modelling analysis and verification of hybrid systems

... application of MATLAB to the analysis and design of control systems Presentations are limited to linear, time-invariant continuous time systems Chapters and include a great number of worked examples and ... types of control systems: (a) Man-made control systems (b) Natural, including biological-control systems (c) Control systems whose components are both man-made and natural ANALYSIS AND DESIGN OF ... magnitude of the sensitivity-function is made arbitrarily small 1.8 CONTROL SYSTEM ANALYSIS AND DESIGN OBJECTIVES Control systems engineering consists of analysis and design of control systems...

Ngày tải lên: 01/01/2014, 18:43

... love and admiration, SEMYON M MEERKOV Brief Contents Preface page xiii Introduction Stochastic Linearization of LPNI Systems 20 Analysis of Reference Tracking in LPNI Systems 66 Analysis of Disturbance ... turns out, Na and Ns are functions of the standard deviations, σu and σy , of u and y, respectively, that is, ˆ ˆ ˆ ˆ Na = Na (σu ) and Ns = Ns (σy ) Therefore, we refer to the system of Figure 0.2 ... devoted to analysis of quasilinear control systems from the point of view of reference tracking and disturbance rejection, respectively (problem P1) Chapters and also address tracking and disturbance...

Ngày tải lên: 23/03/2014, 15:20

... important and interesting results Analysis and computer simulations of mathematical models are important parts of understanding physical and biological phenomena The knowledge created in modeling, analysis, ... studied by Ricker and May [48] g Random processes, including the Law of Large Numbers and ergodic and other limit theorems [82] These and many other useful and interesting aspects of chaos are described ... matches one of the free frequencies of the problem, that is, one of the eigenvalues of A Subresonant forcing occurs when one of the frequencies of g matches an integer multiple of one of the free...

Ngày tải lên: 31/03/2014, 15:09

... important and interesting results Analysis and computer simulations of mathematical models are important parts of understanding physical and biological phenomena The knowledge created in modeling, analysis, ... studied by Ricker and May [48] g Random processes, including the Law of Large Numbers and ergodic and other limit theorems [82] These and many other useful and interesting aspects of chaos are described ... matches one of the free frequencies of the problem, that is, one of the eigenvalues of A Subresonant forcing occurs when one of the frequencies of g matches an integer multiple of one of the free...

Ngày tải lên: 24/04/2014, 16:50

... Cataloging-in-Publication Data [Analyse des systèmes linéaires/Commande des systèmes linéaires eng] Analysis and control of linear systems analysis and control of linear systems/ edited by Philippe de Larminat p cm ... Observability of linear and invariant systems 2.5.3 Case of partially observable systems 2.5.4 Case of partially controllable and partially observable systems 2.6 ... 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...

Ngày tải lên: 09/08/2014, 06:23

... 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 The alternation of slow and fast variations of product ... final value of the response at the end of time T, which is called time constant of the system The response reaches 0.63 K in T and 0.95 K in T 24 Analysis and Control of Linear Systems Figure ... 2π jf0 20 Analysis and Control of Linear Systems Table 1.1 sums up the features of a system’s transfer function, the existence conditions of its frequency response and the possibility of performing...

Ngày tải lên: 09/08/2014, 06:23

... 84 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 ... 3.2 and 3.3 The discretization of continuous-time systems and certain concepts of the sampling theory are dealt with in section 3.4 Discrete-Time Systems 83 3.2 Discrete signals: analysis and ... development of X (z) by polynomial division according to 86 Analysis and Control of Linear Systems the decreasing powers of z −1 or apply the method of deviations, starting from the definition of the...

Ngày tải lên: 09/08/2014, 06:23

... 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 numerous control ... illustrates the invariance properties of the various structures of these canonical forms (indices of controllability, of observability, finite and infinite zeros) and of the associated transformation ... and W t a basis of the canceller at the left of W (i.e a maximal solution of equation WtW = {0}), a basis of LV is obtained by directly preserving only the independent columns of LV A basis of...

Ngày tải lên: 09/08/2014, 06:23

... proximity of ν0 152 Analysis and Control of Linear Systems Figure 5.1 Typical power spectrum of an MA (left) or AR (right) model In the case of a single denominator (nc = 0), we talk of an AR ... [5.9] 144 Analysis and Control of Linear Systems On the other hand, the Fourier transform preserves the energy (Parseval theorem) Indeed, the energy of a continuous-time signal y(t) or of a discrete-time ... 142 Analysis and Control of Linear Systems A discrete-time deterministic signal y[k], k ∈ Z is, by definition, a sequence of complex numbers: y = y[k] k∈Z In short, we often speak of a discrete...

Ngày tải lên: 09/08/2014, 06:23

... 160 Analysis and Control of Linear Systems u (t ) = − K x(t ) + e(t ) [6.2] where K is an m × n matrix (Figure 6.1) and signal e(t ) represents the input of the looped system The equations of ... the result cannot be extended to the 162 Analysis and Control of Linear Systems case of multi-control systems As indicated in Chapter 2, the equations of state can be expressed in companion form: ... control, whereas the increase of ξ leads to better dynamics 164 Analysis and Control of Linear Systems Figure 6.2 Stabilization by pole placement 6.3 Reconstruction of state and observers 6.3.1 General...

