Internal stabilization and external LpL_p stabilization of linear systems subject to constraints

Having studied during the last decade several aspects of several control design problems for linear systems subject to magnitude and rate constraints on control variables, during the last two years the research has broadened to include magnitude constraints on control variables as well as state variables. Recent work by Han et al. (2000), Hou et al. (1998) and Saberi et al. (2002) considered linear systems in a general framework for constraints including both input magnitude constraints as well as state magnitude constraints. In particular, Saberi et al. consider internal stabilization while Han et al. consider output regulation in different frameworks, namely a global, semiglobal, and regional framework. These problems require very strong solvability conditions. Therefore, a main focus for future research should focus on finding a controller with a large domain of attraction and some good rejection properties for disturbances restricted to some bounded se

A Robust Constrained Reference Governor Approach using Linear Matrix Inequalities

The purpose of this paper is to examine and provide a solution to the output reference tracking problem for uncertain systems subject to input saturation. As well-known, input saturation and modelling errors are very common problems at industry, where control schemes are implemented without accounting for such problems. In many cases, it is sometimes difficult to modify the existing implemented control schemes being necessary to provide them with external supervisory control approaches in order to tackle problems with constraints and modelling errors. In this way, a cascade structure is proposed, combining an inner loop containing any proper controller with an outer loop where a generalized predictive controller (GPC) provides adequate references for the inner loop considering input saturations and uncertainties. Therefore, the contribution of this paper consists in providing a state space representation for the inner loop and using linear matrix inequalities (LMI) to obtain a predictive state-vector feedback in such a way that the input reference for the inner loop is calculated to satisfy robust tracking specifications considering input saturations. Hence, the final proposed solution consists in solving a regulation problem to a fixed reference value subjected to a set of constraints described by several LMI and bilinear matrix inequalities (BMI). The main contribution of the paper is that the proposed solution is a non-linear setpoint tracking approach, that is, it is allowed that the system goes into saturation facing the problem of setpoint tracking instead of regulating to the origin. An illustrative numerical example is presented.Ministerio de Ciencia y Tecnología DPI2004-07444-C04-01/0

Robust Output Regulation of Euler-Bernoulli Beam Models

In this thesis, we consider control and dynamical behaviour of flexible beam models which have potential applications in robotic arms, satellite panel arrays and wind turbine blades. We study mathematical models that include flexible beams described by Euler-Bernoulli beam equations. These models consist of partial differential equations or combination of partial and ordinary differential equations depending on the loads and supports in the model. Our goal is to influence the models by control inputs such as external applied forces so that measured deflection profiles of the beams in the models behave as desired. We propose dynamic controllers for the output regulation, where the measurements from the models track desired reference signals in the given time, of flexible beam models. The controller designs are based on the so-called internal model principle and they utilize difference between measurement and desired reference trajectory. Moreover, the controllers are robust in the sense that they can achieve output regulation despite external disturbances and model uncertainties. We also study the output regulation problem when there are certain limitations on the control input. In particular, we generalize the theory of output regulation for dynamical systems described by ordinary differential equations subject to input constraints to a particular class of systems described by partial differential equations. We present set of solvability conditions and a linear output feedback controller for the output regulation

Fast model predictive control for hydrogen outflow regulation in ethanol steam reformers

© 20xx 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.In the recent years, the presence of alternative power sources, such as solar panels, wind farms, hydropumps and hydrogen-based devices, has significantly increased. The reasons of this trend are clear: contributing to a reduction of gas emissions and dependency on fossil fuels. Hydrogen-based devices are of particular interest due to their significant efficiency and reliability. Reforming technologies are among the most economic and efficient ways of producing hydrogen. In this paper we consider the regulation of hydrogen outflow in an ethanol steam reformer (ESR). In particular, a fast model predictive control approach based on a finite step response model of the process is proposed. Simulations performed using a more realistic non-linear model show the effectiveness of the proposed approach in driving the ESR to different operating conditions while fulfilling input and output constraints.Peer ReviewedPostprint (author's final draft

Properties of recoverable region and semi-global stabilization in recoverable region for linear systems subject to constraints

This paper investigates time-invariant linear systems subject to input and state constraints. It is shown that the recoverable region (which is the largest domain of attraction that is theoretically achievable) can be semiglobally stabilized by continuous nonlinear feedbacks while satisfying the constraints. Moreover, a reduction technique is presented which shows, when trying to compute the recoverable region, that we only need to compute the recoverable region for a system of lower dimension which generally leads to a considerable simplification in the computational effort

Extremum Seeking-based Iterative Learning Linear MPC

In this work we study the problem of adaptive MPC for linear time-invariant uncertain models. We assume linear models with parametric uncertainties, and propose an iterative multi-variable extremum seeking (MES)-based learning MPC algorithm to learn on-line the uncertain parameters and update the MPC model. We show the effectiveness of this algorithm on a DC servo motor control example.Comment: To appear at the IEEE MSC 201

Optimised configuration of sensors for fault tolerant control of an electro-magnetic suspension system

For any given system the number and location of sensors can affect the closed-loop performance as well as the reliability of the system. Hence, one problem in control system design is the selection of the sensors in some optimum sense that considers both the system performance and reliability. Although some methods have been proposed that deal with some of the aforementioned aspects, in this work, a design framework dealing with both control and reliability aspects is presented. The proposed framework is able to identify the best sensor set for which optimum performance is achieved even under single or multiple sensor failures with minimum sensor redundancy. The proposed systematic framework combines linear quadratic Gaussian control, fault tolerant control and multiobjective optimisation. The efficacy of the proposed framework is shown via appropriate simulations on an electro-magnetic suspension system

Cooperative distributed MPC for tracking

This paper proposes a cooperative distributed linear model predictive control (MPC) strategy for tracking changing setpoints, applicable to any finite number of subsystems. The proposed controller is able to drive the whole system to any admissible setpoint in an admissible way, ensuring feasibility under any change of setpoint. It also provides a larger domain of attraction than standard distributed MPC for regulation, due to the particular terminal constraint. Moreover, the controller ensures convergence to the centralized optimum, even in the case of coupled constraints. This is possible thanks to the warm start used to initialize the optimization Algorithm, and to the design of the cost function, which integrates a Steady-State Target Optimizer (SSTO). The controller is applied to a real four-tank plant