Analysis and Control of Linear Systems - Chapter 1 pptx

... Figures 1. 23, 1. 24, 1. 25 and 1. 26 illustrate the diagrams presenting the aspect of the frequency response for a second order system with different 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 ... 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. 2...

Ngày tải lên: 09/08/2014, 06:23

... systems analysis and control of linear systems/ edited by Philippe de Larminat. p. cm. ISBN -1 3 : 97 8 -1 -9 0520 9-3 5-4 ISBN -1 0 : 1- 9 0520 9-3 5-5 1. Linear control systems. 2. Automatic control. I. Larminat, ... 11 .5.4. Examples 363 11 .6. Conclusion 370 11 .7. Bibliography 370 xii Analysis and Control of Linear Systems Chapter...

Ngày tải lên: 09/08/2014, 06:23

... modern perspective”, Proceed- ings of the IEEE, vol. 69, no. 11 , p. 13 80 14 19, 19 81. [KWA 91] K WAKERNAAK H., SIVAN R., Modern Signals and Systems, Prentice-Hall, 19 91. [LAR 75] DE LARMINAT P., ... Prentice-Hall, 19 75. [PAP 71] P APOULIS A., Probabilités, variables aléatoires et processus stochastiques, Dunod, Paris, 19 71. 15 0 Analysis and Control of Linear Sy...

Ngày tải lên: 09/08/2014, 06:23

... on [11 .14 ]: ∂≤ ∂∂ − 1 Xmax{V,B(PU)} [11 .16 ] If P ≠ U, then: ∂−≥∂ 11 B(P U) B [11 .17 ] and since by construction: ∂<∂ 1 VB [11 .18 ] ∂∂ − ≥∂ 11 max{ V, B (P U)} B [11 .19 ] 340 Analysis and ... ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ −−+ −−+ −−+ = ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − − − − − = −−−− − − 11 11 111 1 0000 1 2 2 1 0 10 00 0. .00 0 10 0 01 0...

Ngày tải lên: 09/08/2014, 06:23

... plane, of the direct sensitivity functions d σ and complementary sensitivity functions c σ : )()()()()( )()()( 11 111 1 11 1 −−−−−− −−− +∆ ∆ = qRqBqqqSqA qqSqA d σ [12 .13 ] )()()()()( )()( 11 111 1 11 1 −−−−−− −−− +∆ = qRqBqqqSqA qRqBq c σ ... −−− ∆=− + 11 1 ()() ()() ()() r Sq ut Rq yt T q wt [12 .25] with, based on relations [12 .17 ] and [12 .19 ]: − −−−−−−− − =∆+ 1...

Ngày tải lên: 09/08/2014, 06:23

... ⎡⎤ ⎢⎥ ⎢⎥ ⎡ ⎤ ⎢⎥ ⎢ ⎥ ⎢⎥ == ⎢ ⎥ ⎢⎥ ⎢ ⎥ ⎢⎥ ⎣ ⎦ ⎢⎥ ⎢⎥ ⎢⎥ ⎣⎦ 00 0 0 11 2 12 00 0 0 11 1 11 12 11 112 00 0 0 2 212 2 11 1 11 12 00 0 21 2 21 00 0 0 (): : 00 ee ee ses ss es ses ss es ee WW WW WWW WW WW WWW ... matrix. Methodology of the State Approach Control 409 with: () () () () () () () () [] () [] . ,, , , 21 1 2 212 11 1 2 212 2 1 2 212 1 21 1 22 21 1 22 21 22...

Ngày tải lên: 09/08/2014, 06:23

... 2002. 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 ... T q T 1 1 − − = ∆ δ and operator )1( )1( 1 −+= − ∆ qqw D will be used sometimes. Discrete-Time Systems 99 In addition, if we note by 1d p and by 2d p the...

Ngày tải lên: 09/08/2014, 06:23

... EH 011 *1* 11 11 1 1 {0}, , iin AA AAA A [4 .18 ] +− − == ⇒ == 011 *1* 22 222 2 ,, iin HE HEAXA A AA A [4 .19 ] The regularity of the beam [pE-H] can be translated: ⊕= ** 12 , AAXi.e. += ** 12 ... eigenvalues of A appear (certain powers l ij being then equal to 0): 11 0 Analysis and Control of Linear Systems The object of this chapter is to describe cert...

Ngày tải lên: 09/08/2014, 06:23

... the condition of detectability by a careful choice of matrix Q. 16 2 Analysis and Control of Linear Systems case of multi -control systems. As indicated in Chapter 2, the equations of state can ... stronger control. 17 6 Analysis and Control of Linear Systems Figure 6.6. Stabilization by quadratic optimization 16 6 Analysis and Control of...

Ngày tải lên: 09/08/2014, 06:23

... K 2  N 20  1+ 1 2 n 2 N 20  [7.22] Equation [7 .15 ] thus becomes: Q e0 + Q 0 − K 1  N 10  1+ 1 2 n 1 N 10  = A 1 dN 1 dt = A 1 dn 1 dt [7.23] If: S 1 = 2 √ N 10 K 1 [7.24] then: Q 0 − n 1 S 1 = A 1 dn 1 dt [7.25] Based ... development of the square root leads to: Q s1 = K 1  N 10  1+ 1 2 n 1 N 10  [7. 21] 222 Analysis and Contro...

Ngày tải lên: 09/08/2014, 06:23