Mechanical design handbook measurement, analysis, and control of dynamic systems

... 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...

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... 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 An...

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... 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 th...

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... 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...

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... 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 c...

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... 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 Stabiliza...

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... 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 Contro...

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... 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] ... wher...

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... 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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... 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...

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... 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 t...

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... 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 equival...

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... 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 Con...

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... 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 Cont...

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