Linearization a la Taylor

Linearization a la Taylor - Department of Mechanical...

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Unformatted text preview: Department of Mechanical Engineering MICHIGAN STATE UNIVERSITY ME 457: MECHATRONIC SYSTEM Modeling and Simulation Linearization a la Taylor. 1. Example of a first-order system with one input. Consider a single nonlinear state equation in standard form shown below: ) , ( ) ( u x f t x = & [1.1] where x(t) is the state variable and u(t) is the input variable. Find the equilibrium point(s) … EP(s). Let the input be constant, u(t) = u c , and assume that dx/dt(t) = 0. Then [1.2] becomes ) , ( c ep u x f = [1.2] where x ep is the EP value and uc is the constant input. This equation looks easy to solve and sometimes it is, but sometimes it is not. One difficulty, for example, is that there may be no solution, one solution or many solutions . Linearize about an EP. Assume that we have found an EP and it is at [ x ep ,u c ]. Next we want to linearize the system model about that EP. To help us we call on Taylor and his famous series. The variables we will use are these: ). ( ) ( ) ( ) ( t u t...
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Linearization a la Taylor - Department of Mechanical...

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