A Data-driven Approach to Robust Control of Multivariable Systems by Convex Optimization

The frequency-domain data of a multivariable system in different operating points is used to design a robust controller with respect to the measurement noise and multimodel uncertainty. The controller is fully parametrized in terms of matrix polynomial functions and can be formulated as a centralized, decentralized or distributed controller. All standard performance specifications like $H_2$, $H_\infty$ and loop shaping are considered in a unified framework for continuous- and discrete-time systems. The control problem is formulated as a convex-concave optimization problem and then convexified by linearization of the concave part around an initial controller. The performance criterion converges monotonically to a local optimal solution in an iterative algorithm. The effectiveness of the method is compared with fixed-structure controllers using non-smooth optimization and with full-order optimal controllers via simulation examples. Finally, the experimental data of a gyroscope is used to design a data-driven controller that is successfully applied on the real system

Data-driven control design in the Loewner framework: Dealing with stability and noise

International audienceThe L-DDC (Loewner Data Driven Control) algorithm is a data-driven controller design method based on frequency-domain input-output data. The identification of the plant is skipped and the controller is designed directly from the measurements using the Loewner approach, known for model approximation and reduction. However, in the L-DDC method, the identified controller is not guaranteed to be stable and the effect of noise on the identified controller is unknown. In this article, we ensure the stability of the controller and propose a solution to deal with noisy data. The method is validated on a numerical example

Adaptive Data-Driven Control for Linear Time Varying Systems

In this paper, we propose an adaptive data-driven control approach for linear time varying systems, affected by bounded measurement noise. The plant to be controlled is assumed to be unknown, and no information in regard to its time varying behaviour is exploited. First, using set-membership identification techniques, we formulate the controller design problem through a model-matching scheme, i.e., designing a controller such that the closed-loop behaviour matches that of a given reference model. The problem is then reformulated as to derive a controller that corresponds to the minimum variation bounding its parameters. Finally, a convex relaxation approach is proposed to solve the formulated controller design problem by means of linear programming. The effectiveness of the proposed scheme is demonstrated by means of two simulation examples

A Data-Driven Fixed-Structure Control Design Method with Application to a 2-DOF Gyroscope

This paper presents the practical aspects and application of a novel data-driven, fixed-structure, robust control design method. Only the frequency response data of the system is needed for the design, and no parametric model is required. The method can be used to design fully parametrized continuous- or discrete-time matrix transfer function controllers. The control performance is specified as constraints on the $H_{\infty}$ or $H_2$ norm of weighted sensitivity functions, and a convex formulation of the robust design problem is proposed. An application of the presented method is explored on an experimental setup, where a multivariable controller for a gyroscope is designed based only on the measured frequency response of the system

Convex Optimization-Based Control Design for Parallel Grid-Connected Inverters

This paper presents a novel frequency-domain approach toward the control design for parallel grid-connected voltage source inverters (VSIs) with LCL output filters. The proposed method allows the controllers of multiple VSIs to be designed in a single step, and inherently attenuates the resonances introduced by the output filters and coupling effects while guaranteeing stability. Performance specifications such as desired closed-loop bandwidth, decoupling or robustness toward multi-model uncertainty can be specified through frequency-domain constraints. Furthermore, controllers can be designed in a plug-and-play fashion. The designed controllers are equivalent in structure to multi-variable PI controllers with filters. As the control design is based on the frequency response of the system, the algorithm is independent of the model order, which allows the use of large and high-order models. The performance of the method is demonstrated on a relevant example of a low-voltage distribution grid with five VSIs, and the results are validated both in numerical simulation using MATLAB/Simulink as well as in power-hardware-in-the-loop experiments

Decentralized and Distributed Transient Control for Microgrids

This paper treats the problem of primary and secondary control design in low-inertia power grids with mixed lines and a large amount of inverter-interfaced generation. A dynamic phasor model is developed that represents the electromagnetic and electromechanic dynamics of lines, inverters, synchronous machines and constant power loads. The model offers a straightforward way to combine white-, grey- and black-box models, and its structure lends itself well to control design. In a next step, a novel method to design fixed-structure robust controllers based on the frequency response of multivariable systems and convex optimization is presented. The method offers an intuitive way to define the control performance specifications, and is able to directly design discrete-time controllers. Finally, the potential of the control design method and the dynamic phasor model is demonstrated in a comprehensive example. In three scenarios it is illustrated how the approach can be used to significantly improve frequency and voltage transient performance in low-inertia power grids. Decentralized as well as distributed architectures for primary and secondary control are studied, and results are validated in simulation

Frequency-Domain Control Design in Power Systems

The scope of this thesis encompasses two main subjects: fixed-structure data-driven control design on one side, and control design in power systems on the other. The overall goal is to identify challenging and relevant problems in power systems, to express them as rigorous specifications from the viewpoint of control systems, and to solve them by developing and applying advanced methods in robust control. This work aims to combine expertise from both fields to open up a holistic perspective and bridge the gap between control and power systems. First, the derivation of a novel fixed-structure, data-driven frequency-domain control design method for multivariable systems is described. A key feature of the method is that only the frequency response of the plant is required for the design, and no parametric model is required. The designed controllers are fully parametrized in terms of matrix polynomial functions and can take a centralized, decentralized or distributed structure. The controller performance is formulated as H_2 and H_infinity constraints on any loop transfer function. A convex formulation of the optimization problem is derived, and it is shown that the solution converges to a locally optimal solution of the original problem. The versatility of the design method is demonstrated in various simulation examples, as well as in experiments on two electromechanical setups. Next, a frequency-domain modeling approach for power grids is discussed. A model based on dynamic phasors is developed that represents the electromagnetic and electromechanic dynamics of lines, inverters, synchronous machines and constant power loads. It also offers a modular structure that makes it straightforward to combine white-, grey- and blackbox models in a single framework. Then, the control design method and dynamic phasor model are applied in two relevant power systems case studies. First, the design of a decentralized current controller for parallel, grid-connected voltage source inverters in a typical distribution grid is considered. It is shown how performance specifications can be formulated as frequency-domain constraints in order to attenuate the resonances introduced by the output filters and coupling effects, and to provide robustness against model uncertainties and grid topology changes. The controllers for all VSIs are designed in a single step, and stability and performance is guaranteed by design. Furthermore, an approach for plug-and-play control design is presented. The results are validated in numerical simulation as well as in power-hardware-in-the-loop experiments. The second study concerns the design of a distributed controller that combines primary and secondary frequency and voltage control for an islanded, meshed low-voltage grid with any number of voltage source inverters and synchronous generators in a single framework. No assumption on the R/X-ratio of the lines is made, and it is shown how advanced control specifications such as proportional active power sharing, zero frequency steady-state error and decoupling can be formulated as constraints on the norm of weighted sensitivity functions. Furthermore, the communication delays of the distributed controller are considered exactly during the design. The controller is implemented in numerical simulation, and results show significantly improved performance as compared to the classical hierarchical structure