Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)
A family of algorithms for the identification of continuous time nonlinear plants operating in cl... more A family of algorithms for the identification of continuous time nonlinear plants operating in closed-loop is presented. An adjustable output error type predictor is parametrized in terms of the existing controller and the estimated plant model. The algorithms are derived from stability considerations in the absence of noise and assuming that the plant model is in the model set. Subsequently
A fast algorithm for the computation of the optimally frequency-dependent scaled H-norm of a "nit... more A fast algorithm for the computation of the optimally frequency-dependent scaled H-norm of a "nite-dimensional LTI system is presented. It is well known that this quantity is an upper bound to the`-norma; furthermore, it was recently shown to play a special role in the context of slowly time-varying uncertainty. Numerical experimentation suggests that the algorithm generally converges quadratically.
The aim of this paper is to clarify the properties of semibarrelled spaces (also called countably... more The aim of this paper is to clarify the properties of semibarrelled spaces (also called countably quasi-barrelled spaces in the literature). These spaces were studied by several authors, in particular in the classical book of N. Bourbaki "Espaces vectoriels topologiques". However, six incorrect statements can be found in this reference. In particular: a Hausdorff and quasi-complete semi-barrelled space is complete, a semi-barrelled, semi-reflexive space is complete, a locally convex hull of semi-barrelled semi-reflexive spaces is semi-reflexive, a locally convex hull of semi-barrelled reflexive spaces is reflexive. We show through counterexamples that these statements are false. To conclude, we show how these false claims can be corrected and we collect some properties of semi-barrelled spaces.
Proceedings of IEEE Systems Man and Cybernetics Conference - SMC
In the present paper, both ℋ2 and ℋ∞ singular estimation problems are solved in... more In the present paper, both ℋ2 and ℋ∞ singular estimation problems are solved in a new way. The results are obtained by continuity with the regular case. It is shown that, when the singular case is approached, the Riccati equation can be shared in two parts. The first one is a reduced Riccati equation and the second one consists of quantities tending to 0. The asymptotic gain which is then obtained tends to infinity with a special structure. Some observer modes becomes infinite with a finite imaginary part. Finally, the resulting observer becomes singular in singular perturbation sense. It can be calculated by solving a reduced standard problem
Proceedings of 32nd IEEE Conference on Decision and Control
In this paper, both H2 and H∞ singular estimation problems are solved in a new way. The results a... more In this paper, both H2 and H∞ singular estimation problems are solved in a new way. The results are obtained by taking the limit from the regular case. It is shown that at the neighborhood of the singular case, the Riccati equation can be shared into two parts. The first one is a reduced Riccati equation and the second one
Proceedings of 1994 33rd IEEE Conference on Decision and Control
The notion of local lp-stability is defined, and a local version of the small gain theorem is est... more The notion of local lp-stability is defined, and a local version of the small gain theorem is established. This result can be useful for the robustness study of linear time-invariant systems perturbed by nonlinearities which are only locally bounded
199 IEEE Power Engineering Society Summer Meeting. Conference Proceedings (Cat. No.99CH36364)
ABSTRACT State feedback voltage controllers including both active power and rotor speed stabilizi... more ABSTRACT State feedback voltage controllers including both active power and rotor speed stabilizing loops have been successfully used for many years on the French power system: the “Four Loop Regulator” (FLR) is installed on most of the largest French power plants. It will be replaced in the coming years by a robust coordinated AVR+PSS, called the “Desensitized Four Loop Regulator” (DFLR), having a good performance in terms of transient and small signal stability. It is shown here that the DFLR fan be tuned with few design parameters, using a systematic procedure. The opportunity to transform the specific structure of this controller into standard IEEE AVR+PSS structures has been proved. A two step method is therefore proposed for tuning the parameters of a standard IEEE AVR+PSS: (i) design a DFLR; and (ii) make the above-mentioned conversion, which depends on the type of the excitation system. The AVR+PSS obtained in this manner are efficient for damping all kinds of electromechanical oscillations of a large scale power system (including inter-area oscillations). This approach should be combined with modal analysis techniques to determine the best location of the AVR+PSS to be installed or retuned. Its efficiency has been verified on several large scale systems and is illustrated here on a modified version of the New England system. The obtained AVR+PSSs have a good robustness against significant changes in the characteristics of the network
2003 IEEE Bologna Power Tech Conference Proceedings,
This paper presents a general method to convert state feedback controllers to damp power system e... more This paper presents a general method to convert state feedback controllers to damp power system electromechanical oscillations to the standard structure formed by an automatic voltage regulator (AVR) and a power system stabilizer (PSS). The proposed conversion method is based on least squares fitting in the frequency domain.
