which allow the check of structure integrity permanently. This process of structural integrity characterization strategy referred to as Structural Health Monitoring (SHM). Special SHM parameters like material properties and load characteristics are essential when assessment of fatigue life of a structure and its components is done. Therefore, the time history of an external load is an important quantity in the forecast of the remaining lifetime. Furthermore, the load localization problem becomes an important issue, especially in the case of impacts, since the aircraft industry started to use new composite materials more extensively where the impacts cause delaminations which are not detectable by visual inspections. In many practical applications, however, the measurement of external loads is limited or not possible due to sensor limitations or the unknown nature of the external forces. Therefore, indirect load history estimation is a subject of extensive studies in the last two decades. The estimation procedure leads to a so called inverse problem which is \u27ill-posed\u27 in the mathematical sense so that the existence, uniqueness or stability of solution is violated. First of all, this work provides a closer investigation to a variety of existing algorithms of force history reconstruction and location estimation which have been established by mechanical engineers. Secondly, research is carried out for possible candidate methods among the other engineering disciplines. The main focus of the thesis is concentrated on comprehensive design analysis and further development of the qualified algorithms. In particular, model based robust observers are considered as candidates for the online loads and states reconstruction. The aspects of proper model building that allow releasing the sensor placement procedure (from collocated to non-collocated), while simultaneously reducing the model complexity are introduced for the observer design. An innovative model free passive technique for automatic impact location detection is elaborated and extended by incorporation of a fast robust load estimation method. In addition, a novel approach of rank deficiency compensation is proposed for the direct time deconvolution procedure in the non-collocated case. Selected algorithms are grouped according to their ability to fulfill the load reconstruction requirements and tested either in simulation environment or on laboratory structures. The results are systemized in a form of strong and weak sides for every particular algorithm which might serve for the on-field application and future research in this area