A Multivariable Design Methodology for Voltage Control of a Single-DG-Unit Microgrid

This paper proposes a multivariable digital control design methodology for the voltage regulation of an islanded single distributed generation (DG) unit microgrid and its dedicated load. The controller design methodology is based on a family of spectral Multi-Input Multi-Output (MIMO) models of the microgrid system and performs open-loop shaping and system decoupling simultaneously by a convex optimization approach. The control design procedure includes: (i) the determination of a family of nonparametric models of the system at various operating points, (ii) the determination of the class of the controller, and (iii) system open-loop shaping by convex minimization of the summation of the square second norm of the errors between the system open-loop transfer functions and a desired open-loop transfer function. Based on the proposed design methodology, two dq -augmented voltage controllers are proposed to regulate the load voltages of a single-DG-unit microgrid. The proposed controllers guarantee the robust stability and satisfactory dynamic response of the system in spite of load parametric uncertainties and also the presence of nonlinear load. This paper describes the theoretical aspects involved in the design procedure of the controllers and evaluates the performance of the controllers based on simulation studies and experiments.

Fixed-Order H-infinity Controller Design via Convex Optimization Using an Alternative to Youla Prameterization

Alireza Karimi, Hamid Khatibi

All H-infinity controllers of a SISO LTI system are parameterized thanks to the relation between Bounded Real Lemma and Positive Real Lemma and a new concept of strict positive realness of two transfer functions with the same Lyapunov matrix in the matrix inequality of the Kalman-Yakubovic-Popov lemma. This new parameterization shares the same features with Youla parameterization, namely on the convexity of H-infinity norm constraints for the closed-loop transfer functions. However, in contrary to Youla parameterization, it can deal with any controller order and any controller structure such as e.g. PID. The main feature of the proposed method is that it can be extended easily for the systems with polytopic uncertainty. This way, a convex inner approximation of all H-infinity controllers for polytopic systems is given, which can be enlarged by increasing the controller order. In order to design a low-order robust H-infinity controller with less conservatism, rank of the k-th Sylvester resultant matrix of the controller is made to be deficient via a convex approximation of the rank minimization problem. The effectiveness of the proposed method is shown via simulation results.

Institute of Electrical and Electronics Engineers2010

Multivariable Control of Single-Inductor Dual-Output Buck Converters

Behrooz Bahrani, Alireza Karimi, Alfred Rufer

Cross regulation is the main technical drawback of a Single-Inductor Multiple-Output (SIMO) dc-dc converter. This paper proposes a multivariable digital controller to suppress the cross regulation of a Single-Inductor Dual-Output (SIDO) buck converter in Continuous Conduction Mode (CCM) operation. The controller design methodology originates from the openloop shaping of the Multi-Input Multi-Output (MIMO) systems. The control design procedure includes: (i) determination of the non-parametric model of a SIDO buck converter at its rated operating point, (ii) determination of the class of the controller, and (iii) converter open-loop shaping by convex minimization of the square second norm of the error between the converter openloop transfer function and a desired open-loop transfer function. The proposed controller minimizes the coupling between the outputs of the SIDO buck converter and provides satisfactory dynamic performance in CCM operation. This paper describes the theoretical aspects involved in the design procedure of the controller and evaluates the performance of the controller based on simulation studies and experiments.

Ieee2013

A Data-Driven Frequency-Domain Approach for Robust Controller Design via Convex Optimization

Achille Nicoletti

The objective of this dissertation is to develop data-driven frequency-domain methods for designing robust controllers through the use of convex optimization algorithms. Many of today's industrial processes are becoming more complex, and modeling accurate physical models for these plants using first principles may be impossible. With the increased developments in the computing world, large amounts of measured data can be easily collected and stored for processing purposes. Data can also be collected and used in an on-line fashion. Thus it would be very sensible to make full use of this data for controller design, performance evaluation, and stability analysis. The design methods imposed in this work ensure that the dynamics of a system are captured in an experiment and avoids the problem of unmodeled dynamics associated with parametric models. The devised methods consider robust designs for both linear-time-invariant (LTI) single-input-single-output (SISO) systems and certain classes of nonlinear systems. In this dissertation, a data-driven approach using the frequency response function of a system is proposed for designing robust controllers with H∞ performance. Necessary and sufficient conditions are derived for obtaining H∞ performance while guaranteeing the closed-loop stability of a system. A convex optimization algorithm is implemented to obtain the controller parameters which ensure system robustness; the controller is robust with respect to the frequency-dependent uncertainties of the frequency response function. For a certain class of nonlinearities, the proposed method can be used to obtain a best-linear-approximation with an associated frequency dependent uncertainty to guarantee the stability and performance for the underlying linear system that is subject to nonlinear distortions. The concepts behind these design methods are then used to devise necessary and sufficient conditions for ensuring the closed-loop stability of systems with sector-bounded nonlinearities. The conditions are simple convex feasibility constraints which can be used to stabilize systems with multi-model uncertainty. Additionally, a method is proposed for obtaining H∞ performance for an approximate model (i.e., describing function) of a sector-bounded nonlinearity. This work also proposes several data-driven methods for designing robust fixed-structure controllers with H∞ performance. One method considers the solution to a non-convex problem, while another method convexifies the problem and implements an iterative algorithm to obtain the local solution (which can also consider H2 performance). The effectiveness of the proposed method(s) is illustrated by considering several case studies that require robust controllers for achieving the desired performance. The main applicative work in this dissertation is with respect to a power converter control system at the European Organization for Nuclear Research (CERN) (which is used to control the current in a magnet to produce the desired field in controlling particle trajectories in accelerators). The proposed design methods are implemented in order to satisfy the challenging performance specifications set by the application while guaranteeing the system stability and robustness using data-driven design strategies.

EPFL2018

A Data-Driven Frequency-Domain Approach for Robust Controller Design via Convex Optimization

Achille Nicoletti

EPFL2018