Analysis and Control of Linear Systems - Chapter 15 pot

... point of Nyquist plot of the equalized system and the critical point –1. 500 Analysis and Control of Linear Systems a) Robustness of stability b) Robustness of performance Figure 15. 10. ... ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ 22 22 11 11 9.1 1.0 9.1 2 KK KK KK KK KK KK DC BA DC BA DC BA δδ [15. 80] 512 Analysis and Control of Lin...

Ngày tải lên: 09/08/2014, 06:23

... 2 a n-1 a n-3 a n-5 … 3 b 1 =a n-2 -a n a n-3 /a n-1 b 2 =a n-4 -a n a n-5 /a n-1 b 3 =a n-6 -a n a n-7 /a n-1 … 4 c 1 =a n-3 -b 2 a n-1 /b 1 c 2 =a n-5 -b 3 a n-1 /b 1 ... study the case of open loop stable systems, that of integrator systems and finally the case of open loop unstable systems. 270 Analysis and Control of Linear Systems We...

Ngày tải lên: 09/08/2014, 06:23

... order 493 15. 2. The µ -analysis 493 15. 2.1. Analysis diagram and structured single value 495 15. 2.2. Main results of robustness 495 15. 2.3. Example 496 vi Analysis and Control of Linear Systems ... Congress Cataloging-in-Publication Data [Analyse des systèmes linéaires/Commande des systèmes linéaires. eng] Analysis and control of linear systems anal...

Ngày tải lên: 09/08/2014, 06:23

... 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...

Ngày tải lên: 09/08/2014, 06:23

... 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” ... polynomial of an order equal to 1− i n , where i n is the multiplicity order of i λ and i th the eigenvalue of A. 5 A canonical form called controllable...

Ngày tải lên: 09/08/2014, 06:23

... 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...

Ngày tải lên: 09/08/2014, 06:23

... 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 =...

Ngày tải lên: 09/08/2014, 06:23

... 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...

Ngày tải lên: 09/08/2014, 06:23

... 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...

Ngày tải lên: 09/08/2014, 06:23

... order, the 242 Analysis and Control of Linear Systems Consequently, the field of absolute stability of multi-interval methods (implicit or not depending on the value of β 0 ) is the set of µ ∈ C so ... desired and to perform the corre- sponding substitutions. Let us take the example of the classic PID regulator. Let e(t) 230 Analysis and Control of Linear Sys...

Ngày tải lên: 09/08/2014, 06:23