Proceedings of 35th IEEE Conference on Decision and Control
This note deals with the problem of the existence of a canonical (i.e. completely reachable and o... more This note deals with the problem of the existence of a canonical (i.e. completely reachable and observable) realization (CR) for a linear periodic discrete-time (LPDT) system given by its periodic polynomial matrix description (PPMD). Contrary to linear time-invariant (LTI) systems, it is shown here that a CR exists only for a class of LPDT systems and that consequently minimal and canonical ones are not equivalent: namely minimal (i.e. with the least possible dimension) realization (MR) of a LPDT system is linked with controllability and reconstructability, CR is linked with reachability and observability. Minimal order, necessary and sufficient conditions to ensure the existence of a MR and a CR of LPDT systems are characterized
Proceedings of 35th IEEE Conference on Decision and Control
An algebraic theory of linear periodic discrete-time (LPDT) systems is developed in terms of a pe... more An algebraic theory of linear periodic discrete-time (LPDT) systems is developed in terms of a periodic polynomial matrix description (PMD) and in a dynamics (module) structure defined over a non-commutative, non-integral and non-principal ideal ring ℛ (the ring of periodic polynomials). Various properties of matrices and modules over ℛ are explored, and links between algebraic properties of LPDT systems such
A robust coordinated AVR/PSS, called the “desensitized four loops regulator” (DFLR) has been rece... more A robust coordinated AVR/PSS, called the “desensitized four loops regulator” (DFLR) has been recently designed using the “desensitized control” theory. Its synthesis method (which can be applied to problems other than excitation control) and its structure are detailed in this paper. It is a state feedback controller including an integrator on the regulation error. This structure, although well known in
The rotation speed of a turbogenerator is disturbed by its shaft torsion. Obtaining a filtered me... more The rotation speed of a turbogenerator is disturbed by its shaft torsion. Obtaining a filtered measure of this speed is a problem of a g r e a t practical importance for turbine governor. A solution t o this problem is explained in this paper. T h e proposed filter is designed using Kalman's theory. T h e principles of t h e design, simulations a n d tests o n the Electricit6 d e France Micro-Network laboratory a r e presented showing several improvements over the current filter. Moreover, the described solution could be used profitably in all applications where i t is necessary to substantially reduce a signal a t given frequencies without causing too great a phase shift in the pass-band.
on the other parameters that take part in G: Q and 2. Just outside this region, orbits can be fou... more on the other parameters that take part in G: Q and 2. Just outside this region, orbits can be found where IG"(y. z. U:)] + +x. Obviously in practice the choice of the initial conditions is very important to ensure convergence. We have already stated that each point (0, 0, 71') is a fixed point for G: it is also easy to show that G(y. t. U ,) = (0, 0, U !) + (y, 2. ti:) = (0. 0. 7~). The y-axis goes to the z-axis and vice-versa, and if Ibl < 1 it spirals towards the origin, and if Ibl > 1 its modulus grows G(y. 0. 0) = (0, y. 0) G(0. z. 0) = (b z , 0. 0). In addition G(y. z. 1 1 3) = (y', 0. 0) * (y, z. U :) = (0. y'/b, 0) G(y. 2-7 1 ,) = (0, z '. 0) + (y. z. 11,) = (z '. 0. 0). When (hl # 1 there do not exist period-two nor period-three orbits; besides, if b = 1 or b =-1 period-two and period-four orbits can be easily found b = 1 : (y. 0. 0) + (0, y. 0) + (11. 0. 0) b=-1: (y.0.0) + (O.y.0) + (-y.0.0) + (0.-y.0) + (y.0,O). It is easy to detect divergent orbits in the last cases although initial conditions are very close to the reference.
Page 1. I102 The above equation can be interpreted as the HJI equation for a discounted Markovian... more Page 1. I102 The above equation can be interpreted as the HJI equation for a discounted Markovian decision problem. The solution of this discounted Markov decision process may be obtained by either successive approximation ...
HAL (Le Centre pour la Communication Scientifique Directe), 2011
The use of general descriptive names, registered names, trademarks, etc. in this publication does... more The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
The aim of this chapter is the study of structural properties of linear systems. Systems with tim... more The aim of this chapter is the study of structural properties of linear systems. Systems with time-varying coefficients are considered, both in the continuousand discrete-time cases. These two cases are merged into a general framework. This study is based on module theory. Let us briefly explain what a module is, in connection with the theory of differential and difference equations.
Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)
A family of algorithms for the identification of continuous time nonlinear plants operating in cl... more A family of algorithms for the identification of continuous time nonlinear plants operating in closed-loop is presented. An adjustable output error type predictor is parametrized in terms of the existing controller and the estimated plant model. The algorithms are derived from stability considerations in the absence of noise and assuming that the plant model is in the model set. Subsequently
A fast algorithm for the computation of the optimally frequency-dependent scaled H-norm of a "nit... more A fast algorithm for the computation of the optimally frequency-dependent scaled H-norm of a "nite-dimensional LTI system is presented. It is well known that this quantity is an upper bound to the`-norma; furthermore, it was recently shown to play a special role in the context of slowly time-varying uncertainty. Numerical experimentation suggests that the algorithm generally converges quadratically.
The aim of this paper is to clarify the properties of semibarrelled spaces (also called countably... more The aim of this paper is to clarify the properties of semibarrelled spaces (also called countably quasi-barrelled spaces in the literature). These spaces were studied by several authors, in particular in the classical book of N. Bourbaki "Espaces vectoriels topologiques". However, six incorrect statements can be found in this reference. In particular: a Hausdorff and quasi-complete semi-barrelled space is complete, a semi-barrelled, semi-reflexive space is complete, a locally convex hull of semi-barrelled semi-reflexive spaces is semi-reflexive, a locally convex hull of semi-barrelled reflexive spaces is reflexive. We show through counterexamples that these statements are false. To conclude, we show how these false claims can be corrected and we collect some properties of semi-barrelled spaces.
Proceedings of IEEE Systems Man and Cybernetics Conference - SMC
In the present paper, both &Hscr;2 and &Hscr;∞ singular estimation problems are solved in... more In the present paper, both &Hscr;2 and &Hscr;∞ singular estimation problems are solved in a new way. The results are obtained by continuity with the regular case. It is shown that, when the singular case is approached, the Riccati equation can be shared in two parts. The first one is a reduced Riccati equation and the second one consists of quantities tending to 0. The asymptotic gain which is then obtained tends to infinity with a special structure. Some observer modes becomes infinite with a finite imaginary part. Finally, the resulting observer becomes singular in singular perturbation sense. It can be calculated by solving a reduced standard problem
Proceedings of 32nd IEEE Conference on Decision and Control
In this paper, both H2 and H∞ singular estimation problems are solved in a new way. The results a... more In this paper, both H2 and H∞ singular estimation problems are solved in a new way. The results are obtained by taking the limit from the regular case. It is shown that at the neighborhood of the singular case, the Riccati equation can be shared into two parts. The first one is a reduced Riccati equation and the second one
Proceedings of 1994 33rd IEEE Conference on Decision and Control
The notion of local lp-stability is defined, and a local version of the small gain theorem is est... more The notion of local lp-stability is defined, and a local version of the small gain theorem is established. This result can be useful for the robustness study of linear time-invariant systems perturbed by nonlinearities which are only locally bounded
199 IEEE Power Engineering Society Summer Meeting. Conference Proceedings (Cat. No.99CH36364)
ABSTRACT State feedback voltage controllers including both active power and rotor speed stabilizi... more ABSTRACT State feedback voltage controllers including both active power and rotor speed stabilizing loops have been successfully used for many years on the French power system: the “Four Loop Regulator” (FLR) is installed on most of the largest French power plants. It will be replaced in the coming years by a robust coordinated AVR+PSS, called the “Desensitized Four Loop Regulator” (DFLR), having a good performance in terms of transient and small signal stability. It is shown here that the DFLR fan be tuned with few design parameters, using a systematic procedure. The opportunity to transform the specific structure of this controller into standard IEEE AVR+PSS structures has been proved. A two step method is therefore proposed for tuning the parameters of a standard IEEE AVR+PSS: (i) design a DFLR; and (ii) make the above-mentioned conversion, which depends on the type of the excitation system. The AVR+PSS obtained in this manner are efficient for damping all kinds of electromechanical oscillations of a large scale power system (including inter-area oscillations). This approach should be combined with modal analysis techniques to determine the best location of the AVR+PSS to be installed or retuned. Its efficiency has been verified on several large scale systems and is illustrated here on a modified version of the New England system. The obtained AVR+PSSs have a good robustness against significant changes in the characteristics of the network
2003 IEEE Bologna Power Tech Conference Proceedings,
This paper presents a general method to convert state feedback controllers to damp power system e... more This paper presents a general method to convert state feedback controllers to damp power system electromechanical oscillations to the standard structure formed by an automatic voltage regulator (AVR) and a power system stabilizer (PSS). The proposed conversion method is based on least squares fitting in the frequency domain.
