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By Olaf Wolkenhauer

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Example text

PX,Y = - %Y ox where l -l

33) where Cdlz c& a12 a0 HO 9 Linear is is is is is is the the the the the the discharge coefficient of the inter-tank holes. discharge coefficient of the drain tap. combined cross-sectional area of the inter-tank cross-sectional area of the drain tap. height of the drain tap. gravitational acceleration constant. holes. Model The above equations describe the system in their true nonlinear form. For control system analysis and design it is necessary to linearize these equations by considering small variations qi in Qi, ~2 in Q2, hr in HI, and I22 in Hz.

11. Newton’ s particle mechanics provides probably the most convincing case for equations and state variables. mplest mechanical differential 20 SYSTEM ANALYSIS system - a single particle moving on a line under the action of a constant force F. The motion is governed by Newton’s Second Law, which defines the force F acting on a mass point m to be the rate of change of momentum (m . v): d(m 9V) 7 dt F=- where v denotes velocity which, in turn, is defined as rate of change of position or displacement from some origin of coordinates: In order to apply this formulation to an actual system, we must have an independent characterization of the force, expressed in terms of varying quantities x and v.

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