Discussion on: Measurable signal decoupling with dynamic feedforward compensation and unknown-input observation for systems with direct feedthrough
|
|
- Cori Marsh
- 5 years ago
- Views:
Transcription
1 Discussion on: Measurable signal decoupling with dynamic feedforward compensation and unknown-input observation for systems with direct feedthrough H.L. Trentelman 1 The geometric approach In the last four decades, ever since the seminal work of Basile and Marro [1] and Wonham and Morse [6], research efforts have been devoted to analysis and synthesis problems for linear state space systems within the well-known context of the geometric approach. The central issue in this approach is to use basic linear algebraic concepts such as linear mapping and linear subspace to investigate the structural properties of linear systems in terms of properties of the mappings A, B, C, D, etc., appearing in the system equations. For example, properties such as controllability, observability, stabilizability, and detectability can be expressed and characterized very effectively in terms of subspaces generated by these system mappings. Also, important notions such as system invertibility, system zeroes, minimum phase, weak observabilty, and strong controllability are analysed most naturally using the geometric approach. In addition, a large number of synthesis problems has been studied in this framework, such as pole placement and stabilization, observer design, disturbance decoupling by static state feedback or dynamic measurement feedback, observer design in the presence of unknown inputs, problems of output decoupling, problems of tracking and regulation, input-output decoupling, and decentralized control problems. Starting with the famous textbook by W.M. Wonham [7], a treatment of most of these synthesis problems can be found in the textbooks [2] and [4]. In the eighties, the exact versions of many of these control synthesis problems were generalized to their approximative versions, resulting in high gain feedback design problems such as almost disturbance decoupling, almost input-output decoupling, etc., see [5]. Around that time research attention within the systems and control community had been shifted to a large extend to H 2 and H control. However, also in the context of H 2 and H control an important role continued to be played by problems of disturbance decoupling and almost disturbance decoupling, see e.g [4]. Although the intensity of research within the geometric approach has become less, there is still an active community that devotes attention to further developing the area. L. Ntogramatzidis, the author of the paper to be discussed in this note, is clearly an exponent of this community. In this note we intend to explain the contribution of the Mathematics Institute, University of Groningen P.O. Box 800, 9700 AV Groningen, The Netherlands, Phone: , Fax:
2 paper by Ntogramatzidis within the existing theory of the geometric approach. 2 Disturbance decoupling by state feedback and feedforward In this section we explain how the disturbance decoupling problem treated in the paper by Ntogramatzidis fits into the classical framework of disturbance decoupling with stability by state feedback and feedforward, and how his solution differs from the standard one in terms of stabilizable output nulling subspaces. In the paper, a plant is considered, represented by the state space equations ẋ(t) = Ax(t) + Bu(t) + Ew(t), y(t) = Cx(t) + Du(t) + Jw(t), with x(t) R n, u(t) R m, w(t) R r and y(t) R p. In these equations, u(t) is a control input, and w(t) represents a disturbance input. It is assumed that the disturbance w(t) can be measured. For this system, the disturbance decoupling problem with stability and feedforward, DDPSF, is to find linear maps F and G defining the state feedback/disturbance feedforward control law u(t) = F x(t) + Gw(t) such that the controlled system has the following two properties: 1) the transfer matrix T F,G from w to y is equal to zero, and 2) A + BF is stable (i.e., all eigenvalues λ of the linear map A + BF satisfy Re(λ) < 0). In order to obtain conditions for the existence of such F and G, and in order to compute these maps, the concept of output nulling subspace, is introduced: a subspace V of the state space R n is called an output nulling subspace for the system Σ: ẋ(t) = Ax(t) + Bu(t), y(t) = Cx(t) + Du(t), if there exists F such that (A + BF )V V and (C + DF )V = {0}. The class of all output nulling subspaces for Σ is closed under subspace addition. It therefore contains a unique maximal element, which is denoted by V(Σ). A subspace V of the state space R n is called a stabilizable output nulling subspace for the system Σ if if there exists F such that (A + BF )V V, (C + DF )V = {0} and the restriction (A + BF ) V is stable. There exists a maximal stabilizable output nulling subspace, which is denoted by V g (Σ). In case that D = 0 these subspaces coincide with the maximal controlled invariant, and stabilizability subspace, respectively, contained in ker(c). It can be proven using standard techniques (see e.g. [4], chapter 7) that necessary and sufficient conditions for the existence of a control law u(t) = F x(t) + Gw(t) such that T F,G = 0 and A + BF is stable are: E B im (V J g (Σ) {0}) + im (1) D and (A, B) is stabilizable. Although this yields a solution to DDPSF, it has been argued that it is not completely satisfactory because the computation of V g (Σ) requires the computation of eigenspaces, which from a computational point of view is undesired. This has led Basile and Marro in [3] to introduce the notion of self-bounded output nulling subspace. An output nulling 2
