compartment graphs and linear systems

Ngày tải lên: 01/02/2015, 23:46

... where K B and K λ are the matrices representing KerB and Ker(A∗ − λI), and the formula of rAB is the result obtained in [4] By the definitions, it is clear that rAB ≤ min{rA , rB }, and the strict ... obtain Controllability Radii and Stabilizability Radii of Time-Invariant Linear Systems rAB = 499 √ 2, rA = 2, rB = 2, rF = References John S Bay, Fundamentals of Linear State Space System, McGraw-Hill, ... Between controllable and uncontrollable, System & Control Letters (1984) 263–264 N K Son and N D Huy, Maximizing the stability radius of discrete-time linear positive system by linear feedbacks,...

Ngày tải lên: 06/08/2014, 05:20

... and linear discrete systems 2.4 Controllability of systems 2.4.1 General definitions 2.4.2 Controllability of linear and invariant systems ... chapters (1 and 2) Discrete-time systems are, for more clarity, explained in Chapter Chapter explains the structural properties of linear systems Chapter xvi Analysis and Control of Linear Systems ... Designs and Patents Act 1988 Library of Congress Cataloging-in-Publication Data [Analyse des systèmes linéaires/Commande des systèmes linéaires eng] Analysis and control of linear systems analysis and...

Ngày tải lên: 09/08/2014, 06:23

... continuous systems which will have only one input and one output, modeled by continuous signals Chapter written by Dominique BEAUVOIS and Yves TANGUY 4 Analysis and Control of Linear Systems 1.2 ... overflow and the terms ω t r ( t r is the establishment time at 5%) and ω t m according to the damping ξ Figure 1.21 ω0 tr and ω0 tm according to the damping ξ 30 Analysis and Control of Linear Systems ... ) (t ) 16 Analysis and Control of Linear Systems By supposing that x(t ) and y(t ) are continuous functions defined from −∞ to +∞ , continuously differentiable of order m and n, by a two-sided...

Ngày tải lên: 09/08/2014, 06:23

... distinct parts The analysis and manipulation of signals and discrete-time systems are presented in sections 3.2 and 3.3 The discretization of continuous-time systems and certain concepts of the ... Analysis and Control of Linear Systems 3.2.2 Delay and lead operators The concept of an operator is interesting because it enables a compact formulation of the description of signals and systems ... 82 Analysis and Control of Linear Systems A ∈ R nxn , B ∈ R nxm , C ∈ R pxn , D ∈ R pxm , ∈ R pxp , bi ∈ R pxm [3.3] If equations [3.1] and [3.2] can represent intrinsically discrete systems, such...

Ngày tải lên: 09/08/2014, 06:23

... spaces, linear applications Let X and Y be real vector spaces of finite dimension and V ⊂ X and W ⊂ Y, two sub-spaces Let L: X → Y be a linear application LV designates the image of V by L and L−1W ... 110 Analysis and Control of Linear Systems The object of this chapter is to describe certain structural properties of linear systems that condition the resolution of ... satisfied, we say that A and A’ are equivalent This relation is also written T-1[pI-A]T = [pI-A’] and thus A and A’ are equivalent matrices if and only if the beams [pI-A] and [pI-A’] are equivalent...

Ngày tải lên: 09/08/2014, 06:23

... integral is the product of transforms: (y1 ⊗ y2 ) = y1 y2 [5.9] 144 Analysis and Control of Linear Systems On the other hand, the Fourier transform preserves the energy (Parseval theorem) Indeed, ... with the first and second order moments, i.e the mean and the autocorrelation function A discrete-time random signal y[k], k ∈ Z is called stationary in the broad sense if its mean my and its autocorrelation ... instant k and the signal at instant k + κ It is traditional to remain limited only to the mean and the autocorrelation function in order to characterize a stationary random signal and this even...

Ngày tải lên: 09/08/2014, 06:23

... listed in section 6.1 can thus be applied here by replacing matrices A and B (or F and G ) by AT and C T (or F T and CT) and the state feedback K by LT Based on Theorem 6.1, we infer that matrix ... [6.35] are verified and also if: ⎧( F , G ) is stabilizable ⎨ ⎩ ( H , F ) is detectable [6.41] 174 Analysis and Control of Linear Systems there is a unique matrix P , symmetric and positive semi-defined, ... between stabilizability and detectability, we immediately obtain the following result 178 Analysis and Control of Linear Systems THEOREM 6.4.– if conditions [6.52] are verified and also if: ⎧( AT...

