# hw_09 - Department of Mechanical Engineering MICHIGAN STATE...

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Department of Mechanical Engineering MICHIGAN STATE UNIVERSITY ME457: Modeling of Mechatronic Systems /hw_09.doc Page 1 of 4 Problem Set #9. Fluid power. (9-1) Figure 9-1 shows a static (i.e., algebraic) model of a positive-displacement pump. (a) Find an expression for the power efficiency, η , of the pump. The inputs are { w, P h , P l }. The parameters are { R m , D p , R L }. (b) Show that η is less than one. Assume all parameters are positive.

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Department of Mechanical Engineering MICHIGAN STATE UNIVERSITY ME457: Modeling of Mechatronic Systems /hw_09.doc Page 2 of 4 (9-2) Figure 9-2 shows a dynamic model of the same positive-displacement pump as above. (a) Find state equations and identify A and B . Let U = { τ , Q h , P l }. Define your X vector clearly. (b) Find the eigenvalues in terms of the parameters. (c) Find the steady-state response, if U is constant.
Department of Mechanical Engineering MICHIGAN STATE UNIVERSITY ME457: Modeling of Mechatronic Systems /hw_09.doc Page 3 of 4 (9-3) Consider a length of tubing as shown in Figure 9-3a that carries water at 20 C.

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