By J. D. Stringer
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Additional info for Hydraulic Systems Analysis: An Introduction
Note that 1 + n. = - 1/T) determines the response. First-order systems are sometimes called 'simple exponential delays'. 3 Ramp Input and Response for First-order Systems A ramp input means, for a position control system, that the input suddenly starts moving at steady velocity (say Q) and, for other types of device, that the input suddenly starts increasing at a constant rate Q. The ramp input may be written (}1 (or (}i) = 0 for t = o-; (}1 (or (JJ = nt for t = o+' where Q is a constant. 6. Cbo ...
8. For convenience the term exp(iwt) (or 1 sin(wt)) is plotted along the real positive axis as a stationary vector of unit length. 9. ;---vectors at time tb !!.! + E ...... 8. 5 and substitute iw for D in order to obtain the harmonic relation ()2 () 1 1 1 + iwT for 81 = exp(iwt) and a more general relation can also be written as ()2 1 1 -=---or--81 1 + Ts 1 + Tp where s or p represent the complex operator or Laplace operator when the expression is then called the 'transfer function'. The term exp(iwt) is represented as a stationary vector of unit length lying along the real positive axis whatever the frequency may be.
Assuming, as before, that the two pressures are initially equal (and at some positive pressure level), it is clear that an angular displacement of the motor shaft would cause an increase of pressure in one pipeline and a decrease in the other. We also assume for simplicity that there is no fluctuation in flow with angular position-in effect therefore we are assuming that the motor has an infinite number of pistons, vanes or gear teeth so that the 'motor displacement' (designated b,Jrad) is a constant.
Hydraulic Systems Analysis: An Introduction by J. D. Stringer