frequency response of linear systems

... Annals of Mathematics, 160 (2004), 1141–1182 Isomonodromy transformations of linear systems of difference equations By Alexei Borodin Abstract We introduce and study “isomonodromy” transformations of ... note, first of all, that it suffices to provide a proof if one of the κi ’s is equal to ±1 and one of the δj ’s is equal to ∓1 with all other κ’s and δ’s equal to zero The proof will consist of several ... If the ratios of eigenvalues of A0 are not real then Theorem 3.9, Lemma 4.2, and Proposition 4.4 provide a proof of Theorem 4.5 However, our goal is to provide an independent proof of this theorem,...

Ngày tải lên: 14/02/2014, 17:20

... eigenvalue of B Proof As in the proof of Theorem 2, a and b are equivalent For < μ < 1, denote μI − μ B by B μ Suppose now that a holds Let λ be an eigenvalue of B Then μ 1− μ λ is an eigenvalue of ... which approaches to ∞ as k → ∞ This completes the proof We now consider applications of preceding theorems to approximation of solution of a linear system Ax b, where A ∈ Mn and b a given vector ... The index of the eigenvalue of Q−1 A is the R Q−1 A −1 index of eigenvalue of B I − Q A Thus by Lemma 5, Cn Q−1 R A ⊕ N A For every vector v ∈ Cn , let v r and v n denote the component of v in...

Ngày tải lên: 21/06/2014, 20:20

... variability of the behavior of the processes, more than from their possible non-linearity It is necessary to know the basics of linear automated systems before learning about the theory of non -linear systems ... in terms of operator 3.3.4 Transfer function and frequency response 3.3.5 Time response of basic systems 3.4 Discretization of continuous-time systems ... Analysis and control of linear systems analysis and control of linear systems/ edited by Philippe de Larminat p cm ISBN-13: 978-1-905209-35-4 ISBN-10: 1-905209-35-5 Linear control systems Automatic...

Ngày tải lên: 09/08/2014, 06:23

... transform of the impulse response, the frequency response of the system considered 1.4.7.2 Existence conditions of a frequency response The frequency response is the Fourier transform of the impulse response ... 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 a harmonic ... 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...

Ngày tải lên: 09/08/2014, 06:23

... 94 Analysis and Control of Linear Systems NOTE 3.3.– the class of rational systems that can be described by [3.16] or [3.18] is a sub-class of DLTI systems To be certain of this, let us consider ... 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 ... 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 The manipulation...

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 problems ... 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 L–1W is ... indices per rows of the observability beam are exactly equal to the observability indices of the 124 Analysis and Control of Linear Systems pair (C, A) The finite elementary divisors of the observability...

Ngày tải lên: 09/08/2014, 06:23

... unknown white noise of spectrum q, g the impulse response of the system and h the impulse response of the shaper filter We suppose that h and g are the impulse responses of the systems with rational ... Statistical Models 153 5.4 Modeling of LTI systems and ARMAX modeling Let us take a linear time-invariant (LTI) system, of impulse response g The response of this system at the known deterministic ... 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...

Ngày tải lên: 09/08/2014, 06:23

... 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: ⎛ x1 (t ... Control of Linear Systems Figure 6.5 Observer by pole placement Figure 6.5 shows the evolution of the two state variables in response to the initial condition x(0) = (1 1)T and the evolutions of the ... 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 looped...

Ngày tải lên: 09/08/2014, 06:23

... 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, irrespective of everything, ... view of the control, we can use direct methods based on the use of experimental recordings Two methods are available: the use of the harmonic response of the system or the analysis of time responses ... 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 monitoring,...

Ngày tải lên: 09/08/2014, 06:23

... 228 Analysis and Control of Linear Systems 8.1.1 About linear equations The specific techniques of linear differential equations are fundamentally exact integration ... 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 ... observations Through an extension of the notations introduced at the 236 Analysis and Control of Linear Systems beginning of this chapter, we will deal with equations of the form: ◦ x (t) = f (x,...

Ngày tải lên: 09/08/2014, 06:23

... Control of Linear Systems Figure 9.3 shows, in Bode plane, the approximate trace (in full line), of the gain curve of the closed loop frequency response Figure 9.3 Approximate trace of the closed ... percentage Figure 9.5 (a) Time response in CL and (b) frequency response in CL 258 Analysis and Control of Linear Systems When the system has good damping, let ξ be the value of the damping coefficient ... circle of radius ε , p = ε e jθ (Figure 9.9c) The image of the ray ] + , + ∞ [ is the trace of the frequency response in open loop covered in the direction of increasing ω When ω → + , the gain of...