Ngày tải lên: 09/08/2014, 06:23

... one hand, the problem of identification (and also the problem of simulation and control) is made much easier by the computing tool and is already well known in data analysis (linear or non -linear ... response Graphs to use The two graphs to use are parameterized by damping ζ Their use is described below, based on the unit-step response in Figure 7.2 206 Analysis and Control of Linear Systems ... fact be used on non -linear representations and that is why we also use it in order to parameterize the knowledge methods mentioned above 198 Analysis and Control of Linear Systems 7.2 Modeling...

Ngày tải lên: 09/08/2014, 06:23

... speed and accuracy accessible in simulation 8.2 Standard linear equations 8.2.1 Definition of the problem We will adopt the notations usually used to describe the state forms and linear dynamic systems ... elegant and robust solution consists of obtaining simultaneously Φ and Γ through the relation: Φ Γ A B h [8.7] = exp I 0 230 Analysis and Control of Linear Systems The sizes of blocks and I are ... B and C are constant and verify A ∈ Rn×n , B ∈ Rn×m As for X and U , their size is given by X ∈ Rn×m and U ∈ Rm×m To establish the solution of these equations, we examine the free state, and...

Ngày tải lên: 09/08/2014, 06:23

... E and ω : E0 = vM γM and ω = γM vM [9.53] 278 Analysis and Control of Linear Systems hence the condition: µ1 µ β p= j γM vM ≤ ε d max vM [9.54] γM We note that this condition is necessary and, ... with this latter transformation and we will study the case of open loop stable systems, that of integrator systems and finally the case of open loop unstable systems Analysis by Classic Scalar ... reaches –180° These margins, noted by ∆φ and ∆G , are represented in Bode, Nyquist and Black-Nichols planes in Figure 9.13 268 Analysis and Control of Linear Systems Figure 9.13 Bode plane (a), Nyquist...

Ngày tải lên: 09/08/2014, 06:23

... Points A and B are thus the separations of cases and Synthesis of Closed Loop Control Systems Between A and B: µ1 µ µ β > and B: µ1 µ µ β < µ1 µ β C µ1 µ β C 317 , i.e µ C > (1st case) and outside ... frequencies ω and ) and therefore in order to obtain the desired stability, a phase lead term τ1 must be added The corrected OL is represented in Figure 10.24 306 Analysis and Control of Linear Systems ... maintain the requirements of precision and stability They are inserted into a looped system as represented in Figure 10.3 288 Analysis and Control of Linear Systems Figure 10.3 Corrector in a looped...

Ngày tải lên: 09/08/2014, 06:23

... PGCD and PPCM of polynomials If G and L are respectively the PGCD and the PPCM of A and B (A, B, G and L ∈ℜ[x]), we will write: G = A ∧ B and L = A ∨ B 330 Analysis and Control of Linear Systems ... A' S + B' R D [11.24] and of course A' S + B ' R ≠ Am Ao We suppose that: C= Nc + − Dc Dc and D = Nd + − Dd Dd [11.25] 334 Analysis and Control of Linear Systems where Nx and Dx are polynomials ... hand, according to [11.2(b)], since B1 divides Ao and B it also divides AS However, A and B are prime between themselves by hypothesis and − therefore B1 divides S and S1 (since B1 is stable and...

Ngày tải lên: 09/08/2014, 06:23

... the one hand the model corresponding to the asymptotical behavior of the closed internal loop and on the other hand the model issued from the external 386 Analysis and Control of Linear Systems ... Nu and: ⎨ y ε u (t + j ) = ∆u (t + j ) − ∆u r (t + j ) ⎩ Based on relations [12.16], [12.17] and [12.18], we notice that, on the one hand, the increments of control errors and, on the other hand, ... form of the model, the quadratic criterion and up to the examination of adjustment parameters The formalism and the 390 Analysis and Control of Linear Systems calculation necessary to the analytical...