3 subspace V for Σ is called self-bounded if V(Σ) B ker(d) V. In contrast to the class of output nulling subspaces for Σ, the class of self-bounded output nulling subspaces for Σ forms a lattice under subspace addition and intersection, and therefore the intersection of any two self-bounded output nulling subspaces is a self-bounded output nulling subspace again. This implies that there exists a unique smallest self-bounded output nulling subspace for Σ, which is denoted by R(Σ). In the following, an important role is played by R( ), the smallest self-bounded output nulling subspace for the plant = (A, (B E), C, (D J)). It turns out that necessary and sufficient conditions for solvability of DDPSF can now alternatively be formulated using the smallest self-bounded output nulling subspace R( ) associated with the plant as follows: there exists a feedback control law u(t) = F x(t) + Gw(t) such that T F,G = 0 and A + BF is stable if and only if E B im (V(Σ) {0}) + im, (2) J D (A, B) is stabilizable, and R( ) is a stabilizable output nulling subspace for Σ (the condition (2) can be shown to imply that R( ) automatically is an output nulling subspace for the system Σ). The latter set of conditions indeed does not require computation of eigenspaces. In the paper by Ntogramatzidis, a slightly different version of the problem DDPSF is studied: there is no static state feedback part, but instead the problem is to find a dynamic feedforward controller for the plant, using w(t) as its input, of the form Σ c : ξ c (t) = A c ξ c (t) + B c w(t), u(t) = C c ξ c (t) + D c w(t), (3) such that the closed loop transfer matrix T Σc is zero, and the closed loop system is internally stable. Ntogramatzidis calls this the problem of measurable signal decoupling with dynamic feedforward compensation, MSDPS. In the paper by Ntogramatzidis it is shown that, under the assumption that A is stable, there exists Σ c such that T Σc = 0 and the controlled system is internally stable if and only if the subspace inclusion (2) holds, and R( ) is a stabilizable output nulling subspace for Σ. In fact, the existence of all these controllers is well-known to be related to solvability of a linear matrix equation involving the transfer matrices associated with the plant. For the system denote the transfer matrix from u to y by G u,y and from w to y by G w,y. Consider the linear equation G u,y X + G w,y = 0 (4) in the unknown real rational matrix X(s). Then the following statements are equivalent: (i) the equation (4) has a proper, stable, real rational solution X, (ii) the subspace inclusion (1) holds, (iii) the subspace inclusion (2) holds, and R( ) is a stabilizable output nulling subspace for Σ. Under the assumption that A is stable, statements ((i), (ii) and (iii) are equivalent to: 3
4 (iv) there exists a feedforward controller Σ c of the form (3) such that the controlled system is internally stable and T Σc = 0. Under the assumption that (A, B) is stabilizable, statements (i), (ii) and (iii) are equivalent to: (v) there exist linear maps F and G such that with the controller u(t) = F x(t) + Gw(t) we have that T F,G = 0 and A + BF is stable. 3 Observers in the presence of unknown inputs In the context of observer design the paper considers the observed linear plant Ω, represented by the state space equations ẋ(t) = Ax(t) + Bw(t), z(t) = Hx(t) + Jw(t), y(t) = Cx(t) + Dw(t), with x(t) R n, w(t) R m, z(t) R q and y(t) R p. In these equations, w(t) represents a disturbance input, y(t) a measured output, and z(t) a to be estimated output. The unknown input observation problem, UIO, that is studied in the paper by Ntogramatzidis is the following: find an observer Σ o of the form ξ o (t) = A o ξ o (t) + B o y(t), ẑ(t) = C o ξ o (t) + D o y(t), (5) such that in the interconnection of Ω and Σ o the transfer matrix T w,e from w to the estimation error e := z ẑ is zero, and the interconnected system is internally stable. In [4], section 5.3, this problem was studied for the case that the direct feedtrough matrices J and D are zero. There it was called the problem of estimation in the presence of disturbances. In the latter problem no internal stability is required, but only stability of the transfer matrix from the state (x, ξ o ) of the interconnected system to the estimation error e. It is quite straightforward to extend the estimation problem in [4] to the case that the direct feedthrough matrices J and D are possibly nonzero. This requires the notion of input containing subspaces as defined in the paper by Ntogramatzidis. Consider the system Σ: ẋ(t) = Ax(t) + Bw(t), y(t) = Cx(t) + Dw(t). A subspace S of the state space R n is called an input containing subspace for Σ if there exists a linear map G such that (A + GC)S S and im(b + GD) S. It is called a stabilizable input containing subspace for Σ if in addition G can be chosen such that the quotient map (A + GC) R n /S is stable. There exist a smallest input containing subspace S(Σ) and a smallest stabilizable input containing subspace S g (Σ). Note that if the direct feedthrough map D is zero, then S(Σ) and S g (Σ) are the smallest conditioned invariant, and detectability subspace containing im(b), respectively. It is rather straightforward using the methods in [4], section 5.3 to obtain the following conditions for the existence of an estimator: there exists an observer Σ o of the form (5) for 4
