Mechanical design handbook measurement, analysis, and control of dynamic systems
Analysis and Control of Linear Systems - Chapter 0 pptx
... 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 Linear control systems Automatic control I Larminat, Philippe de TJ2 20. A5313 200 6 ... 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 13: 97 8-1 - 905 20 9-3 5-4 ... 96 98 99 100 101 102 103 104 105 107 107 Chapter Structural Properties of Linear Systems Michel MALABRE 109 4.1 Introduction: basic tools for a structural analysis of systems ...
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Analysis and Control of Linear Systems - Chapter 1 pptx
... values of ξ 10 -1 0 -2 0 Phase (degree) -3 0 -4 5 -9 0 -1 35 -1 80 T1 T2 Figure 1. 23 Bode diagram of a second order system with ξ ≥ 32 Analysis and Control of Linear Systems Figure 1. 24 Bode diagram of ... ) πfT0 41 42 Analysis and Control of Linear Systems 1. 7 Bibliography [AZZ 88] D’ÀZZO J.J., HOUPIS C.H., Linear Control System Analysis and Design, McGraw-Hill, 19 88 (3rd edition) [BAS 71] BASS ... = 4.8 T The gaps δ G and δφ between the real curves and the closest asymptotic plots are listed in the table of Figures 1. 17 and 1. 18 26 Analysis and Control of Linear Systems ω 8T 4T 2T T T...
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Analysis and Control of Linear Systems - Chapter 3 pps
... parts The analysis and manipulation of signals and discrete-time systems are presented in sections 3. 2 and 3. 3 The discretization of continuous-time systems and certain concepts of the sampling ... rows of the table ( a0 , b0 , c0 , etc.) are all strictly positive 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] ... 82 Analysis and Control of Linear Systems A ∈ R nxn , B ∈ R nxm , C ∈ R pxn , D ∈ R pxm , ∈ R pxp , bi ∈ R pxm [3. 3] If equations [3. 1] and [3. 2] can represent intrinsically discrete systems, ...
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Analysis and Control of Linear Systems - Chapter 4 ppt
... 110 Analysis and Control of Linear Systems The object of this chapter is to describe certain structural properties of linear systems that condition the resolution of numerous control problems ... Journal of Control, vol 72, no 15, p 139 2-1 40 1, 1999 [MOR 73] MORSE A.S., “Structural invariants of linear multivariable systems , SIAM Journal of Control & Optimization, vol 11, p 44 6 -4 65, 1973 ... [4. 14] From the point of view of terminology, the pi singularities are called eigenvalues of A, (internal) poles of the dynamic system [4. 12] and zeros of the beam [pI-A] The companion form of...
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Analysis and Control of Linear Systems - Chapter 5 pptx
... zero of a module close to and of argument 2π ν0 , then the ˘ power spectrum is almost zero in the proximity of ν0 152 Analysis and Control of Linear Systems Figure 5. 1 Typical power spectrum of ... y2 [5. 9] 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 ... transform of the autocorrelation function and the two characterizations defined above coincide: Syy (ν) = r yy (ν) +∞ = κ=−∞ ryy [κ] e−j 2π νκ [5. 28] [5. 29] 148 Analysis and Control of Linear Systems...
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Analysis and Control of Linear Systems - Chapter 6 ppsx
... case of multi -control systems at the expense of additional developments (see [DOR 95, FRI 86] ) 188 Analysis and Control of Linear Systems Figure 6. 10 Control by the observer, compared to control ... stronger control 1 76 Analysis and Control of Linear Systems Figure 6. 6 Stabilization by quadratic optimization Kalman’s Formalism for State Stabilization and Estimation 177 6. 5 Resolution of the ... whereas the increase of ξ leads to better dynamics 164 Analysis and Control of Linear Systems Figure 6. 2 Stabilization by pole placement 6. 3 Reconstruction of state and observers 6. 3.1 General principles...
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Analysis and Control of Linear Systems - Chapter 7 docx
... 0.35 0. 37 0.38 0.39 0.40 0.4 07 0.413 T u /T n 0.104 0.22 0.32 0.41 0.49 0. 57 0.64 0 .71 0 .77 T n /τ 2 .7 3 .7 4.46 5.12 5 .7 6.2 6 .7 7.2 7. 7 T u /τ 0.28 0.8 1.42 2.1 2.81 3.55 4.31 5.08 5. 87 ti /τ ... N20 + n2 [7. 18] Qe = Qe0 + Q0 [7. 19] Qs1 = K1 [7. 20] N10 + n1 The limited development of the square root leads to: Qs1 = K1 N10 + n1 N10 [7. 21] 202 Analysis and Control of Linear Systems and similarly: ... ∆E − e−( τ ) for t [7. 44] Two parameters must be identified: the static gain of system K and the time constant τ 208 Analysis and Control of Linear Systems Figure 7. 5 Unit-step response for a...
