Analysis and Control of Linear Systems - Chapter 13 pptx

... )(tm and consequently the rejection of the 412 Analysis and Control of Linear Systems the zeros of transmission of )( 12 sG and )( 21 sG . In addition, the remaining invariant zero are non-controllable ... operation environment of the system. 422 Analysis and Control of Linear Systems Theorem 13. 3 ( 2 H REGULATOR AND INTERNAL MODEL).– let us s...

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... Congress 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 ... Philippe de Larminat. p. cm. ISBN -1 3: 97 8-1 -9 0520 9-3 5-4 ISBN-10: 1-9 0520 9-3 5-5 1. Linear control systems. 2. Automatic control. I. Larm...

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... values of ξ . 10 0 -1 0 -2 0 -3 0 0 -4 5 -9 0 -1 35 -1 80 1 T 1 1 T 2 Module (dB)Phase (degree) Figure 1.23. Bode diagram of a second order system with ξ ≥ 1 20 Analysis and Control of Linear Systems ... of Linear Systems Figure 1.19. Unit-step response of the second order system ξ ≥ 1 1= ξ : critical state. The roots of the deno...

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... 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 ... proximity of ν 0 . 142 Analysis and Control of Linear Systems A discrete-time deterministic signal y[k],k ∈Zis, by definition, a sequence of complex numbers: y =...

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... appearance of instability). Finally, in [11.89], the fact of hiding the oscillating poles of the process leads to a rejection of oscillating interference. 364 Analysis and Control of Linear Systems ... y A N u A N v o y o u += [11.62] 338 Analysis and Control of Linear Systems The number of equations is the number of rows in the Sylvester system and...

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... Consequently, this type of control favors the selection of short sampling periods and it proves to be well-adapted to the control of fast electro-mechanical systems (machine-tool, high-speed machining, ... regulator of this restated problem in terms of error signals: )()()()( 11 tqRtqS yoptu εε −− −= [12.24] 392 Analysis and Control of Linear Systems Hence,...

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... 104 Analysis and Control of Linear Systems Figure 3.5. Bode diagram of the continuous system and its discretization 3.4.5. The problem of sub-sampling Let us consider the case of a “standardized” ... i n is the multiplicity order of i λ and i th the eigenvalue of A. 5 A canonical form called controllable companion. 88 Analysis and Control of L...

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... eigenvalues of A appear (certain powers l ij being then equal to 0): 110 Analysis and Control of Linear Systems The object of this chapter is to describe certain structural properties of linear systems ... and intersection of sub-spaces (the sum and intersection of two A-invariant sub-spaces are A-invariant). Consequently, for any L ⊂ X sub-space, there...

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... the condition of detectability by a careful choice of matrix Q. 162 Analysis and Control of Linear Systems case of multi -control systems. As indicated in Chapter 2, the equations of state can ... at the expense of a stronger control. 176 Analysis and Control of Linear Systems Figure 6.6. Stabilization by quadratic optimization 166 Analysis a...

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... from the point of view of calculation, in terms of linear regression (or linearized), i.e. it leads to a quadratic 196 Analysis and Control of Linear Systems in performing the roles of the procedure, ... [7.44] Two parameters must be identified: the static gain of system K and the time con- stant τ. 216 Analysis and Control of Linear Systems so-called “sha...

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