Lorenzo Fagiano

High Altitude Wind Energy Generation Using Controlled Power Kites

This paper presents simulation and experimental results regarding a new class of wind energy generators, denoted as KiteGen, which employ power kites to capture high altitude wind power. A realistic kite model, which includes the kite aerodynamic characteristics and the effects of line weight and drag forces, is used to describe the system dynamics. Nonlinear model predictive control techniques, together with an efficient implementation based on set membership function approximation theory, are employed to maximize the energy obtained by KiteGen, while satisfying input and state constraints. Two different kinds of KiteGen are investigated through numerical simulations, the yo-yo configuration and the carousel configuration, respectively. For each configuration, a generator with the same kite and nominal wind characteristics is considered. A novel control strategy for the carousel configuration, with respect to previous works, is also introduced. The simulation results show that the power generation potentials of the yo-yo and carousel configurations are very similar. Thus, the choice between these two configurations for further development of a medium-to-large scale generator will be made on the basis of technical implementation problems and of other indexes like construction costs and generated power density with respect to land occupation. Experimental data, collected using the small-scale KiteGen prototype built at Politecnico di Torino, are compared to simulation results. The good matching between simulation and real measured data increases the confidence with the presented simulation results, which show that energy generation with controlled power kites can represent a quantum leap in wind power technology, promising to obtain renewable energy from a source largely available almost everywhere, with production costs lower than those of fossil sources.

Robust Model Predictive Control via Scenario Optimization

This paper discusses a novel probabilistic approach for the design of robust model predictive control (MPC) laws for discrete-time linear systems affected by parametric uncertainty and additive disturbances. The proposed technique is based on the iterated solution, at each step, of a finite-horizon optimal control problem (FHOCP) that takes into account a suitable number of randomly extracted scenarios of uncertainty and disturbances, followed by a specific command selection rule implemented in a receding horizon fashion. The scenario FHOCP is always convex, also when the uncertain parameters and disturbance belong to nonconvex sets, and irrespective of how the model uncertainty influences the systems matrices. Moreover, the computational complexity of the proposed approach does not depend on the uncertainty/disturbance dimensions, and scales quadratically with the control horizon. The main result in this work is related to the analysis of the closed loop system under receding-horizon implementation of the scenario FHOCP, and essentially states that the devised control law guarantees constraint satisfaction at each step with some a priori assigned probability p, while the systems state reaches the target set either asymptotically, or in finite time with probability at least p. The proposed method may be a valid alternative when other existing techniques, either deterministic or stochastic, are not directly usable due to excessive conservatism or to numerical intractability caused by lack of convexity of the robust or chance-constrained optimization problem.

Vehicle Yaw Control via Second-Order Sliding-Mode Technique

The problem of vehicle yaw control is addressed in this paper using an active differential and yaw rate feedback. A reference generator, designed to improve vehicle handling, provides the desired yaw rate value to be achieved by the closed loop controller. The latter is designed using the second-order sliding mode (SOSM) methodology to guarantee robust stability in front of disturbances and model uncertainties, which are typical of the automotive context. A feedforward control contribution is also employed to enhance the transient system response. The control derivative is constructed as a discontinuous signal, attaining an SOSM on a suitably selected sliding manifold. Thus, the actual control input results in being continuous, as it is needed in the considered context. Simulations performed using a realistic nonlinear model of the considered vehicle show the effectiveness of the proposed approach.

Automatic Crosswind Flight of Tethered Wings for Airborne Wind Energy: Modeling, Control Design, and Experimental Results

An approach to control tethered wings for airborne wind energy is proposed. A fixed length of the lines is considered, and the aim of the control system is to obtain figure-eight crosswind trajectories. The proposed technique is based on the notion of the wings “velocity angle” and, in contrast with most existing approaches, it does not require a measurement of the wind speed or of the apparent wind at the wings location. In addition, the proposed approach features few parameters, whose effects on the systems behavior are very intuitive, hence simplifying tuning procedures. A simplified model of the steering dynamics of the wing is derived from first-principle laws, compared with experimental data and used for the control design. The control algorithm is divided into a low-level loop for the velocity angle and a high-level guidance strategy to achieve the desired flight patterns. The robustness of the inner loop is verified analytically, and the overall control system is tested experimentally on a small-scale prototype, with varying wind conditions and using different wings.