Ngày tải lên: 09/08/2014, 06:23

... irrespective of 286 Analysis and Control of Linear Systems the frequency For any frequency sinusoidal input in the bandwidth, we can then consider that the output is a faithful image of the input ... second order, we connect this concept of frequency response resonance of the closed loop to the damping coefficient ξ of the poles and hence to the phase margin of the open loop ξ ∆Φ in degrees Resonance ... 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 297 Since...

Ngày tải lên: 09/08/2014, 06:23

... Influence of the choice of the degree of Ao on u/n 11.5.3 Choice of the dynamics of Am and Ao Section 11.5.1 shows the influence of the dynamics of these polynomials on the performances of corrected ... constant of 0.5 s 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 ... 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 rows in the...

Ngày tải lên: 09/08/2014, 06:23

... 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 ... control of robots arms, of monitoring the temperature profile of the applications in home automation, etc 12.1.2 Explicit prediction of future behavior The method requires the definition of a numerical ... Analysis and Control of Linear Systems on the horizon of some points beyond the present moment) This constraint which makes it possible to make good use of all the resources of the method, necessarily...

Ngày tải lên: 09/08/2014, 06:23

... used to talk of direct methods 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 ... interesting interpretation of standard H of G (s ) : = ⎜ ⎟ is as follows ⎝ C 0⎠ Let B•1, B• , B• m be the columns of B Let y Li be the free response of the system on the basis of the initial condition ... non-linearities (criterion of the circle [SAF 80]) and a certain type of dynamic uncertainties5 These properties are obtained at the beginning of the process Figure 13.4 Analysis of robustness of...

Ngày tải lên: 09/08/2014, 06:23

... 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 ... 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 ... is of size m, it is possible to impose m − decoupling constraints (number of rows of E0 and F0 ) 14.4.2.2 Considering the insensitivity of eigenvalues The concept of insensitivity consists of...

Ngày tải lên: 09/08/2014, 06:23

... 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 single ... the looping of an invariant system of transfer matrix K (s ) and of a response of matrix Θ(t ) (Figure 15.15) Robust H∞/LMI Control 513 Figure 15.15 Structures of the system and of the corrector ... of τ in dotted line): we see that stability is ensured for any value of τ less than 0.2 Figure 15.6 Determination of a bound value of the neglected time constant 488 Analysis and Control of Linear...

Ngày tải lên: 09/08/2014, 06:23

... and Control of linear Systems Generally, the existence of the Euclidian division implies the existence of the RHD [ORE 33] 16.1.3 Explicit formulation of RLCM Based on all the factors of the Euclidian ... Linear Time-Variant Systems 529 16.4 Algebra of non-stationary linear systems A major interest in the transfer function is due to the possibility of easily calculating the transfer function of ... 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 (λ) = Q2 (λ)−1 P2 (λ) respectively; the transfer function of the...

Ngày tải lên: 09/08/2014, 06:23

... List of Figures List of Figures 2.1 2.2 2.3 2.4 2.5 2.6 Uniform Distribution: Range of x1 with randomly generated samples of ∆ Uniform Distribution: Range of x2 with randomly generated samples of ... function of r2 143 Plot of trajectories for the gPC coefficients of u1 (t, ∆) in Subsystem 145 Plot of trajectories for the gPC coefficients of u2 (t, ∆) in Subsystem 146 Plot of ... set of real numbers Rn set of n-dimensional real vectors R+ set of non-negative real numbers Rω set of infinite-dimensional real vectors N the set of all natural numbers including or the set of...

Ngày tải lên: 10/09/2015, 09:25

... RESPONSE OF YARN SYSTEMS TO IMPACT LOADING KOH CHIEN-PING, ADRIAN (BEng (Hons), National University of Singapore) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ... Verification of Composite Yarn Material Parameters 164 6.3 Simulation of Impact Response of Spectra® 903 Fabric 167 6.3.1 Assignment of Failure Regions 167 6.3.2 Prevention of Excessive ... strength of a highly oriented polymer is influenced by the stiffness of the links, the number of links per unit cross-sectional area and the extent of the network of links 15 The deficiency of the...

Ngày tải lên: 14/09/2015, 14:06