Analysis and Control of Linear Systems - Chapter 4 ppt
Analysis and Control of Linear Systems - Chapter 4 ppt
... the use of rollouts and in particular the fixed poles and the remaining degrees of freedom, we can mention [MAL 93, MAL 97] and [MAR 94, MAR 99]. 126 Analysis and Control of Linear Systems ... [], and ppp−−−⎡⎤⎡ ⎤−−⎢⎥⎢ ⎥−−⎣⎦⎣ ⎦IA IA BIA BCC0 [4. 13] 128 Analysis and Control of Linear Systems 4. 2.5. Notes and references The general context of matrix pencils, and particularly ... Analysis and Control of Linear Systems []}{][ 4 11inMMMpdiagpp−−−=−=− BAICBAIC 44 where ni, i = 1 to r is the size of each block in part 4 which is in controllable and observable...
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Analysis and Control of Linear Systems - Chapter 0 pptx
... interpretation of grammians 44 0 13.6 .4. Zeros of a multivariable system 44 0 13.6.5. Standardization of a system 44 1 13.7. Bibliography 44 1 Chapter 14. Multi-variable Modal Control 44 5 Yann LE ... GORREC and Jean-Francois MAGNI 14. 1. Introduction 44 5 14. 2. The eigenstructure 44 6 14. 2.1. Notations 44 6 14. 2.2. Relations among signals, modes and eigenstructures 44 8 14. 3. Modal analysis 45 3 ... of state 44 2.1.2. Equations of state and equations of measurement for continuous systems 46 2.1.3. Case of linear systems 47 2.1 .4. Case of continuous and invariant linear systems 48 2.2....
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Analysis and Control of Linear Systems - Chapter 1 pptx
... 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. 100 -1 0 -2 0 -3 00 -4 5 -9 0 -1 35 -1 801T11T2Module ... diagram of a second order system with ξ ≥ 1 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 ... of Linear Systems Figure 1.19. Unit-step response of the second order system ξ ≥ 1 1=ξ: critical state. The roots of the denominator of the transfer function are real and merged, and...
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Analysis and Control of Linear Systems - Chapter 5 pptx
... 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 ... admits a zero of a module close to 1 and of argument 2πν0, then thepower spectrum is almost zero in the proximity of ν0. 142 Analysis and Control of Linear Systems A discrete-time deterministic ... e[k].Signals: Deterministic and Statistical Models 1535 .4. Modeling of LTI systems and ARMAX modelingLet us take a linear time-invariant (LTI) system, of impulse response g. Theresponse of this system...
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Analysis and Control of Linear Systems - Chapter 11 pptx
... appearance of instability). Finally, in [11.89], the fact of hiding the oscillating poles of the process leads to a rejection of oscillating interference. 3 64 Analysis and Control of Linear Systems ... [11.17] and since by construction: ∂<∂1VB [11.18] ∂∂ − ≥∂11max{ V, B (P U)} B [11.19] 340 Analysis and Control of Linear Systems Figure 11.2. Choice of the degrees of Am and Ao’ ... yANuANvoyou+= [11.62] 338 Analysis and Control of Linear Systems The number of equations is the number of rows in the Sylvester system and thus: number of equations = 1om+∂+∂ AA [11.36b]...
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Analysis and Control of Linear Systems - Chapter 12 pptx
... regulator of this restated problem in terms of error signals: )()()()(11tqRtqSyoptuεε−−−= [12. 24] 392 Analysis and Control of Linear Systems Hence, the calculation of the future control ... [12.19] Figure 12 .4 sums up the principle of this structure with reference models [IRV 86]. Figure 12 .4. Principle of GPC/MRM algorithm 3 94 Analysis and Control of Linear Systems 12.3.7. ... ∑==+bnkkbkjutjtu1 )( )()(µ [12 .44 ] 378 Analysis and Control of Linear Systems 12.2.1 .4. Synthesis of the equivalent polynomial RST regulator The minimization of the criterion is based on writing...
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Analysis and Control of Linear Systems - Chapter 13 pptx
... )(tm and consequently the rejection of the 41 2 Analysis and Control of Linear Systems the zeros of transmission of )(12sG and )(21sG . In addition, the remaining invariant zero are non-controllable ... operation environment of the system. 42 2 Analysis and Control of Linear Systems Theorem 13.3 (2H REGULATOR AND INTERNAL MODEL).– let us suppose satisfied the hypotheses of the generalized ... state-based control methodology which is largely inspired by the “standard state control suggested by de Larminat [LAR 00]. Chapter written by Philippe CHEVREL. 40 4 Analysis and Control...
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Analysis and Control of Linear Systems - Chapter 16 ppt
... 395, 40 0, 40 1, 41 4- 4 16, 43 6, 44 5, 47 3, 47 6, 47 9 -4 82, 48 5, 49 3, 49 5, 500, 506 Routh criterion 285, 265, 266 S Shannon condition 101 signal continuous-time 4, 81, 100, 142 , 144 , 148 deterministic ... loop closed 25 3-2 58, 260, 26 4- 2 67, 269, 280, 281, 28 3-2 86, 309, 3 24, 332, 382, 390, 40 8, 40 9, 44 9, 45 8 -4 60, 46 3, 46 5, 47 2, 47 3, 47 5, 48 5, 49 9, 503, 533 open 253, 2 54, 256, 25 8-2 65, 272, 273, ... 212, 2 14, 244 , 24 6-2 48 , 2 54, 255, 25 7-2 61, 263, 269, 270, 278, 280, 281, 2 84, 285, 293, 297, 299, 303, 306, 307, 310, 31 3-3 16, 319, 322, 3 24, 376, 377, 380, 48 2, 48 3, 48 5, 49 4, 49 6, 49 7, 506,...
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Analysis and Control of Linear Systems - Chapter 3 pps
... 1 04 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” ... Theory and application of the z-transform, John Wiley, 19 64. [LAR 02] DE LARMINAT P. (ed.), Commande des systèmes linéaires, Hermès, IC2 series, Paris, 2002. 94 Analysis and Control of Linear Systems ... the γ-operator”, Automatica, vol. 34, no. 11, p. 145 5-1 45 7, 1998. 96 Analysis and Control of Linear Systems 3.3 .4. Transfer function and frequency response Let us consider a stable system...
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Analysis and Control of Linear Systems - Chapter 6 ppsx
... expense of a stronger control. 176 Analysis and Control of Linear Systems Figure 6.6. Stabilization by quadratic optimization 166 Analysis and Control of Linear Systems Figure 6 .4. Structure ... 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 ... 1 74 Analysis and Control of Linear Systems there is a unique matrix P, symmetric and positive semi-defined, solution of the following equation (called discrete...
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