5 the observed plant Ω such that: (1) the transfer matrix T w,e from w to the estimation error e := z ẑ is zero, and (2) the transfer matrix from the state (x, ξ o ) of the interconnected system to the estimation error e is stable, if and only if the subspace inclusion (S g (Σ) R m ) ker(c D) ker(h J) (6) holds. Under the assumption that A is stable, condition (6) is also necessary and sufficient for solvability of the unknown input observation problem UIO (which requires internal stability of the interconnected system). Again, condition (6) is not completely satisfactory because computations around S g (Σ) require computations of eigenspaces. This has led to the introduction of self-hidden input containing subspaces in [3]. In the paper by Ntogramatzidis this concept is generalized to the case that a direct feedthrough map D is present. An input containing subspace S for Σ is called self-hidden if S(Σ) S + C 1 im(d). The class of self-hidden input containing subspaces for Σ forms a lattice under addition and intersection, and therefore there exists a largest self-hidden input containing subspace, denoted by N(Σ). In the paper by Ntogramatzidis it is proven that, under the condition that A is stable, the unknown input observation problem UIO for the observed plant Ω admits a solution if and only if the subspace inclusion (S(Σ) R m ) ker(c D) ker(h J) (7) holds, and N(Ω) is a stabilizable input containing subspace for Σ (the subspace inclusion (7) implies that N(Ω) is input containing for Σ). For the existence of an estimator (in the sense of [4], so without the requirement that the interconnected system is internally stable) the same conditions are necessary and sufficient, without the additional assumption that the system map A is stable. References [1] G. Basile and G. Marro, Controlled and conditioned invariant subspaces in linear system theory, Journal of Optimization Theory and Applications, 3 (5), pp , [2] G. Basile and G. Marro, Controlled and Conditioned Invariants in Linear System Theory, Prentice Hall, Englewood Cliffs, new Jersey, [3] G. Basile and G. Marro, Self-bounded controlled invariant subspaces: a straightforward approach to constrained controllability, Journal of Optimization Theory and Applications, 38 (1), pp , [4] H.L. Trentelman, A.A. Stoorvogel and M.L.J. Hautus, Control Theory For Linear Systems, Springer, U.K., [5] J.C. Willems, Almost invariant subspaces, an approach to high gain feedback design - Part I, almost controlled invariant subspaces, IEEE Transactions on Automatic Control, AC 26, pp , [6] W.M. Wonham and S. Morse, Decoupling and pole assignment in linear multivariable systems, SIAM Journal of Control, 8 (1), pp. 1-18,
6 [7] W.M. Wonham, Linear Multivariable Control: A Geometric Approach, Springer Verlag, New York, third edition,
Education in Linear System Theory with the Geometric Approach Tools
Education in Linear System Theory with the Geometric Approach Tools Giovanni Marro DEIS, University of Bologna, Italy GAS Workshop - Sept 24, 2010 Politecnico di Milano G. Marro (University of Bologna)
LQR and H 2 control problems
LQR and H 2 control problems Domenico Prattichizzo DII, University of Siena, Italy MTNS - July 5-9, 2010 D. Prattichizzo (Siena, Italy) MTNS - July 5-9, 2010 1 / 23 Geometric Control Theory for Linear
Geometric Control of Patterned Linear Systems
Geometric Control of Patterned Linear Systems Sarah C Hamilton and Mireille E Broucke Abstract We introduce and study a new class of linear control systems called patterned systems Mathematically, this
Disturbance Decoupling and Unknown-Input Observation Problems
Disturbance Decoupling and Unknown-Input Observation Problems Lorenzo Ntogramatzidis Curtin University of Technology, Australia MTNS - July 5-9, 2010 L. Ntogramatzidis (Curtin University) MTNS - July 5-9,
Almost disturbance decoupling: static state feedback solutions with maximal pole assignment
29 American Control Conference Hyatt Regency Riverfront, St. Louis, MO, USA June 1-12, 29 WeA15.2 Almost disturbance decoupling: static state feedback solutions with maximal pole assignment Runmin Zou
POLYNOMIAL EMBEDDING ALGORITHMS FOR CONTROLLERS IN A BEHAVIORAL FRAMEWORK
1 POLYNOMIAL EMBEDDING ALGORITHMS FOR CONTROLLERS IN A BEHAVIORAL FRAMEWORK H.L. Trentelman, Member, IEEE, R. Zavala Yoe, and C. Praagman Abstract In this paper we will establish polynomial algorithms
A Notion of Zero Dynamics for Linear, Time-delay System
Proceedings of the 17th World Congress The International Federation of Automatic Control A Notion of Zero Dynamics for Linear, Time-delay System G. Conte A. M. Perdon DIIGA, Università Politecnica delle
Control for Coordination of Linear Systems
Control for Coordination of Linear Systems André C.M. Ran Department of Mathematics, Vrije Universiteit De Boelelaan 181a, 181 HV Amsterdam, The Netherlands Jan H. van Schuppen CWI, P.O. Box 9479, 19 GB
Federico Barbagli' Giovanni Marro2 Domenico Prattichizz~~
Proceedings of the 39" IEEE Conference on Deasion and Control Sydney, Australia December, 2000 Solving signal decoupling problems through self=bounded controlled invariants Federico Barbagli' Giovanni
AN OPTIMIZATION-BASED APPROACH FOR QUASI-NONINTERACTING CONTROL. Jose M. Araujo, Alexandre C. Castro and Eduardo T. F. Santos
ICIC Express Letters ICIC International c 2008 ISSN 1881-803X Volume 2, Number 4, December 2008 pp. 395 399 AN OPTIMIZATION-BASED APPROACH FOR QUASI-NONINTERACTING CONTROL Jose M. Araujo, Alexandre C.