Ngày tải lên: 09/08/2014, 06:23

... 196 Analysis and Control of Linear Systems in performing the roles of the procedure, in connection with a structure and behavior of components They are used for the design of procedure ... determining the value of x = τ2 /τ1 Calculating the numeric values of τ1 and τ2 with: τ1 = τsum 1+x τ2 = x τsum 1+x 1+x Inferring [7.46] 210 Analysis and Control of Linear Systems Similar method ... 214 Analysis and Control of Linear Systems recording of a specific response We need to be aware of the fact that it is essential to have a little, even very little, noise on the responses and, ...

Ngày tải lên: 09/08/2014, 06:23

... 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 such that the partitioned matrices are of size (m + n) × ◦ (m + n) This result is ... the integration of [8.1] is done from [8.5] The calculation of Φ and Γ is ˆ ˆ obtained via the estimation N of N Finally, the calculation of N goes through that of the upper bound of sampling interval ... poles are eigenvalues of M = In2 ⊗ A1 + AT ⊗ In1 , i.e the set of pairs λi + µj where λi and µj are the eigenvalues of A1 and A2 The stiff systems (ρ 100) are by nature systems which are difficult...

Ngày tải lên: 09/08/2014, 06:23

... equation of n order The roots of this equation are of strictly negative real part if and only if the terms of this first column of the table have the same sign and are not zero Statement of Routh’s ... number of unstable poles of equation [9.18] and hence of µ ( p ) β ( p) Figure 9.7 Contour and image of the Nyquist curve Contour C is chosen in such as way as to surround the poles of possible ... 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 Approach 261 Case Open loop...

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 ... 296 Analysis and Control of Linear Systems Figure 10.12 Bode graph with insufficient phase margin Figure 10.13 Bode graph in OL of the corrected system Synthesis of Closed Loop Control Systems ... 284 Analysis and Control of Linear Systems 10.1.1 Analysis of systems behavior 10.1.1.1 Static errors For a zero static error: –...

Ngày tải lên: 09/08/2014, 06:23

... degree of polynomial A We will assume that the concepts of polynomials division are known, as well as those of PGCD and PPCM of polynomials If G and L are respectively the PGCD and the PPCM of A and ... and R and thus5: number of unknown factors = ∂S + ∂R + A polynomial of degree n has n + coefficients [11.36a] 338 Analysis and Control of Linear Systems The number of equations is the number of ... neglected in the model 366 Analysis and Control of Linear Systems Figure 11.17 Evolution of sA Ao (⎯ο⎯) .of sAS ' Ao Am ⎛ ⎞ ⎟ Ao = ⎜ s + ⎜ To ⎟ ⎝ ⎠ and of B Am (⎯⎯) in the case of From these answers...

Ngày tải lên: 09/08/2014, 06:23

... ideas of the method, starting with the 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 ... the number of estimated values of the sequence 376 Analysis and Control of Linear Systems 12.2 Generalized predictive control (GPC) 12.2.1 Formulation of the control law The objective of this section ... j , J j are single solutions of Diophantus equations, which are obtained by equality of the inputs and output of transfer functions of equations [12.1] and [12.3] and they are solved recursively:...

Ngày tải lên: 09/08/2014, 06:23

... formulated in the standard form of Figure 13.1 408 Analysis and Control of Linear Systems Figure 13.1 Standard feedback diagram The quadripole G , also called a standard model, and feedback K are ... 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 associated ... observable part by y is solution of Let us give the idea of the equivalence proof of properties and 2., the equivalence of properties and resulting by duality Methodology of the State Approach Control...

Ngày tải lên: 09/08/2014, 06:23

... 14.5 Area of 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 ... Shift of a set of poles with minimum dispersion 464 Analysis and Control of Linear Systems EXAMPLE 14.4 To illustrate these points, let us take a set of models pertaining to the lateral side of ... mode ξi (t) does not have any effect on z k 452 Analysis and Control of Linear Systems 14.2.2.7 Summarization The analysis of the time behavior of a controlled system was done in the modal basis...

Ngày tải lên: 09/08/2014, 06:23

... 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 on inequalities [15.20.a, b, c] of ... [15.48] 500 Analysis and Control of Linear Systems a) Robustness of stability b) Robustness of performance Figure 15.10 Upper bounds of the structured single value 15.2.4 Evaluation of structured ... family and no longer on an unique pattern about which we know that it is not capable to represent the set of possible behaviors of a process 494 Analysis and Control of Linear Systems 15.2.1 Analysis...

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 ... Time-Variant Systems 531 16.5 Applications In this section, two types of usage of this algebra are presented in the field of modeling and control 16.5.1 Modeling One of the methods of signal and control ... 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) respectively; the transfer function of the system ∑ obtained by serializing ∑1 and...

Ngày tải lên: 09/08/2014, 06:23