Design of Low-Order Controllers using Optimization Techniques

In many applications, especially in the process industry, low-level controllers are the workhorses of the automated production lines. The aim of this study has been to provide simple tuning procedures, either optimization-based methods or tuning rules, for design of low-order controllers. The first part of this thesis deals with PID tuning. Design methods or both SISO and MIMO PID controllers based on convex optimization are presented. The methods consist of solving a nonconvex optimization problem by deriving convex approximations of the original problem and solving these iteratively until convergence. The algorithms are fast because of the convex approximations. The controllers obtained minimize low-frequency sensitivity subject to constraints that ensure robustness to process variations and limitations of control signal effort. The second part of this thesis deals with tuning of feedforward controllers. Tuning rules that minimize the integrated-squared-error arising from measurable step disturbances are derived for a controller that can be interpreted as a filtered and possibly time-delayed PD controller. Using a controller structure that decouples the effects of the feedforward and feedback controllers, the controller is optimal both in open and closed loop settings. To improve the high-frequency noise behavior of the feedforward controller, it is proposed that the optimal controller is augmented with a second-order filter. Several aspects on the tuning of this filter are discussed. For systems with PID controllers, the response to step changes in the reference can be improved by introducing set-point weighting. This can be interpreted as feedforward from the reference signal to the control signal. It is shown how these weights can be found by solving a convex optimization problem. Proportional set-point weight that minimizes the integrated-absolute-error was obtained for a batch of over 130 different processes. From these weights, simple tuning rules were derived and the performance was evaluated on all processes in the batch using five different feedback controller tuning methods. The proposed tuning rules could improve the performance by up to 45% with a modest increase in actuation

Switch actuators in process control: constraint problems and corrections

The paper deals with switch actuators in process control. The inclusion of a signal modulator required for commanding the actuator in proportional-integral-derivative (PID) controller structures is discussed. In particular, it is analysed how the restrictions of this modulator may worsen the well-known problems of process-input saturation, such as windup or loss of control directionality among others. From this analysis a simple correction methodology is proposed for simultaneously addressing constraints in both modulator and actuator. This methodology is easily implemented from feeding back a modulator signal and takes advantage of the wide knowledge existing in anti-windup techniques. Two examples (SISO and MIMO) are presented to assess the effectiveness of the proposed correction.Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señale

Switch actuators in process control: constraint problems and corrections

The paper deals with switch actuators in process control. The inclusion of a signal modulator required for commanding the actuator in proportional-integral-derivative (PID) controller structures is discussed. In particular, it is analysed how the restrictions of this modulator may worsen the well-known problems of process-input saturation, such as windup or loss of control directionality among others. From this analysis a simple correction methodology is proposed for simultaneously addressing constraints in both modulator and actuator. This methodology is easily implemented from feeding back a modulator signal and takes advantage of the wide knowledge existing in anti-windup techniques. Two examples (SISO and MIMO) are presented to assess the effectiveness of the proposed correction.Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señale

Control Schemes for a Quadruple Tank Process

This paper deals with the control of a quadruple tank process. A gain scheduling controller, a linear parameter varying controller and an input-output feedback linearization controller are proposed for the quadruple tank process. The derivation of the three control schemes is presented in details. Moreover, the proposed control schemes are implemented using an experimental setup. The experimental results indicate that the developed control schemes work well and are able to regulate the output of the process to its desired value. Additionally, the implementation results demonstrate that the input-output feedback linearization controller gave the best performance