Spectral factorization and H 2 -model following
Spectral factorization and H 2 -model following Fabio Morbidi Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA MTNS - July 5-9, 2010 F. Morbidi (Northwestern Univ.) MTNS
Linear Control Theory. in Geometric Terms
CIRA Summer School Antonio Ruberti Bertinoro, July 15 20 2002 Linear Control Theory in Geometric Terms Giovanni MARRO Lorenzo NTOGRAMATZIDIS Domenico PRATTICHIZZO Elena ZATTONI DEIS, University of Bologna,
The geometric approach and Kalman regulator
Kalman filtering: past and future Bologna, September 4, 2002 The geometric approach and Kalman regulator Giovanni MARRO DEIS, University of Bologna, Italy The purpose of this talk is to show that not only
WEAK STRUCTURE AT INFINITY AND ROW-BY-ROW DECOUPLING FOR LINEAR DELAY SYSTEMS
KYBERNETIKA VOLUME 40 (2004), NUMBER 2, PAGES 181 195 WEAK STRUCTURE AT INFINITY AND ROW-BY-ROW DECOUPLING FOR LINEAR DELAY SYSTEMS Rabah Rabah and Michel Malabre We consider the row-by-row decoupling
Stabilization and Self bounded Subspaces
Stabilization and Self bounded Subspaces Lorenzo Ntogramatzidis Curtin University of Technology, Australia MTNS - July 5-9, 2010 L. Ntogramatzidis (Curtin University) MTNS - July 5-9, 2010 1 / 23 Geometric
Equivalence of dynamical systems by bisimulation
Equivalence of dynamical systems by bisimulation Arjan van der Schaft Department of Applied Mathematics, University of Twente P.O. Box 217, 75 AE Enschede, The Netherlands Phone +31-53-4893449, Fax +31-53-48938
Observers for linear time-varying systems
Observers for linear time-varying systems Jochen Trumpf 1 Dept. of Information Engineering, RSISE, Bldg. 115, ANU ACT 0200, Australia Abstract We give characterizations and necessary and sufficient existence
Chapter 3. LQ, LQG and Control System Design. Dutch Institute of Systems and Control
Chapter 3 LQ, LQG and Control System H 2 Design Overview LQ optimization state feedback LQG optimization output feedback H 2 optimization non-stochastic version of LQG Application to feedback system design
Null Controllability of Discrete-time Linear Systems with Input and State Constraints
Proceedings of the 47th IEEE Conference on Decision and Control Cancun, Mexico, Dec. 9-11, 2008 Null Controllability of Discrete-time Linear Systems with Input and State Constraints W.P.M.H. Heemels and
Stability, Pole Placement, Observers and Stabilization
Stability, Pole Placement, Observers and Stabilization 1 1, The Netherlands DISC Course Mathematical Models of Systems Outline 1 Stability of autonomous systems 2 The pole placement problem 3 Stabilization
Stabilization, Pole Placement, and Regular Implementability
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 47, NO. 5, MAY 2002 735 Stabilization, Pole Placement, and Regular Implementability Madhu N. Belur and H. L. Trentelman, Senior Member, IEEE Abstract In this
Research Article Generalized S C, A, B -Pairs for Uncertain Linear Infinite-Dimensional Systems
Journal of Applied Mathematics Volume 2009, Article ID 169790, 16 pages doi:10.1155/2009/169790 Research Article Generalized S C, A, B -Pairs for Uncertain Linear Infinite-Dimensional Systems Naohisa Otsuka
Design Methods for Control Systems
Design Methods for Control Systems Maarten Steinbuch TU/e Gjerrit Meinsma UT Dutch Institute of Systems and Control Winter term 2002-2003 Schedule November 25 MSt December 2 MSt Homework # 1 December 9
Controllability of Linear Systems with Input and State Constraints
Proceedings of the 46th IEEE Conference on Decision and Control New Orleans, LA, USA, Dec. 12-14, 2007 Controllability of Linear Systems with Input and State Constraints W.P.M.H. Heemels and M.K. Camlibel
The norms can also be characterized in terms of Riccati inequalities.
9 Analysis of stability and H norms Consider the causal, linear, time-invariant system ẋ(t = Ax(t + Bu(t y(t = Cx(t Denote the transfer function G(s := C (si A 1 B. Theorem 85 The following statements
On linear quadratic optimal control of linear time-varying singular systems
On linear quadratic optimal control of linear time-varying singular systems Chi-Jo Wang Department of Electrical Engineering Southern Taiwan University of Technology 1 Nan-Tai Street, Yungkung, Tainan
This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and
This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution
Zeros and zero dynamics
CHAPTER 4 Zeros and zero dynamics 41 Zero dynamics for SISO systems Consider a linear system defined by a strictly proper scalar transfer function that does not have any common zero and pole: g(s) =α p(s)
ECEN 605 LINEAR SYSTEMS. Lecture 8 Invariant Subspaces 1/26