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Analysis and Control of Linear Systems - Chapter 8 ppsx
... 2 28 Analysis and Control of Linear Systems 8. 1.1 About linear equations The specific techniques of linear differential equations are fundamentally ... extension of the notations introduced at the 236 Analysis and Control of Linear Systems beginning of this chapter, we will deal with equations of the form: ◦ x (t) = f (x, t), x(t0 ) = x0 [8. 29] ... where zi is a root of the polynomial: r p(z) = i=0 αi z r−i + µ r i=0 βi z r−i [8. 42] 242 Analysis and Control of Linear Systems Consequently, the field of absolute stability of multi-interval methods...
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Analysis and Control of Linear Systems - Chapter 9 pot
... Linear Systems Then, we create Table 9. 1 (with n + rows) an an-2 an-4 … an-1 an-3 an-5 … b1=an-2 -an an-3 /an-1 b2=an-4 -an an-5 /an-1 b3=an-6 -an an-7 /an-1 … c1=an-3 -b2 an-1 /b1 c2=an-5 -b3 an-1 ... approximations [9. 10] and [9. 11]: If µ ( jω ) β ( jω ) >> then S ( jω ) ≈ E ( jω ) β ( jω ) [9. 10] If µ ( jω ) β ( jω ) ...
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Analysis and Control of Linear Systems - Chapter 10 doc
... 284 Analysis and Control of Linear Systems 10. 1.1 Analysis of systems behavior 10. 1.1.1 Static errors For a zero static error: – with respect ... Figure 10. 3 288 Analysis and Control of Linear Systems Figure 10. 3 Corrector in a looped system The control magnitude can be a function of ε , x, b or e Based on the signals considered and the ... system 10. 1.3 Parallel correction This type of corrector is grafted in parallel on an element of the direct chain as shown in Figure 10. 5 290 Analysis and Control of Linear Systems Figure 10. 5...
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Analysis and Control of Linear Systems - Chapter 11 pptx
... of PGCD and PPCM of polynomials If G and L are respectively the PGCD and the PPCM of A and B (A, B, G and L ∈ℜ[x]), we will write: G = A ∧ B and L = A ∨ B 330 Analysis and Control of Linear Systems ... to the asymptotic follow-up of a step function setting (see section 11. 2.2) 340 Analysis and Control of Linear Systems Figure 11. 2 Choice of the degrees of Am and Ao’ 11. 3.1.3 Example Let us ... ∂A + ∂Dc − ∂B1 − Figure 11. 3 represents these inequalities geometrically Figure 11. 3 Choice of degrees of Am and Ao’ [11. 52] 344 Analysis and Control of Linear Systems 11. 3.2.2 Example Let us...
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Analysis and Control of Linear Systems - Chapter 12 pptx
... the number of estimated values of the sequence 376 Analysis and Control of Linear Systems 12. 2 Generalized predictive control (GPC) 12. 2.1 Formulation of the control law The objective of this section ... on the control; – λ : weighting coefficient on the control [12. 6] 378 Analysis and Control of Linear Systems 12. 2.1.4 Synthesis of the equivalent polynomial RST regulator The minimization of the ... 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,...
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Analysis and Control of Linear Systems - Chapter 13 pptx
... closed loop control can be formulated in the standard form of Figure 13. 1 408 Analysis and Control of Linear Systems Figure 13. 1 Standard feedback diagram The quadripole G , also called a standard ... dual problems and we can infer the solution of one from the other by the relation of duality L = K T Figure 13. 13 Standard feedback diagram 440 Analysis and Control of Linear Systems 13. 6.3 Another ... ⎠ 13. 12): 434 Analysis and Control of Linear Systems Figure 13. 12 Definition of the H2 problem The H problem that consists of calculating K (s) ensuring the internal stability of GSAR (s) and...
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Analysis and Control of Linear Systems - Chapter 14 pdf
... Figure 14. 5) Figure 14. 5 Area of the complex plane corresponding to the desired performances and to the constraints on the bandwidth 460 Analysis and Control of Linear Systems 14. 4.2 Choice of eigenvectors ... Figure 14. 14 shows the four modal simulations between βc , Φc and β, Φ We note that the decouplings were taken into consideration 476 Analysis and Control of Linear Systems Figure 14. 14 Inputs-outputs ... mode ξi (t) does not have any effect on z k 452 Analysis and Control of Linear Systems 14. 2.2.7 Summarization The analysis of the time behavior of a controlled system was done in the modal basis...
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