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Unformatted text preview: ME 344 — What is a dynamic system? ° The system whose behavior as a function of time is
important — How to understand a dynamic system?  Model _  Linear
— Nonlinear — How to control a dynamic system?  Classic
° Modern ME 344  Example 1:  Example 2: "V ‘H/KTVC +VL:0
NW  WWW, laws :
l/L : A“ /\:L1; MK, .5? I‘qu Lew
Va =——g;
w(/ + YKRT%—+L :9
Cab/“(77140? CK : {L = , ‘ "1% 00 i 7”: W ,e i“ W 7W
Hwé‘éiféi ban! 6 (Co/71mm W i W. +9 32% +21%; ’5 ,, wezéeéangﬁéZ‘ii W" E‘LKHL 5%??? +z’—%6w * TTT f PM” ' “rm 0W ,
* (ﬁg/“0%” WL‘YWW FED:
we wxwéx—ebkrwr : M Mzow'XkaX)
;> we kr ’522: mkam WM
gﬁvzcﬁirgl “Hum 551 r; Mme «m :> m? +b>‘<+%e><= birbklxlf (x 7ng +5 >'< »~‘ >'< «we ' 0&7?
: ‘ A‘ A” v’ ‘ “A. A It X A ' z
3 ‘ I AA “'er ‘F‘ v _—:> mr%>‘<z=m>‘<>‘<‘»l<xr>é+tx>é >0? ‘ . ‘ Q EX *5 :MX ' Xr+l<
950%?) = mk‘*%CXr~X u ‘T +197?le “HZXV’ FUNDAMENTAL DESCRIPTION OF SYSTEMS IN TERMS OF ENERGY Energy: ability to do work (joules—nm) 2
E = JFdx => Work done by a force, F, in going from point 1 to point 2
1 Power: rate of change of energy _aE p___
at We define systems in terms of energy and power using conservation laws.
Recall First Law of Themodynamics: Q=U+W—static behavior Qzenergy supplied to system
U=change in internal energy of the system
W=work done by the system Differentiating this expression with respect to time, we obtain the analogous expression
for power. ipini :a—E+ipouti
1 ' at ‘ l
=> Net power into system 2 Time rate of change of energy in system + Net power out of system Alternatively : ipini'ipomiza—E
1 ' 1 ' at Point: it is possible to determine the dynamic (static) responses of a system by accounting
for the power (energy) flow in the system. Energy Storage and Dissipation Elements  . O
Conant.“
Electrical System gs‘ .
Mk” E = jvidt = Jv(idt) = Jvdq Potential Energy Capacitance q=q(v) q=Cy E = Jvidt = Ji(vdt) = Jidk Kinetic Energy Inductance >\=)\(i) )\=Li E = Jvidt Dissipation Resistance =v(i) v=Ri
Translation System B = J‘det = {P(vdt) = IFdx Potential Energy Spring x=x(F) x=F/k E = Jdet = Jv(th) = Jvdp Kinetic Energy Mass p=p(v) p=Mv E 2 Idet Dissipation Damper =F(v) F=bv Rotation System B = erdt = [1((DClt) = [1116 Potential Energy Rotary Spring
E = Irwdt = Imﬁdt) = Icodh Kinetic Energy Mass
E: [det 0= 6 (T)
=h(w) 0= T/k
h= Jco
Dissipation Damper T = ’1’ (co) _ T =Bw Fluid System B = jPth = [P(th) = deU Potential Energy Fluid Cap. U= U(P) U=CP
E = {mm = jQ(Pdt) = der Kinetic Energy Fluid Inertance r: P(Q) I‘=IQ
E = [13th Dissipation Fluid Resistance P = P(Q) P =RQ Note: k is a measure of spring stiffness (force need for a given displacement)
C is a measure of spring compliance (displacement resulting from a given force) Gmliswis t’Olém‘ f‘r €5.11on
WNW/h FUNDAMENTALS OF BOND GRAPH‘MODELING METHOD Conservation of Energy is key (note power and energy are scalar quantities): 6E
ZPinJ = a. + zpouLj Net power into system=rate of change of energy in systemLinet power out of system Deﬁne Power Conjugates variables: Translation F, force V, velocity
Rotation T, torque Q , angular velocity
' Fluid/Hydraulic P, pressure Q, ﬂow rate
Electrical _ e, voltage i, current H
Thermal T, temperature £15 , timerate of change of entropy, 5 dt , .
FlowEffort variables (developed by James C. Maxwell) '
Effort variables “e”: ‘pushing’: F, T, P, e, T » . .1) y_ t ' ’ ' 11:9— '
Flow variables . f. motlon .V,9, (2:1: dt ) Power, P=ef I. Energy, E= IPdt = Jefdt Deﬁne energy variables:
Generalized momentum: p = jedt Generalized displacement: q = det Energy of a system can be rewritten as: E = dep “kinetic” energy
E = Jedq “potential” energy ...
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This document was uploaded on 04/02/2012.
 Spring '09

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