1/26 ECEN 605 LINEAR SYSTEMS Lecture 8 Invariant Subspaces Subspaces Let ẋ(t) = A x(t) + B u(t) y(t) = C x(t) (1a) (1b) denote a dynamic system where X, U and Y denote n, r and m dimensional vector spaces,
BUMPLESS SWITCHING CONTROLLERS. William A. Wolovich and Alan B. Arehart 1. December 27, Abstract
BUMPLESS SWITCHING CONTROLLERS William A. Wolovich and Alan B. Arehart 1 December 7, 1995 Abstract This paper outlines the design of bumpless switching controllers that can be used to stabilize MIMO plants
Pole placement control: state space and polynomial approaches Lecture 2
: state space and polynomial approaches Lecture 2 : a state O. Sename 1 1 Gipsa-lab, CNRS-INPG, FRANCE Olivier.Sename@gipsa-lab.fr www.gipsa-lab.fr/ o.sename -based November 21, 2017 Outline : a state
Detectability Subspaces and Observer Synthesis for Two-Dimensional Systems
Detectability Subspaces and Observer Synthesis for Two-Dimensional Systems Lorenzo Ntogramatzidis Michael Cantoni Department of Mathematics and Statistics, Curtin University of Technology, Perth, 684 WA,
Systems & Control Letters. controllability of a class of bimodal discrete-time piecewise linear systems including
Systems & Control Letters 6 (3) 338 344 Contents lists available at SciVerse ScienceDirect Systems & Control Letters journal homepage: wwwelseviercom/locate/sysconle Controllability of a class of bimodal
The Role of Exosystems in Output Regulation
1 The Role of Exosystems in Output Regulation Lassi Paunonen In this paper we study the role of the exosystem in the theory of output regulation for linear infinite-dimensional systems. The main result
Linear Algebra. P R E R E Q U I S I T E S A S S E S S M E N T Ahmad F. Taha August 24, 2015
THE UNIVERSITY OF TEXAS AT SAN ANTONIO EE 5243 INTRODUCTION TO CYBER-PHYSICAL SYSTEMS P R E R E Q U I S I T E S A S S E S S M E N T Ahmad F. Taha August 24, 2015 The objective of this exercise is to assess
INVERSE MODEL APPROACH TO DISTURBANCE REJECTION AND DECOUPLING CONTROLLER DESIGN. Leonid Lyubchyk
CINVESTAV Department of Automatic Control November 3, 20 INVERSE MODEL APPROACH TO DISTURBANCE REJECTION AND DECOUPLING CONTROLLER DESIGN Leonid Lyubchyk National Technical University of Ukraine Kharkov
Regulation transients in discrete-time linear parameter varying systems: a geometric approach to perfect elimination
Proceedings of the 2007 American Control Conference Marriott Marquis Hotel at Times Square New York City, USA, July 11-13, 2007 FrB084 Regulation transients in discrete-time linear parameter varying systems:
OUTPUT REGULATION OF RÖSSLER PROTOTYPE-4 CHAOTIC SYSTEM BY STATE FEEDBACK CONTROL
International Journal in Foundations of Computer Science & Technology (IJFCST),Vol., No., March 01 OUTPUT REGULATION OF RÖSSLER PROTOTYPE-4 CHAOTIC SYSTEM BY STATE FEEDBACK CONTROL Sundarapandian Vaidyanathan
Model Following with Global Asymptotic Stability in Hybrid Systems with Periodic State Jumps
Model Following with Global Asymptotic Stability in Hybrid Systems with Periodic State Jumps ELENA ZATTONI Alma Mater Studiorum University of Bologna Department of Electrical Electronic and Information
A Simple Derivation of Right Interactor for Tall Transfer Function Matrices and its Application to Inner-Outer Factorization Continuous-Time Case
A Simple Derivation of Right Interactor for Tall Transfer Function Matrices and its Application to Inner-Outer Factorization Continuous-Time Case ATARU KASE Osaka Institute of Technology Department of
CONTROL DESIGN FOR SET POINT TRACKING
Chapter 5 CONTROL DESIGN FOR SET POINT TRACKING In this chapter, we extend the pole placement, observer-based output feedback design to solve tracking problems. By tracking we mean that the output is commanded
CONTROL SYSTEMS, ROBOTICS AND AUTOMATION Vol. VII Multivariable Poles and Zeros - Karcanias, Nicos
MULTIVARIABLE POLES AND ZEROS Karcanias, Nicos Control Engineering Research Centre, City University, London, UK Keywords: Systems, Representations, State Space, Transfer Functions, Matrix Fraction Descriptions,
Modern Control Systems
Modern Control Systems Matthew M. Peet Arizona State University Lecture 09: Observability Observability For Static Full-State Feedback, we assume knowledge of the Full-State. In reality, we only have measurements
Decentralized control with input saturation
Decentralized control with input saturation Ciprian Deliu Faculty of Mathematics and Computer Science Technical University Eindhoven Eindhoven, The Netherlands November 2006 Decentralized control with
A Control of an Electromagnetic Actuator Using Model Predictive Control
Proceedings of the 3 International Conference on Applied Mathematics and Computational Methods in Engineering A Control of an Electromagnetic Actuator Using Model Predictive Control Paolo Mercorelli Abstract