Proceedings of 35th IEEE Conference on Decision and Control
This note deals with the problem of the existence of a canonical (i.e. completely reachable and o... more This note deals with the problem of the existence of a canonical (i.e. completely reachable and observable) realization (CR) for a linear periodic discrete-time (LPDT) system given by its periodic polynomial matrix description (PPMD). Contrary to linear time-invariant (LTI) systems, it is shown here that a CR exists only for a class of LPDT systems and that consequently minimal and canonical ones are not equivalent: namely minimal (i.e. with the least possible dimension) realization (MR) of a LPDT system is linked with controllability and reconstructability, CR is linked with reachability and observability. Minimal order, necessary and sufficient conditions to ensure the existence of a MR and a CR of LPDT systems are characterized
Proceedings of 35th IEEE Conference on Decision and Control
An algebraic theory of linear periodic discrete-time (LPDT) systems is developed in terms of a pe... more An algebraic theory of linear periodic discrete-time (LPDT) systems is developed in terms of a periodic polynomial matrix description (PMD) and in a dynamics (module) structure defined over a non-commutative, non-integral and non-principal ideal ring &amp;amp;Rscr; (the ring of periodic polynomials). Various properties of matrices and modules over &amp;amp;Rscr; are explored, and links between algebraic properties of LPDT systems such
A robust coordinated AVR/PSS, called the “desensitized four loops regulator” (DFLR) has been rece... more A robust coordinated AVR/PSS, called the “desensitized four loops regulator” (DFLR) has been recently designed using the “desensitized control” theory. Its synthesis method (which can be applied to problems other than excitation control) and its structure are detailed in this paper. It is a state feedback controller including an integrator on the regulation error. This structure, although well known in
The rotation speed of a turbogenerator is disturbed by its shaft torsion. Obtaining a filtered me... more The rotation speed of a turbogenerator is disturbed by its shaft torsion. Obtaining a filtered measure of this speed is a problem of a g r e a t practical importance for turbine governor. A solution t o this problem is explained in this paper. T h e proposed filter is designed using Kalman's theory. T h e principles of t h e design, simulations a n d tests o n the Electricit6 d e France Micro-Network laboratory a r e presented showing several improvements over the current filter. Moreover, the described solution could be used profitably in all applications where i t is necessary to substantially reduce a signal a t given frequencies without causing too great a phase shift in the pass-band.
on the other parameters that take part in G: Q and 2. Just outside this region, orbits can be fou... more on the other parameters that take part in G: Q and 2. Just outside this region, orbits can be found where IG"(y. z. U:)] + +x. Obviously in practice the choice of the initial conditions is very important to ensure convergence. We have already stated that each point (0, 0, 71') is a fixed point for G: it is also easy to show that G(y. t. U ,) = (0, 0, U !) + (y, 2. ti:) = (0. 0. 7~). The y-axis goes to the z-axis and vice-versa, and if Ibl < 1 it spirals towards the origin, and if Ibl > 1 its modulus grows G(y. 0. 0) = (0, y. 0) G(0. z. 0) = (b z , 0. 0). In addition G(y. z. 1 1 3) = (y', 0. 0) * (y, z. U :) = (0. y'/b, 0) G(y. 2-7 1 ,) = (0, z '. 0) + (y. z. 11,) = (z '. 0. 0). When (hl # 1 there do not exist period-two nor period-three orbits; besides, if b = 1 or b =-1 period-two and period-four orbits can be easily found b = 1 : (y. 0. 0) + (0, y. 0) + (11. 0. 0) b=-1: (y.0.0) + (O.y.0) + (-y.0.0) + (0.-y.0) + (y.0,O). It is easy to detect divergent orbits in the last cases although initial conditions are very close to the reference.
Page 1. I102 The above equation can be interpreted as the HJI equation for a discounted Markovian... more Page 1. I102 The above equation can be interpreted as the HJI equation for a discounted Markovian decision problem. The solution of this discounted Markov decision process may be obtained by either successive approximation ...
HAL (Le Centre pour la Communication Scientifique Directe), 2011
The use of general descriptive names, registered names, trademarks, etc. in this publication does... more The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
The aim of this chapter is the study of structural properties of linear systems. Systems with tim... more The aim of this chapter is the study of structural properties of linear systems. Systems with time-varying coefficients are considered, both in the continuousand discrete-time cases. These two cases are merged into a general framework. This study is based on module theory. Let us briefly explain what a module is, in connection with the theory of differential and difference equations.
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