The scenario approach for Stochastic Model Predictive Control with bounds on closed-loop constraint violations

Many practical applications in control require that constraints on the inputs and states of the system are respected, while some performance criterion is optimized. In the presence of model uncertainties or disturbances, it is often sufficient to satisfy the state constraints for at least a prescribed share of the time, such as in building climate control or load mitigation for wind turbines. For such systems, this paper presents a new method of Scenario-Based Model Predictive Control (SCMPC). The basic idea is to optimize the control inputs over a finite horizon, subject to robust constraint satisfaction under a finite number of random scenarios of the uncertainty and/or disturbances. Previous SCMPC approaches have suffered from a substantial gap between the rate of constraint violations specified in the optimal control problem and that actually observed in closed-loop operation of the controlled system. This paper identifies the two theoretical explanations for this gap. First, accounting for the special structure of the optimal control problem leads to a substantial reduction of the problem dimension. Second, the probabilistic constraints have to be interpreted as average-in-time, rather than pointwise-in-time. Based on these insights, a novel SCMPC method can be devised for general linear systems with additive and multiplicative disturbances, for which the number of scenarios is significantly reduced. The presented method retains the essential advantages of the general SCMPC approach, namely a low computational complexity and the ability to handle arbitrary probability distributions. Moreover, the computational complexity can be adjusted by a sample-and-remove strategy.

High-Altitude Wind Power Generation

The paper presents the innovative technology of high-altitude wind power generation, indicated as Kitenergy, which exploits the automatic flight of tethered airfoils (e.g., power kites) to extract energy from wind blowing between 200 and 800 m above the ground. The key points of this technology are described and the design of large scale plants is investigated, in order to show that it has the potential to overcome the limits of the actual wind turbines and to provide large quantities of renewable energy, with competitive cost with respect to fossil sources. Such claims are supported by the results obtained so far in the Kitenergy project, undergoing at Politecnico di Torino, Italy, including numerical simulations, prototype experiments, and wind data analyses.

Airborne Wind Energy: An overview

In the last decade, several research groups and companies around the world have been developing a new class of wind generators, aimed at harnessing the energy of winds blowing at high elevation above the ground. This kind of technology is usually referred to as Airborne Wind Energy (AWE) or High-Altitude Wind Energy. All of the proposed solutions exploit the high-speed flight of tethered wings, or aircrafts, and their operation heavily relies on automatic control. This paper provides a tutorial on the fundamental concepts of AWE and on the different technologies that are being investigated, with particular emphasis on control-related aspects, highlighting the accomplished results and the issues that still need to be solved.

Comparing Internal Model Control and Sliding-Mode Approaches for Vehicle Yaw Control

In this paper, the problem of vehicle yaw control using a rear active differential is investigated. The proposed control structure employs a reference generator designed to improve vehicle handling, a feedforward contribution that enhances the transient system response, and a feedback controller. Due to system uncertainties and the wide range of operating situations, which are typical of the automotive context, a robust control technique is needed to guarantee system stability. Two different robust feedback controllers, which are based on internal model control and sliding mode methodologies, respectively, are designed, and their performances are compared by means of extensive simulation tests performed using a realistic 14-degree-of-freedom (DOF) model of the considered vehicle. The obtained results show the effectiveness of the proposed control structure with both feedback controllers and highlight their respective benefits and drawbacks. The presented comparative study is a first step to devise a new mixed control strategy that is able to exploit the benefits of both the considered techniques.

On Sensor Fusion for Airborne Wind Energy Systems

A study on filtering aspects of airborne wind energy generators is presented. This class of renewable energy systems aim to convert the aerodynamic forces generated by tethered wings, flying in closed paths transverse to the wind flow, into electricity. The accurate reconstruction of the wings position, velocity, and heading is of fundamental importance for the automatic control of these kinds of systems. The difficulty of the estimation problem arises from the nonlinear dynamics, wide speed range, large accelerations, and fast changes of direction that the wing experiences during operation. It is shown that the overall nonlinear system has a specific structure allowing its partitioning into subsystems, hence leading to a series of simpler filtering problems. Different sensor setups are then considered, and the related sensor fusion algorithms are presented. The results of experimental tests carried out with a small-scale prototype and wings of different sizes are discussed. The designed filtering algorithms rely purely on kinematic laws, hence they are independent of features such as wing area, aerodynamic efficiency, mass, and so on. Therefore, the presented results are representative for systems with larger size and different wing design, different number of tethers and/or rigid wings also.

Randomized Model Predictive Control for stochastic linear systems

This paper is concerned with the design of state-feedback control laws for linear time invariant systems that are subject to stochastic additive disturbances, and probabilistic constraints on the states. The design is based on a stochastic Model Predictive Control (MPC) approach, for which a randomization technique is applied in order to find a suboptimal solution to the underlying, generally non-convex chance constrained program. The proposed method yields a linear or quadratic program to be solved online at each time step, whose complexity is the same as that of a nominal MPC problem, i.e. if no disturbances were present. Furthermore, it is shown how the quality of the sub-optimal solution can be improved through a procedure for the removal of sampled constraints a-posteriori, at the price of increased online computation efforts. Finally, this randomized approach can be combined with further constraint tightening, in order to guarantee recursive feasibility for the closed loop system.