CONTROL SYSTEMS, ROBOTICS, AND AUTOMATION Vol. III Controller Design - Boris Lohmann
CONROL SYSEMS, ROBOICS, AND AUOMAION Vol. III Controller Design - Boris Lohmann CONROLLER DESIGN Boris Lohmann Institut für Automatisierungstechnik, Universität Bremen, Germany Keywords: State Feedback
arxiv: v1 [math.oc] 2 Sep 2016
Structured Optimal Feedback in Multi-Agent Systems: A Static Output Feedback Perspective Shen Zeng a, Frank Allgöwer a a Institute for Systems Theory and Automatic Control, University of Stuttgart, 755
Closed-Loop Structure of Discrete Time H Controller
Closed-Loop Structure of Discrete Time H Controller Waree Kongprawechnon 1,Shun Ushida 2, Hidenori Kimura 2 Abstract This paper is concerned with the investigation of the closed-loop structure of a discrete
arxiv: v1 [cs.sy] 12 Oct 2018
Contracts as specifications for dynamical systems in driving variable form Bart Besselink, Karl H. Johansson, Arjan van der Schaft arxiv:181.5542v1 [cs.sy] 12 Oct 218 Abstract This paper introduces assume/guarantee
Multivariable MRAC with State Feedback for Output Tracking
29 American Control Conference Hyatt Regency Riverfront, St. Louis, MO, USA June 1-12, 29 WeA18.5 Multivariable MRAC with State Feedback for Output Tracking Jiaxing Guo, Yu Liu and Gang Tao Department
Optimal Polynomial Control for Discrete-Time Systems
1 Optimal Polynomial Control for Discrete-Time Systems Prof Guy Beale Electrical and Computer Engineering Department George Mason University Fairfax, Virginia Correspondence concerning this paper should
The disturbance decoupling problem (DDP)
CHAPTER 3 The disturbance decoupling problem (DDP) Consider the system 3.1. Geometric formulation { ẋ = Ax + Bu + Ew y = Cx. Problem 3.1 (Disturbance decoupling). Find a state feedback u = Fx+ v such that
Applications of Controlled Invariance to the l 1 Optimal Control Problem
Applications of Controlled Invariance to the l 1 Optimal Control Problem Carlos E.T. Dórea and Jean-Claude Hennet LAAS-CNRS 7, Ave. du Colonel Roche, 31077 Toulouse Cédex 4, FRANCE Phone : (+33) 61 33
only nite eigenvalues. This is an extension of earlier results from [2]. Then we concentrate on the Riccati equation appearing in H 2 and linear quadr
The discrete algebraic Riccati equation and linear matrix inequality nton. Stoorvogel y Department of Mathematics and Computing Science Eindhoven Univ. of Technology P.O. ox 53, 56 M Eindhoven The Netherlands
Output Regulation of the Tigan System
Output Regulation of the Tigan System Dr. V. Sundarapandian Professor (Systems & Control Eng.), Research and Development Centre Vel Tech Dr. RR & Dr. SR Technical University Avadi, Chennai-6 6, Tamil Nadu,
FEL3210 Multivariable Feedback Control
FEL3210 Multivariable Feedback Control Lecture 8: Youla parametrization, LMIs, Model Reduction and Summary [Ch. 11-12] Elling W. Jacobsen, Automatic Control Lab, KTH Lecture 8: Youla, LMIs, Model Reduction
Stabilization and Passivity-Based Control
DISC Systems and Control Theory of Nonlinear Systems, 2010 1 Stabilization and Passivity-Based Control Lecture 8 Nonlinear Dynamical Control Systems, Chapter 10, plus handout from R. Sepulchre, Constructive
OUTPUT CONTROLLABILITY AND STEADY-OUTPUT CONTROLLABILITY ANALYSIS OF FIXED SPEED WIND TURBINE
PHYSCON 2011, León, Spain, September, 5 September, 8 2011 OUTPUT CONTROLLABILITY AND STEADY-OUTPUT CONTROLLABILITY ANALYSIS OF FIXED SPEED WIND TURBINE J.L. Domínguez-García Electrical Engineering Area
Balancing of Lossless and Passive Systems
Balancing of Lossless and Passive Systems Arjan van der Schaft Abstract Different balancing techniques are applied to lossless nonlinear systems, with open-loop balancing applied to their scattering representation.
Control Systems Design
ELEC4410 Control Systems Design Lecture 14: Controllability Julio H. Braslavsky julio@ee.newcastle.edu.au School of Electrical Engineering and Computer Science Lecture 14: Controllability p.1/23 Outline
Approximate Hierarchies of Linear Control Systems
Approximate Hierarchies of Linear Control Systems Antoine Girard and George J. Pappas Abstract Recently, a hierarchical control approach based on the notion of approximate simulation relations has been
Disturbance Attenuation for a Class of Nonlinear Systems by Output Feedback
Disturbance Attenuation for a Class of Nonlinear Systems by Output Feedback Wei in Chunjiang Qian and Xianqing Huang Submitted to Systems & Control etters /5/ Abstract This paper studies the problem of
Zeros and Zero Dynamics for Linear, Time-delay System
Zeros and Zero Dynamics for Linear, Time-delay System Giuseppe Conte Anna Maria Perdon Abstract The aim of this paper is to discuss a notion of Zero Module and Zero Dynamics for linear, time-delay systems.
