A quasi-Newton optimal method for the global linearisation of the output feedback pole assignment

The paper deals with the problem of output feedback pole assignment by static and dynamic compensators using a powerful method referred to as global linearisation which has addressed both solvability conditions and computation of solutions. The method is based on the asymptotic linearisation of the pole assignment map around a degenerate point and is aiming to reduce the multilinear nature of the problem to the solution of a linear set of equations by using algebro-geometric notions and tools. This novel framework is used as the basis to develop numerical techniques which make the method less sensitive to the use of degenerate solutions. The proposed new computational scheme utilizes a quasi-Newton method modified accordingly so it can be used for optimization goals while achieving (exact or approximate) pole placement. In the present paper the optimisation goal is to maximise the angle between a solution and the degenerate compensator so that less sensitive solutions are achieved

A Grassmann Matrix Approach for the Computation of Degenerate Solutions for Output Feedback Laws

The paper is concerned with the improvement of the overall sensitivity properties of a method to design feedback laws for multivariable linear systems which can be applied to the whole family of determinantal type frequency assignment problems, expressed by a unified description, the so-called Determinantal Assignment Problem (DAP). By using the exterior algebra/algebraic geometry framework, DAP is reduced to a linear problem (zero assignment of polynomial combinants) and a standard problem of multilinear algebra (decomposability of multivectors) which is characterized by the set of Quadratic Plücker Relations (QPR) that define the Grassmann variety of P. This design method is based on the notion of degenerate compensator, which are the solutions that indicate the boundaries of the control design and they provide the means for linearising asymptotically the nonlinear nature of the problems and hence are used as the starting points to generate linearized feedback laws. A new algorithmic approach is introduced for the computation and the selection of degenerate solutions (decomposable vectors) which allows the computation of static and dynamic feedback laws with reduced sensitivity (and hence more robust solutions). This approach is based on alternative, linear algebra type criterion for decomposability of multivectors to that defined by the QPRs, in terms of the properties of structured matrices, referred to as Grassmann Matrices. The overall problem is transformed to a nonlinear maximization problem where the objective function is expressed via the Grassmann Matrices and the first order conditions for optimality are reduced to a nonlinear eigenvalue-eigenvector problem. Hence, an iterative method similar to the power method for finding the largest modulus eigenvalue and the corresponding eigenvector is proposed as a solution for the above problem

Structure assignment problems in linear systems: Algebraic and geometric methods

The Determinantal Assignment Problem (DAP) is a family of synthesis methods that has emerged as the abstract formulation of pole, zero assignment of linear systems. This unifies the study of frequency assignment problems of multivariable systems under constant, dynamic centralized, or decentralized control structure. The DAP approach is relying on exterior algebra and introduces new system invariants of rational vector spaces, the Grassmann vectors and Plücker matrices. The approach can handle both generic and non-generic cases, provides solvability conditions, enables the structuring of decentralisation schemes using structural indicators and leads to a novel computational framework based on the technique of Global Linearisation. DAP introduces a new approach for the computation of exact solutions, as well as approximate solutions, when exact solutions do not exist using new results for the solution of exterior equations. The paper provides a review of the tools, concepts and results of the DAP framework and a research agenda based on open problems

An Innovative Control Framework for District Heating Systems: Conceptualisation and Preliminary Results

This paper presents a holistic innovative solution for the transformation of the current district heating and cooling systems to automated more efficient systems. A variety of technological advancements have been developed and integrated to support the effective energy management of future district heating and cooling sector. First, we identify and discuss the main challenges and needs that are in line with the EU objectives and policy expectations. We give an overview of the main parts that our solution consists of, with emphasis on the forecasting tools and an advanced control system that addresses unit commitment and economic load dispatch problems. The proposed control approach employs distributed and scalable optimisation algorithms for optimising the short-term operations of a district heating and cooling plant subject to technical constraints and uncertainties in the energy demand. To test the performance and validate the proposed control system, a district heating plant with multiple energy generation units and real-life heat load data were used. Simulation experiments were also used to evaluate the benefits of using thermal storage units in district heating systems. The results show that the proposed method could achieve significant cost savings when energy storage is employed. The proposed control strategy can be applied for both operating optimally district heating plants with storage and supporting investment planning for new storage units

Development of Future EU District Heating and Cooling Network Solutions, Sharing Experiences and Fostering Collaborations

Heating and cooling consume half of the EU’s energy and much of it is wasted. The lion’s share of heating and cooling is still generated from fossil fuels, mainly natural gas, while only 18% is generated from renewable energy. In order to fulfil the EU’s climate and energy goals, the heating and cooling sector must therefore sharply reduce its energy consumption and cut its use of fossil fuels. To this end the European Commission adopted a heating and cooling strategy in February 2016 as part of the wider Energy Union Package. A number of activities and projects funded by the programmes of European Union are supporting this new EU heating and cooling strategy

