Christoffer Sloth

Active and passive fault-tolerant LPV control of wind turbines

This paper addresses the design and comparison of active and passive fault-tolerant linear parameter-varying (LPV) controllers for wind turbines. The considered wind turbine plant model is characterized by parameter variations along the nominal operating trajectory and includes a model of an incipient fault in the pitch system. We propose the design of an active fault-tolerant controller (AFTC) based on an existing LPV controller design method and extend this method to apply for the design of a passive fault-tolerant controller (PFTC). Both controllers are based on output feedback and are scheduled on the varying parameter to manage the parameter-varying nature of the model. The PFTC only relies on measured system variables and an estimated wind speed, while the AFTC also relies on information from a fault diagnosis system. Consequently, the optimization problem involved in designing the PFTC is more difficult to solve, as it involves solving bilinear matrix inequalities (BMIs) instead of linear matrix inequalities (LMIs). Simulation results show the performance of the active fault-tolerant control system to be slightly superior to that of the passive fault-tolerant control system.

Compositional safety analysis using barrier certificates

This paper proposes a compositional method for verifying the safety of a dynamical system, given as an interconnection of subsystems. The safety verification is conducted by the use of the barrier certificate method; hence, the contribution of this paper is to show how to obtain compositional conditions for safety verification. We show how to formulate the verification problem, as a composition of coupled subproblems, each given for one subsystem. Furthermore, we show how to find the compositional barrier certificates via linear and sum of squares programming problems. The proposed method makes it possible to verify the safety of higher dimensional systems, than the method for centrally computed barrier certificates. This is demonstrated by verifying the safety of an emergency shutdown of a wind turbine.

Robust LMI-based control of wind turbines with parametric uncertainties

This paper considers the design of robust LMIbased controllers for a wind turbine along its entire nominal operating trajectory. The proposed robust controller design takes into account parametric uncertainties in the model using a structured uncertainty description, which makes the controllers less conservative than controllers designed using unstructured uncertainty descriptions. The LMI-based approach enables additional constraints to be included in the design, which is exploited to include requirements for minimizing fatigue loads and actuator usage.

DiSC: A simulation framework for distribution system voltage control

This paper presents the MATLAB simulation framework, DiSC, for verifying voltage control approaches in power distribution systems. It consists of real consumption data, stochastic models of renewable resources, flexible assets, electrical grid, and models of the underlying communication channels. The simulation framework makes it possible to validate control approaches, and thus advance realistic and robust control algorithms for distribution system voltage control. Two examples demonstrate the potential voltage issues from penetration of renewables in the distribution grid, along with simple control solutions to alleviate them.

Converse Barrier Certificate Theorems

This paper presents a converse barrier certificate theorem for a generic dynamical system. We show that a barrier certificate exists for any safe dynamical system defined on a compact manifold. Other authors have developed a related result, by assuming that the dynamical system has no singular points in the considered subset of the state space. In this paper, we redefine the standard notion of safety to comply with generic dynamical systems with multiple singularities. Afterwards, we prove the converse barrier certificate theorem and illustrate the differences between ours and previous work by simple examples.

Verification of continuous dynamical systems by timed automata

This paper presents a method for abstracting continuous dynamical systems by timed automata. The abstraction is based on partitioning the state space of a dynamical system using positive invariant sets, which form cells that represent locations of a timed automaton. The abstraction is intended to enable formal verification of temporal properties of dynamical systems without simulating any system trajectory, which is currently not possible. Therefore, conditions for obtaining sound, complete, and refinable abstractions are set up.The novelty of the method is the partitioning of the state space, which is generated utilizing sub-level sets of Lyapunov functions, as they are positive invariant sets. It is shown that this partition generates sound and complete abstractions. Furthermore, the complete abstractions can be composed of multiple timed automata, allowing parallelization of the verification process. The proposed abstraction is applied to two examples, which illustrate how sound and complete abstractions are generated and the type of specification we can check. Finally, an example shows how the compositionality of the abstraction can be used to analyze a high-dimensional system.

A Youla-Kucera approach to gain-scheduling with application to wind turbine control

This paper addresses bumpless transfer between observer-based controllers with integral action in a gainscheduling architecture with application to wind turbine control. Two methods based on the Youla-Kucera parameterization are applied to achieve bumpless transfer between controllers having equal or different number of control signals and integrators while preserving stability guarantees. Both methods handle reference signals to the controllers.

On the existence of compositional barrier certificates

This paper provides a necessary and sufficient condition for the compositional verification of a continuous system with additively separable barrier functions. The compositional safety verification enables the verification of an interconnection of subsystems. The idea behind the compositional analysis is to allow the verification of systems with a high dimension, by the verification of multiple lower dimensional subproblems. In the compositional safety analysis, a particular structure is imposed on the barrier certificate, restricting the applicability of the method. We show an example of a system that cannot be verified using the compositional method, but can be verified using a centralized method. This example highlights how not to decompose systems, and should be used to guide the decomposition of a system into appropriate subsystems. Finally, we provide a second condition for the compositional safety analysis that enables the verification of the counterexample, by imposing a less restrictive structure of the barrier function. This shows that the counterexample can be solved with a compositional method, but at an increased computational complexity.

Structured Linear Parameter Varying Control of Wind Turbines

High performance and reliability are required for wind turbines to be competitive within the energy market. To capture their nonlinear behavior, wind turbines are often modeled using parameter-varying models. In this chapter, a framework for modelling and controller design of wind turbines is presented. We specifically consider variable-speed, variable-pitch wind turbines with faults on actuators and sensors. Linear parameter-varying (LPV) controllers can be designed by a proposed method that allows the inclusion of faults in the LPV controller design. Moreover, the controller structure can be arbitrarily chosen: static output feedback, dynamic (reduced order) output feedback, decentralized, among others. The controllers are scheduled on an estimated wind speed to manage the parametervarying nature of the model and on information from a fault diagnosis system. The optimization problems involved in the controller synthesis are solved by an iterative LMI-based algorithm. The resulting controllers can also be easily implemented in practice due to low data storage and simple math operations. The performance of the LPV controllers is assessed by nonlinear simulations results.

Abstraction of continuous dynamical systems utilizing Lyapunov functions

This paper considers the development of a method for abstracting continuous dynamical systems by timed automata. The method is based on partitioning the state space of dynamical systems with invariant sets, which form cells representing locations of the timed automata.