Patterned Linear Systems: Rings, Chains, and Trees
Patterned Linear Systems: Rings Chains and Trees Sarah C Hamilton and Mireille E Broucke Abstract In a first paper we studied system theoretic properties of patterned systems and solved classical control
Passivity-based Stabilization of Non-Compact Sets
Passivity-based Stabilization of Non-Compact Sets Mohamed I. El-Hawwary and Manfredi Maggiore Abstract We investigate the stabilization of closed sets for passive nonlinear systems which are contained
Integral action in state feedback control
Automatic Control 1 in state feedback control Prof. Alberto Bemporad University of Trento Academic year 21-211 Prof. Alberto Bemporad (University of Trento) Automatic Control 1 Academic year 21-211 1 /
Intrinsic diculties in using the. control theory. 1. Abstract. We point out that the natural denitions of stability and
Intrinsic diculties in using the doubly-innite time axis for input-output control theory. Tryphon T. Georgiou 2 and Malcolm C. Smith 3 Abstract. We point out that the natural denitions of stability and
WEIGHTING MATRICES DETERMINATION USING POLE PLACEMENT FOR TRACKING MANEUVERS
U.P.B. Sci. Bull., Series D, Vol. 75, Iss. 2, 2013 ISSN 1454-2358 WEIGHTING MATRICES DETERMINATION USING POLE PLACEMENT FOR TRACKING MANEUVERS Raluca M. STEFANESCU 1, Claudiu L. PRIOROC 2, Adrian M. STOICA
University of Groningen. Bisimulation equivalence of differential-algebraic systems Megawati, Noorma Yulia; van der Schaft, Arjan
University of Groningen Bisimulation equivalence of differential-algebraic systems Megawati Noorma Yulia; van der Schaft Arjan Published in: International Journal of Control DOI: 1.18/27179.216.1266519
OUTPUT REGULATION OF THE SIMPLIFIED LORENZ CHAOTIC SYSTEM
OUTPUT REGULATION OF THE SIMPLIFIED LORENZ CHAOTIC SYSTEM Sundarapandian Vaidyanathan Research and Development Centre, Vel Tech Dr. RR & Dr. SR Technical University Avadi, Chennai-600 06, Tamil Nadu, INDIA
ME 234, Lyapunov and Riccati Problems. 1. This problem is to recall some facts and formulae you already know. e Aτ BB e A τ dτ
ME 234, Lyapunov and Riccati Problems. This problem is to recall some facts and formulae you already know. (a) Let A and B be matrices of appropriate dimension. Show that (A, B) is controllable if and
On at systems behaviors and observable image representations
Available online at www.sciencedirect.com Systems & Control Letters 51 (2004) 51 55 www.elsevier.com/locate/sysconle On at systems behaviors and observable image representations H.L. Trentelman Institute
WHAT IS THE MINIMUM FUNCTION OBSERVER ORDER
WHAT IS THE MINIMUM FUNCTION OBSERVER ORDER Chia-Chi Tsui 743 Clove Road, NY 10310, USA, ctsui@ny.devry.edu poles (or the eigenvalues of F) of Keywords:function observer order, much lower & lowest possible
CONTROL SYSTEMS, ROBOTICS, AND AUTOMATION Vol. III Extended Control Structures - Boris Lohmann
EXTENDED CONTROL STRUCTURES Boris Lohmann Institut für Automatisierungstechnik, Universität Bremen, Germany Keywords: State Space, Control Structures, State Feedback, State Observer, pole placement, model
Fall 線性系統 Linear Systems. Chapter 08 State Feedback & State Estimators (SISO) Feng-Li Lian. NTU-EE Sep07 Jan08
Fall 2007 線性系統 Linear Systems Chapter 08 State Feedback & State Estimators (SISO) Feng-Li Lian NTU-EE Sep07 Jan08 Materials used in these lecture notes are adopted from Linear System Theory & Design, 3rd.
Geometric Control Theory for Hybrid Systems
Geometric Control Theory for Hybrid Systems Evren Yurtseven H&NS 2010.03 Master s thesis Coach(es): Committee: prof.dr.ir. W.P.M.H. Heemels (supervisor) dr. M.K. Camlibel dr. M.K. Camlibel prof.dr.ir.
Linear System Theory. Wonhee Kim Lecture 1. March 7, 2018
Linear System Theory Wonhee Kim Lecture 1 March 7, 2018 1 / 22 Overview Course Information Prerequisites Course Outline What is Control Engineering? Examples of Control Systems Structure of Control Systems
State and input observability for structured linear systems: A graph-theoretic approach
State and input observability for structured linear systems: A graph-theoretic approach Taha Boukhobza, Frédéric Hamelin, Sinuhé Martinez-Martinez To cite this version: Taha Boukhobza, Frédéric Hamelin,
Observer design for rotating shafts excited by unbalances
Observer design for rotating shafts excited by unbalances R. S. Schittenhelm, Z. Wang, S. Rinderknecht Institute for Mechatronic Systems in Mechanical Engineering, Technische Universität Darmstadt, Germany
Tilburg University. An equivalence result in linear-quadratic theory van den Broek, W.A.; Engwerda, Jacob; Schumacher, Hans. Published in: Automatica
Tilburg University An equivalence result in linear-quadratic theory van den Broek, W.A.; Engwerda, Jacob; Schumacher, Hans Published in: Automatica Publication date: 2003 Link to publication Citation for
Control Systems I. Lecture 2: Modeling. Suggested Readings: Åström & Murray Ch. 2-3, Guzzella Ch Emilio Frazzoli
Control Systems I Lecture 2: Modeling Suggested Readings: Åström & Murray Ch. 2-3, Guzzella Ch. 2-3 Emilio Frazzoli Institute for Dynamic Systems and Control D-MAVT ETH Zürich September 29, 2017 E. Frazzoli
ẋ n = f n (x 1,...,x n,u 1,...,u m ) (5) y 1 = g 1 (x 1,...,x n,u 1,...,u m ) (6) y p = g p (x 1,...,x n,u 1,...,u m ) (7)