Ngày tải lên: 09/08/2014, 06:23

... versus iterative methods For linear stationary systems 402 Analysis and Control of Linear Systems In fact, the biggest difficulty is not in the choice of the standard used (working in H ∞ would ... Definition of the standard H2 problem [DOY 89] Any closed loop control can be formulated in the standard form of Figure 13.1 408 Analysis and Control of Linear Systems Figure 13.1 Standard feedback ... response g(⋅) = TL−1 (⋅) u G(s) y Standard whose physical importance in terms of energy is obvious 404 Analysis and Control of Linear Systems The “H2 standard” of the input-output operator...

Ngày tải lên: 09/08/2014, 06:23

... the complex plane corresponding to the desired performances and to the constraints on the bandwidth 460 Analysis and Control of Linear Systems 14.4.2 Choice of eigenvectors of the closed loop The ... (respectively equal to a two degree step function and to a 20 degree step function) 468 Analysis and Control of Linear Systems Figure 14.10 Decouplings between β and φ by output static feedback We can ... Notes in Control and Information Sciences 224, p 22–32, 1997 [HAM 89] HAMDAN A.M.A., NAYFEH A.H., “Measures of modal controllability and observability for first and second-order linear systems , Journal...

Ngày tải lên: 09/08/2014, 06:23

... with 498 Analysis and Control of Linear Systems K ( s ) = ) We easily identify the matrices ∆ (s ) and H (s ) of the general diagram in Figure 15.7 by considering v = (v1 v v d )T and z = (z1 z z ... ) T ⎟ ⎜ ⎟⎜ − γ I ne ⎟ ⎝ ⎠ ⎞ ⎟< I ne ⎟ ⎠ 512 Analysis and Control of Linear Systems where N R and N S form a base of cores of ( Bu T Deu T ) and (C y Dyw ) respectively Inequalities [15.70], calculated ... ) ⎟ ⎠ ⎝ and we shall suppose as verified the following hypotheses: H8) D yu = ; H9) ( A, Bu ) can be stabilized and (C y , A) can be detected [15.73] 514 Analysis and Control of Linear Systems...

Ngày tải lên: 09/08/2014, 06:23

... λ + t and H (λ ) = λ−1 so ∑ y(t ) = u(t ) 1 530 Analysis and Control of linear Systems 16.4.2 Parallel systems Let ∑1 and ∑ be two systems of transfer functions H1 (λ) = Q1 (λ )−1 P (λ) and H ... transfer function of associated systems, either serially or in parallel 16.4.1 Serial systems Let ∑1 and ∑ be two systems of transfer functions H1 (λ) = Q1 (λ )−1 P (λ) and H (λ) = Q2 (λ)−1 P2 (λ) ... (a + b) = a + b and ab = a b + a b Linear Time-Variant Systems 523 when coefficient an (t ) is equal to 1, polynomial P(λ ) is standardized The set Π(λ ) including addition and multiplication...

Ngày tải lên: 09/08/2014, 06:23

... randomized algorithms was proposed [50], which utilizes random search and uncertainty randomization for probabilistic robustness analysis and controller design In [51], the authors studied randomized ... analysis and distribution control of stochastic systems under the framework of gPC theory In particular, we assume that the systems are linear, Chapter Introduction time-invariant and contain random ... analysis and control of systems with random parametric uncertainties The subsequent contents of this thesis are organized as follows: Chapters and study the stability analysis of systems with random...

Ngày tải lên: 10/09/2015, 09:25

... performance and robustness of model predictive control (MPC) controllers for (1) constrained linear systems with bounded disturbances (LBD systems) ; (2) constrained piecewise linear systems with ... Finite Horizon KKT Karush-Kuhn-Tucker LBD systems Linear Systems with Bounded Disturbances LDI Linear Difference Inclusion LMI Linear Matrix Inequality LP Linear Programming MPC Model Predictive ... systems in general and piecewise linear (PWL) or piecewise affine (PWA) systems in particular The rising interest in this class of constrained PWL/PWA systems is due to the fact that many nonlinear...

Ngày tải lên: 11/09/2015, 14:29