Convention Two - Modeling of Physical Systems - Home Work, Exercises of Mathematical Modeling and Simulation

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Modeling of Physical Systems: HW 5-due 10/9/12 Page 1 For problems 1 through 3 below, do the following: a) develop a bond graph model, a) assign power convention, number and label the bonds, c) assign causality, d) use causality to identify the number of independent states and write the state vector, x, e) derive state equations in state space form. Assume model elements have linear constitutive relations only if a parameter is explicitly indicated (e.g., bearing friction, b, means bearing imparts torque, T, = bw). Problem 1: Model the system from problem 4-3(f) from Karnopp, et al. (as shown below) Massless_ vw Solution: Note: had meant for you to consider all linear elements here. In, . Ta, 2 Pe LY, Pa |Me. 6 ! Fs’ Fa uF + FQ) 4) F Neer 5 ve th “a +r Me the E re als - acts ote. a a wa Ce RB eR mk, yr da) States: Ry Pad DO xe. ky Wt Ve = ine oA KO ow % Bee fe FR Fs Fy = Fa Ra = Rye tba My Kat by Xe Fee Ky%g 4 by -m, mth) FT = Fat fg = KqiXa + by Me = Kyxgt b, Me ial Far KsXst by [v7 Mad Ey xy - b he Pot Kaky — mm, % + by YMD 7 Key ~eat s ie bap = Kg Xs ~ (Re ba) Py Kg Xq Pia e by Yl) . to = - 2 et _ . My Ry Mes Vay = Ve Me © i hy Rg Pi, fo. Pa = Fe + Apt Fy? = Kp re + Be gg 7 5 Pia + gl aw R.G. Longoria, Fall 2012 ME 383Q, UT-Austin Docsity.com