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 ... order, the 242 Analysis and Control of Linear Systems Consequently, the field of absolute stability of multi-interval methods (implicit or not depending on the value of β 0 ) is the set of µ ∈ C so ... b...

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... 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 ... at the expense of a stronger control. 176 Analysis and Control of Linear Systems Figure 6.6. Stabilization by quadratic optimization 166 Analysis a...

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... systems analysis and control of linear systems/ edited by Philippe de Larminat. p. cm. ISBN-13: 97 8- 1 -9 0520 9-3 5-4 ISBN-10: 1-9 0520 9-3 5-5 1. Linear control systems. 2. Automatic control. I. Larminat, ... equations 2 28 8. 1.2. About non -linear equations 2 28 8. 2. Standard linear equations 2 28 8. 2.1. Definition of the problem 2 28 8....

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... 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 (dB)Phase (degree) Figure 1.23. Bode diagram of a second order system with ξ ≥ 1 20 Analysis and Control of Linear Systems ... of Linear Systems Figure 1.19. Unit-step response of the second order system ξ ≥ 1 1= ξ : critical state. The roots of the de...

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... i n is the multiplicity order of i λ and i th the eigenvalue of A. 5 A canonical form called controllable companion. 88 Analysis and Control of Linear Systems Hence, if we suppose that ... 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 Le...

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... eigenvalues of A appear (certain powers l ij being then equal to 0): 110 Analysis and Control of Linear Systems The object of this chapter is to describe certain structural properties of linear systems ... 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]. 12...

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... 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 2πν 0 , then the power spectrum is almost zero in the proximity of ν 0 . 142 Analysis and Control of Linea...

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... from the point of view of calculation, in terms of linear regression (or linearized), i.e. it leads to a quadratic 196 Analysis and Control of Linear Systems in performing the roles of the procedure, ... [7.44] Two parameters must be identified: the static gain of system K and the time con- stant τ. 216 Analysis and Control of Linear Systems so-called “sha...

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... 2 a n-1 a n-3 a n-5 … 3 b 1 =a n-2 -a n a n-3 /a n-1 b 2 =a n-4 -a n a n-5 /a n-1 b 3 =a n-6 -a n a n-7 /a n-1 … 4 c 1 =a n-3 -b 2 a n-1 /b 1 c 2 =a n-5 -b 3 a n-1 /b 1 ... study the case of open loop stable systems, that of integrator systems and finally the case of open loop unstable systems. 270 Analysis and Control of Linear Systems We...

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... 1 2 8 ' = τ v KK ⇒ 2 8 ' τ = v KK 81 =+ v K λ ⇒ 7= v K λ ⇒ v K K τ 264 = and v K 7 = λ 314 Analysis and Control of Linear Systems In certain cases, the transfer function of a system is ... and Control of Linear Systems Figure 10.12. Bode graph with insufficient phase margin Figure 10.13. Bode graph in OL of the corrected system 306...

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