Commande Robuste et Contraintes d'Optimisation

This thesis presents an overview of my research activities carried out since my PhD in 2001. In the first section, description of the projects, my different contributions to robust control applied to the spatial field and underwater robotics, are highlighted. My research project for the coming years is then presented; I propose an original and efficient methodology to compute simple control laws by combining \textit{robust control} and \textit{global optimization}. The second part of this thesis is dedicated to the scientific aspects that will help clarify the proposed research project. As a starting point, Youla parametrization is presented as a tool to \textit{render convex} the control problem, and the subsequent work is used as a foundation to establish specifications based on the constraints related to optimization. This theme has served as a driving thread in illustrating how industrial requirements could lead to a control problem. Parallel to this, the question also arose as to the practical realization of results from these methodologies, that is, how they might be implemented in an embedded system. Ariane 5 launcher control is taken as an example for research on the structured control and validation.Ce mémoire présente un panorama des activités de recherche menées depuis ma thèse de doctorat en 2001. Dans une première partie, à travers la description des projets, sont mises en avant les différentes contributions à la commande robuste appliquée au monde spatial et au monde de la robotique sous-marine. On montre alors comment s'est construit le projet de recherche proposé pour les années à venir. Il s'agit de proposer une méthodologie originale et efficace pour régler des lois de commande simple à implémenter en combinant \textit{commande robuste} et \textit{optimisation globale}. La seconde partie de ce mémoire est consacrée à quelques aspects scientifiques qui aident à comprendre le projet de recherche proposé. On y trouve comme point de départ la paramétrisation de Youla en tant qu'outil pour \textit{convexifier} le problème de commande et les travaux qui en ont découlés pour traduire un cahier des charges en terme de contrainte dans un problème d'optimisation. Cette thématique a été un fil conducteur important pour faire le lien avec la demande industrielle de savoir comment les exigences étaient traduites dans le problème de commande. En parallèle, s'est posée la question de la réalisation pratique des résultats issues de ces méthodologies, c'est-à-dire leur implémentation sur un système embarqué. On prendra comme exemple les activités de recherche sur la structuration de correcteur et leur qualification pour les lois de pilotage des lanceurs Ariane 5

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

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

Fixed-structure Control of LTI Systems with Polytopic-type Uncertainty:Application to Inverter-interfaced Microgrids

This thesis focuses on the development of robust control solutions for linear time-invariant interconnected systems affected by polytopic-type uncertainty. The main issues involved in the control of such systems, e.g. sensor and actuator placement, control configuration selection, and robust fixed-structure control design are included. The problem of fixed-structure control is intrinsically nonconvex and hence computationally intractable. Nevertheless, the problem has attracted considerable attention due to the great importance of fixed-structure controllers in practice. In this thesis, necessary and sufficient conditions for fixed-structure H_inf control of polytopic systems with a single uncertain parameter in terms of a finite number of bilinear matrix inequalities (BMIs) are developed. Increasing the number of uncertain parameters leads to sufficient BMI conditions, where the number of decision variables grows polynomially. Convex approximations of robust fixed-order and fixed-structure controller design which rely on the concept of strictly positive realness (SPRness) of transfer functions in state space setting are presented. Such approximations are based on the use of slack matrices whose duty is to decouple the product of unknown matrices. Several algorithms for determination and update of the slack matrices are given. It is shown that the problem of sensor and actuator placement in the polytopic interconnected systems can be formulated as an optimization problem by minimizing cardinality of some pattern matrices, while satisfying a guaranteed level of H_inf performance. The control configuration design is achieved by solving a convex optimization problem whose solution delivers a trade-off curve that starts with a centralized controller and ends with a decentralized or a distributed controller. The proposed approaches are applied to inverter-interfaced microgrids which consist of distributed generation (DG) units. To this end, two important control problems associated with the microgrids are considered: (i) Current control of grid-connected voltage-source converters with L/LCL filters and (ii) Voltage control of islanded microgrids. The proposed control strategies are able to independently regulate the direct and quadrature (dq) components of the converter currents and voltages at the point of common couplings (PCC) in a fully decoupled manner and provide satisfactory dynamic responses. The important problem of plug-and-play (PnP) capability of DGs in the microgrids is also studied. It is shown that an inverter-interfaced microgrid consisting of multi DGs under PnP functionality can be cast as a system with polytopic-type uncertainty. By virtue of this novel description and use of the results from theory of robust control, the stability of the microgrid system under PnP operation of DGs is preserved. Extensive case studies, based on time-domain simulations in MATLAB/SimPowerSystems Toolbox, are carried out to evaluate the performance of the proposed controllers under various test scenarios, e.g., load change, voltage and current tracking. Real-time hardware-in-the-loop case studies, using RT-LAB real-time platform of OPAL-RT Technologies, are also conducted to validate the performance of the designed controllers and demonstrate their insensitivity to hardware implementation issues, e.g., noise and PWM non-idealities. The simulation and experimental results demonstrate satisfactory performance of the designed controllers