EEE582 Topical Outline A.A. Rodriguez Fall 2007 GWC 352, 965-3712 The following represents a detailed topical outline of the course. It attempts to highlight most of the key concepts to be covered and
Analysis of undamped second order systems with dynamic feedback
Control and Cybernetics vol. 33 (24) No. 4 Analysis of undamped second order systems with dynamic feedback by Wojciech Mitkowski Chair of Automatics AGH University of Science and Technology Al. Mickiewicza
1 Introduction QUADRATIC CHARACTERIZATION AND USE OF OUTPUT STABILIZABLE SUBSPACES 1
QUADRATIC CHARACTERIZATION AND USE OF OUTPUT STABILIZABLE SUBSPACES Eugênio B. Castelan 2, Jean-Claude Hennet and Elmer R. Llanos illarreal LCMI / DAS / UFSC 88040-900 - Florianópolis (S.C) - Brazil E-mail:
PARAMETERIZATION OF STATE FEEDBACK GAINS FOR POLE PLACEMENT
PARAMETERIZATION OF STATE FEEDBACK GAINS FOR POLE PLACEMENT Hans Norlander Systems and Control, Department of Information Technology Uppsala University P O Box 337 SE 75105 UPPSALA, Sweden HansNorlander@ituuse
The generalised continuous algebraic Riccati equation and impulse-free continuous-time LQ optimal control
The generalised continuous algebraic iccati equation and impulse-free continuous-time LQ optimal control Augusto Ferrante Lorenzo Ntogramatzidis arxiv:135.5312v1 math.ds 23 May 213 Dipartimento di Ingegneria
Observability. It was the property in Lyapunov stability which allowed us to resolve that
Observability We have seen observability twice already It was the property which permitted us to retrieve the initial state from the initial data {u(0),y(0),u(1),y(1),...,u(n 1),y(n 1)} It was the property
Linear Quadratic Gausssian Control Design with Loop Transfer Recovery
Linear Quadratic Gausssian Control Design with Loop Transfer Recovery Leonid Freidovich Department of Mathematics Michigan State University MI 48824, USA e-mail:leonid@math.msu.edu http://www.math.msu.edu/
Multi-Modal Control of Systems with Constraints
Multi-Modal Control of Systems with Constraints WeM12-3 T. John Koo Department of EECS University of California Berkeley, CA 9720 koo@eecs.berkeley.edu George J. Pappas Department of EE University of Pennsylvania
Linear Quadratic Zero-Sum Two-Person Differential Games Pierre Bernhard June 15, 2013
Linear Quadratic Zero-Sum Two-Person Differential Games Pierre Bernhard June 15, 2013 Abstract As in optimal control theory, linear quadratic (LQ) differential games (DG) can be solved, even in high dimension,
A graph-theoretical characterization of power network vulnerabilities
A graph-theoretical characterization of power network vulnerabilities Fabio Pasqualetti, Antonio Bicchi, and Francesco Bullo Abstract This work is concerned with the security of a power network against
FEMLAB-BASED OUTPUT REGULATION OF NONHYPERBOLICALLY NONMINIMUM PHASE SYSTEM AND ITS REAL-TIME IMPLEMENTATION
FEMLAB-BASED OUTPUT REGULATION OF NONHYPERBOLICALLY NONMINIMUM PHASE SYSTEM AND ITS REAL-TIME IMPLEMENTATION Branislav Rehák,1 Jorge Orozco-Mora Sergej Čelikovský,2 Javier Ruiz-León Czech Technical University,
Systems. Active Vibration Isolation of Multi-Degree-of-Freedom
Active Vibration Isolation of Multi-Degree-of-Freedom Systems WASSIM M. HADDAD School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150 USA ALI RAZAVI George W Woodruff
Any domain of attraction for a linear constrained system is a tracking domain of attraction
Any domain of attraction for a linear constrained system is a tracking domain of attraction Franco Blanchini, Stefano Miani, Dipartimento di Matematica ed Informatica Dipartimento di Ingegneria Elettrica,
Partial Eigenvalue Assignment in Linear Systems: Existence, Uniqueness and Numerical Solution
Partial Eigenvalue Assignment in Linear Systems: Existence, Uniqueness and Numerical Solution Biswa N. Datta, IEEE Fellow Department of Mathematics Northern Illinois University DeKalb, IL, 60115 USA e-mail:
Control Systems Design, SC4026. SC4026 Fall 2010, dr. A. Abate, DCSC, TU Delft
Control Systems Design, SC4026 SC4026 Fall 2010, dr. A. Abate, DCSC, TU Delft Lecture 4 Controllability (a.k.a. Reachability) and Observability Algebraic Tests (Kalman rank condition & Hautus test) A few
Robust Anti-Windup Controller Synthesis: A Mixed H 2 /H Setting
Robust Anti-Windup Controller Synthesis: A Mixed H /H Setting ADDISON RIOS-BOLIVAR Departamento de Sistemas de Control Universidad de Los Andes Av. ulio Febres, Mérida 511 VENEZUELA SOLBEN GODOY Postgrado
A Decentralized Stabilization Scheme for Large-scale Interconnected Systems
A Decentralized Stabilization Scheme for Large-scale Interconnected Systems OMID KHORSAND Master s Degree Project Stockholm, Sweden August 2010 XR-EE-RT 2010:015 Abstract This thesis considers the problem
Research Article State-PID Feedback for Pole Placement of LTI Systems
Mathematical Problems in Engineering Volume 211, Article ID 92943, 2 pages doi:1.1155/211/92943 Research Article State-PID Feedback for Pole Placement of LTI Systems Sarawut Sujitjorn and Witchupong Wiboonjaroen
EL2520 Control Theory and Practice
EL2520 Control Theory and Practice Lecture 8: Linear quadratic control Mikael Johansson School of Electrical Engineering KTH, Stockholm, Sweden Linear quadratic control Allows to compute the controller