Analysis and Control of Linear Systems - Chapter 0 pptx
Analysis and Control of Linear Systems - Chapter 0 pptx
... systems analysis and control of linear systems/ edited by Philippe de Larminat. p. cm. ISBN-13: 97 8-1 - 905 20 9-3 5-4 ISBN- 10: 1-9 05 20 9-3 5-5 1. Linear control systems. 2. Automatic control. I. Larminat, ... TJ2 20. A5313 200 6 629.8'32 dc22 200 603 3665 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 10: 1-9 05 20 9-3 5-5 ISBN ... 10: 1-9 05 20 9-3 5-5 ISBN 13: 97 8-1 - 905 20 9-3 5-4 Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire. x Analysis and Control of Linear Systems 8.3.2. Solving principle...
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Analysis and Control of Linear Systems - Chapter 1 pptx
... 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 1T11T2Module ... )21yupjfHpjf 40 Analysis and Control of Linear Systems 1.6.4. Laplace transforms of ordinary causal signals x(t) X(p) σ 0 convergence abscissa )0( δ 1 −∞ )( )0( nδ np −∞ 00 )( 01 )(<=≥=ttUttU ... unit-step response is: −⎛⎞⎛⎞⎜⎟=−+⎜⎟⎜⎟⎝⎠⎜⎟⎝⎠ 0 0() 1 1tTtit K eT Figure 1. 20. Unit-step response of the second order system ξ < 1 22 Analysis and Control of Linear Systems...
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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 ... 2πν 0 , then thepower spectrum is almost zero in the 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 ... product of transforms:(y1⊗ y2)=y1y2[5.9]152 Analysis and Control of Linear Systems Figure 5.1. Typical power spectrum of an MA (left)or AR (right) modelIn the case of a single...
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Analysis and Control of Linear Systems - Chapter 11 pptx
... ⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎡=⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎡⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎡∂∂∂∂∂∂∂∂∂C1 0 Y 0 X1 0 ABABAB11 01 01 01 01 00 cccyyxxx. 0 0a0b0a0b0abbabbaa0bb0aa 00 b00a####%#%#%#%###%#%#%#%#%#%#%""" ... ⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎣⎡−−+−−+−−+=⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎡−−−−−=−−−−−−11111111 00 00 1221 0 10 00 0. .00 0 10 0 01 0 00 AnnnnnnnnnnnnBρρσττσρρσττσρρσττσσσσσσ####%%####%%%####%%% [11.59] 11.4.3. Management of saturations 11.4.3.1. ... obtain: 5 .05 .0 35 .05 .0 222++=+=++=ssTssSssR Hence, the control verifies: YssCssUss )5 .05 .0( )5 .05 .0( )3(222++−++=+ By leaving on the left the term in U of highest degree and by dividing...
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Analysis and Control of Linear Systems - Chapter 12 pptx
... 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, ... function + ramp + parabola Step function 0 0 0 Ramp Cte ≠ 0 0 0 Parabola ∞ Cte ≠ 0 0 Table 12.1. Error psw − for a non-integrator system 12.3.5. Structure of the optimal predictor The predicted ... 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...
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Analysis and Control of Linear Systems - Chapter 13 pptx
... ()⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛=⎟⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎜⎝⎛⎟⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎜⎝⎛=∆ 0 0: 00 00 00 00 00 00 21212121212121212DCDCBBAIQRsGIQRsGooMCCccH Methodology of the State Approach Control 423 mode )(tm on )(tz ... (): 0 ee ssee ssWW WWesWW WWAB BAB ABGs C D D Ws WsCD CDCD ⇓ ⎡⎤⎢⎥⎢⎥⎡⎤⎢⎥⎢⎥⎢⎥==⎢⎥⎢⎥⎢⎥⎢⎥⎣⎦⎢⎥⎢⎥⎢⎥⎣⎦ 00 0 011212 00 0 011 1 11 1211112 00 0 02212211 1 11 12 00 ... space of the standard model )(sG can be directly deduced from those presumed minimal of )(sWe, )( 0 sG and )(sWs: ⎡⎤⎢⎥⎡⎤⎡⎤⎢⎥⎢⎥⎢⎥===⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦⎢⎥⎣⎦ 00 0 12 00 0 0 1 11 12 00 221():...
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Analysis and Control of Linear Systems - Chapter 3 pps
... stability of the system [3.16] without explicitly calculating the poles of H(q), by simple examination of coefficients naaa ,,,21" with the help of Table 3.4. 01 222 01 01 10 01 00 01 0 12 0 01 01 11 0 with:nnnnnnknnknnkknnknkaaa ... Theory and application of the z-transform, John Wiley, 1964. [LAR 02 ] DE LARMINAT P. (ed.), Commande des systèmes linéaires, Hermès, IC2 series, Paris, 200 2. 94 Analysis and Control of Linear Systems ... 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”...
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Analysis and Control of Linear Systems - Chapter 4 ppt
... ⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡=⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡−= 00 10 00 01 200 0 00 00 0 100 00 00 ccBA The general structure of matrices (Ac, Bc) in Brunovsky’s canonical form is the following: {}⎡⎤⎡⎤==⎢⎥⎢⎥⎢⎥⎣⎦⎣⎦ 0 {} 0 0cicinon ... Properties of Linear Systems 123 with: ⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎣⎡=⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎣⎡=1 0 0 0 , 00 000 100 00 0 0 100 0 0 10 ciciBA [4.33] Blocks Aci are of size εi×εi; ... of invariants: {(p-ai) kij} = {p-3}, {εi} = {2}, {ηi} = {1} and {νi} = {2}: ⎡⎤⎢⎥⎡⎤⎡⎤ ⎡⎤⎢⎥−= =− = = =⎢⎥⎢⎥ ⎢⎥⎢⎥⎣⎦⎣⎦ ⎣⎦⎢⎥⎣⎦ 00 0 00 0 10 1[] with [3], ,, 00 0 0 1 1 01 00 0KKabppppapbcdcpdEH...
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Analysis and Control of Linear Systems - Chapter 6 ppsx
... returns to 0, but at the 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 ... 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 ... indicated in Chapter 2, the equations of state can be expressed in companion form: )(1 0 0 0 )()(1 00 00 100 00 10 )()(11211tutxtxaaaatxtxnnnnn⎟⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎜⎝⎛+⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛⎟⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎜⎝⎛−−−−=⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−−##"%"##%#%"#...
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Analysis and Control of Linear Systems - Chapter 7 docx
... unit-step response given in Figure 7.6.1. Rise time is defined between instants t1 and t2such as s(t1)=s(t− 0 ) +0. 1 K ∆E,s(t2)=s(t− 0 ) +0. 9 K ∆E.226 Analysis and Control of Linear Systems Finally, ... K1N 10 1+12n1N 10 [7.21]222 Analysis and Control of Linear Systems iteration, unstable), interrupt the simulation and the calculation of sensitivity func-tions, hence of the gradient, ... from the point of view of calculation, in terms of linear regression (or linearized), i.e. it leads to a quadratic196 Analysis and Control of Linear Systems in performing the roles of the procedure,...
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