By Philippe de Larminat
Automation of linear platforms is a primary and crucial thought. This ebook bargains with the speculation of continuous-state automatic platforms.
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Singular perturbations and time-scale ideas have been brought to manage engineering within the overdue Sixties and feature on the grounds that turn into universal instruments for the modeling, research, and layout of keep an eye on platforms. during this SIAM Classics variation of the 1986 ebook, the unique textual content is reprinted in its entirety (along with a brand new preface), delivering once more the theoretical beginning for consultant keep watch over purposes.
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Additional info for Analysis and control of linear systems
24. 25. 26. 6. 1. Fourier transform Any signal has a reality in time and frequency domains. Our ear is sensitive to amplitude (sound level) and frequency of a sound (low or high-pitched tone). These time and frequency domains, which are characterized by variables that are opposite to one another, are taken in the broad sense: if a magnitude evolves according to a distance (atmospheric pressure according to altitude), the concept of frequency will be homogenous, contrary to a length. The Fourier transform is the mathematical tool that makes it possible to link these two domains.
The coefficients of the numerator and denominator polynomials are real due to their physical importance in the initial differential equation. Hence, the numerator roots, called zeros, and the denominator roots, called transfer function poles, are conjugated real or complex numbers. If x(t ) and y(t ) are causal functions, the Laplace transform of the differential equation entails terms based on initial input values x(0), x ′(0), x ( m −1) (0) and output values y (0), y ′(0), y ( n −1) (0) ; the concept of state will make it possible to overcome this dependence.
T → +∞ h(t ) ~ t n −1 Holomorphy Directly impossible harmonic analysis impossible directly except for a simple pole at the origin H(p) has poles on the right of the imaginary axis. t → +∞ h(t ) ~ ekt * k>0 * Holomorphy Possible analysis if the system is introduced in a stable looping and H ( jω ) = H ( p) p= jω H(p) has poles on the imaginary axis. 1. Unit-step responses, transfer functions and existence conditions of the frequency response Transfer Functions and Spectral Models 21 Frequency responses are generally characterized according to impulse ω = 2π j f and data H ( jω ) and Φ ( jω ) grouped together as diagrams.