Innovative Technologies for District Heating and Cooling: InDeal Project

The paper discusses the outcomes of the conference organized by the InDeal project. The conference took place on 12 December 2018 in Montpellier as part of the EnerGaia energy forum 2018. A holistic interdisciplinary approach for district heating and cooling (DHC) networks is presented that integrates heterogeneous innovative technologies from various scientific sectors. The solution is based on a multi-layer control and modelling framework that has been designed to minimize the total plant production costs and optimize heating/cooling distribution. Artificial intelligence tools are employed to model uncertainties associated with weather and energy demand forecasts, as well as quantify the energy storage capacity. Smart metering devices are utilized to collect information about all the crucial heat substations’ parameters, whereas a web-based platform offers a unique user environment for network operators. Three new technologies have been further developed to improve the efficiency of pipe design of DHC systems: (i) A new sustainable insulation material for reducing heat losses, (ii) a new quick-fit joint for an easy installation, and (iii) a new coating for reducing pressure head losses. The results of a study on the development and optimization of two energy harvesting systems are also provided. The assessment of the environmental, economic and social impact of the proposed holistic approach is performed through a life cycle analysis. The validation methodology of the integrated solution is also described, whereas conclusions and future work are finally given

Selection of Decentralised Schemes and Parametrisation of the Decentralised Degenerate Compensators

The design of decentralised control schemes has two major aspects. The selection of the decentralised structure and then the design of the decentralised controller that has a given structure and addresses certain design requirements. This paper deals with the parametrisation and selection of the decentralized structure such that problems such as the decentralised pole assignment may have solutions. We use the approach of global linearisation for the asymptotic linearisation of the pole assignment map around a degenerate compensator. Thus, we examine in depth the case of degenerate compensators and investigate the conditions under which certain degenerate structures exist. This leads to a parametrisation of decentralised structures based on the structural properties of the system. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved

A Grassmann Matrix Approach for the Computation of Degenerate Solutions for Output Feedback Laws

The paper is concerned with the improvement of the overall sensitivity properties of a method to design feedback laws for multivariable linear systems which can be applied to the whole family of determinantal type frequency assignment problems, expressed by a unified description, the so-called Determinantal Assignment Problem (DAP). By using the exterior algebra/algebraic geometry framework, DAP is reduced to a linear problem (zero assignment of polynomial combinants) and a standard problem of multilinear algebra (decomposability of multivectors) which is characterized by the set of Quadratic Plucker Relations (QPR) that define the Grassmann variety of P. This design method is based on the notion of degenerate compensator, which are the solutions that indicate the boundaries of the control design and they provide the means for linearising asymptotically the nonlinear nature of the problems and hence are used as the starting points to generate linearized feedback laws. A new algorithmic approach is introduced for the computation and the selection of degenerate solutions (decomposable vectors) which allows the computation of static and dynamic feedback laws with reduced sensitivity (and hence more robust solutions). This approach is based on alternative, linear algebra type criterion for decomposability of multivectors to that defined by the QPRs, in terms of the properties of structured matrices, referred to as Grassmann Matrices. The overall problem is transformed to a nonlinear maximization problem where the objective function is expressed via the Grassmann Matrices and the first order conditions for optimality are reduced to a nonlinear eigenvalue-eigenvector problem. Hence, an iterative method similar to the power method for finding the largest modulus eigenvalue and the corresponding eigenvector is proposed as a solution for the above problem. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved

Structure assignment problems in linear systems: Algebraic and geometric methods

The Determinantal Assignment Problem (DAP) is a family of synthesis methods that has emerged as the abstract formulation of pole, zero assignment of linear systems. This unifies the study of frequency assignment problems of multivariable systems under constant, dynamic centralized, or decentralized control structure. The DAP approach is relying on exterior algebra and introduces new system invariants of rational vector spaces, the Grassmann vectors and Plücker matrices. The approach can handle both generic and non-generic cases, provides solvability conditions, enables the structuring of decentralisation schemes using structural indicators and leads to a novel computational framework based on the technique of Global Linearisation. DAP introduces a new approach for the computation of exact solutions, as well as approximate solutions, when exact solutions do not exist using new results for the solution of exterior equations. The paper provides a review of the tools, concepts and results of the DAP framework and a research agenda based on open problems. © 2018 Elsevier Lt

System Degeneracy and the Output Feedback Problem: Parametrisation of the Family of Degenerate Compensators

The paper provides a new characterisation of constant and dynamic degenerate compensators for proper multivariable systems. The motivation stems from the very important property that degenerate feedback gains may be used for the linearisation of the pole assignment limp and enable frequency assignment. The objective is the characterisation and parametrisation of all feedback gains that may allow the asymptotic linearisation of the pole placement map. Such a parametrisation introduces new degrees of freedom for the linearisation of the related frequency assignment map and plays an important role to the solvability of the output, feedback pole assignment problem. The paper reviews the Global Asymptotic Linearisation method associated with the core versions of determinantal pole assignment problems and defines the conditions which characterises degenerate solutions of different types. Using the theory of ordered minimal bases, we provide a parametrisation of special families of degenerate compensators according to their degree. Finally, the special properties of degenerate solutions that allow frequency assignment are considered. 2016, IFAC (International Federation of Automatic Control) Hosting, by Elsevier Ltd. All rights reserved