Analysis and design of quadratically bounded QPV control systems

© 2019. ElsevierA nonlinear system is said to be quadratically bounded (QB) if all its solutions are bounded and this is guaranteed using a quadratic Lyapunov function. This paper considers the QB analysis and state-feedback controller design problems for quadratic parameter varying (QPV) systems. The developed approach, which relies on a linear matrix inequality (LMIs) feasibility problem, ensures that the QB property holds for an invariant ellipsoid which contains a predefined polytopic region of the state space. An example is used to illustrate the main characteristics of the proposed approach and to confirm the validity of the theoretical results.Peer ReviewedPostprint (author's final draft

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Design of parameter-scheduled state-feedback controllers using shifting specifications

In this paper,the problem of designing aparameter-scheduled state-feedback controller is investigated. The paper presents an extension of the classical regional pole placement, H2 control and H1 control problems, so as to satisfy new specifications, that will be referred to as shifting pole placement control, shifting H2 control and shifting H1 control, respectively. By introducing some parameters, or using the existing ones, the controller can be designed in such away that different values of the separameters imply different regions where the closed-loop poles are situated, or different performances in the H2 or H1 sense. The proposed approach is derived within the so-called Lyapunov Shaping Paradigm, where a single quadratic Lyapunov function is used for ensuring stability and desired performances in spite of arbitrary parameter time variation. The problem is analyzed in the continuous-time LPV case, oventhough the developed theory could be applied to LTI systems in cases when it is desired to vary the control system performances online. Results obtained in simulation demonstrate the effectiveness and the relevant features of the proposed approach.Peer ReviewedPostprint (published version

On the optimization of actuator saturation limits for LTI systems: an LMI-based invariant ellipsoid approach

This paper considers the problem of optimal actuator dimensioning for LTI systems, in the sense of choosing appropriate saturation limits for a given set of admissible initial conditions and for a predefined integral state-feedback control law. By using an invariant ellipsoid argument, it is shown that this problem can be described as a linear matrix inequality (LMI)-based optimization that can be solved efficiently. Moreover, the paper shows that the optimal actuator dimensioning is connected to the choice of the initial conditions of the integral states of the controller, which can be included in the overall optimization to improve further the results. Two different methods are described and analyzed by means of numerical simulation.publishedVersio

Virtual Sensors and Actuators

This chapter introduces the design of virtual sensors and actuators using the classical eigenvalue assignment approach, widely used for the design of controllers and observers in state-space. It presents a linear matrix inequality (LMI)-based procedure. The attractiveness of this solution is that the virtual sensor/actuator technique described so far can be extended easily to work with the nonlinear systems described by convex representations, such as the linear parameter varying system. The chapter illustrates the virtual sensor and actuator approach using a well-known case study: the four-tank system. It also presents a separate formulation of virtual sensors/virtual actuators. The main advantage of the LMI-based design is the fact that it enables the extension of the virtual sensor/actuator technique to linear parameter varying systems. The chapter concludes with a presentation of the conclusions and some outlooks on the current trends of virtual sensors and actuators.acceptedVersio

An improved delay and state observer for SISO LTI systems withknown delay lower bound

It is known that the presence of delays hinders the performance achievable by a feedback control system, and it can even lead to closed-loop instability if not considered during the design. For this reason, predictors are often included in the loop, although they typically require the knowledge of the exact value of the delay, which in some applications is hard to obtain in practice. This paper presents a method to design an observer that simultaneously estimates the unknown state and the time-varying input delay of a plant based on an available model and the measurements coming from the sensors. In particular, the main contribution of this paper is to show that by accounting for a known lower bound of the input delay, it is possible to improve the observer’s performance when compared to state-of-the-art approaches encountered in the literature. Simulations are used to illustrate the efficiency of the proposed design method.publishedVersio

Robust fault tolerant control framework using uncertain Takagi-Sugeno fuzzy models

This chapter is concerned with the introduction of a fault tolerant control (FTC) framework using uncertain Takagi-Sugeno (FS) fuzzy models. Depending on how much information is available about the fault, the framework gives rise to passive FTC, active FTC without controller reconfiguration and active FTC with controller reconfiguration. The design is performed using a Linear Matrix Inequality (LMI)-based synthesis that directly takes into account the TS description of the system and its uncertainties. An example based on a mobile robot is used to show the application of this methodologyPeer ReviewedPreprin

Analysis and design of quadratic parameter varying (QPV) control systems with polytopic attractive region

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper proposes a gain-scheduling approach for systems with a quadratic structure. Both the stability analysis and the state-feedback controller design problems are considered for quadratic parameter varying (QPV) systems. The developed approach assesses/enforces the belonging of a polytopic region of the state space to the region of attraction of the origin, and relies on a linear matrix inequality (LMI) feasibility problem. The main characteristics of the proposed approach are illustrated by means of examples, which confirm the validity of the theoretical results.Peer ReviewedPostprint (author's final draft

Optimizing output regulation for a class of underactuated LPV systems

@ 2017 IEEE. Personal use of these materials is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating news collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksIn this paper the problem of optimizing the output regulation of an underactuated LPV system is considered. When the system is underactuated, only a subset of the outputs can be arbitrarily controlled, and the remaining ones are constrained. The problem of finding the input that minimizes a cost function of the overall output tracking error is investigated for a special class of LPV systems that admit steady-states. Moreover, it is shown how such solution is related to the inputs associated to the singularly optimal regulation of each output.Peer ReviewedPostprint (author's final draft

Robust control of systems with output hysteresis and input saturation using a finite time stability approach

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This paper presents a robust control approach for a class of nonlinear dynamic systems consisting of a linear plant connected in series with a hysteresis operator, and affected by control input saturation. Such a class of systems commonly appears in applications concerning smart materials, in particular thermal shape memory alloys wire actuators. The goal of this paper is to design a robust controller, in the form of an output PI law, which ensures set-point regulation with a desired decay rate and, at the same time, accounts for the effects of both hysteresis and input saturation. The resulting controller appears as attractive on the implementation stand-point, since no accurate hysteresis compensator is required. In order to deal with the proposed problem, the hysteretic plant is first reformulated as a linear parameter-varying system. Subsequently, a finite time stability approach is used to impose constraints on the control input. A new set of bilinear matrix inequalities is developed, in order to perform the design with reduced conservatism by properly exploiting some structural properties of the model. The effectiveness of the method is finally validated by means of a numerical case of study. © 2018 IEEE.Peer ReviewedPostprint (author's final draft