By J. Lowen Shearer
This textbook is perfect for an undergraduate path in Engineering process Dynamics and Controls. it really is meant to supply the reader with an intensive knowing of the method of constructing mathematical (and computer-based) versions of actual platforms. the fabric is particular to lumped parameter versions, that are these types during which time is the one self sufficient variable. It assumes a easy wisdom of engineering mechanics and usual differential equations. the recent version has increased topical insurance and plenty of extra new examples and workouts.
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Additional info for Dynamic Modeling and Control of Engineering Systems
Some interesting observations can be made from the plot. 0016 m. Second, it is quite clear that the linearization error, or the difference in the vertical direction between the nonlinear function and the tangent line, will increase as the spring deflection deviates from the normal operating point. 28. 8. linear approximation is better as the normal operating point moves farther away from the spring-relaxed position, x = 0. In summary, although linearized models should be used whenever possible (because they lend themselves to powerful analytical methods), it should be kept in mind that they constitute local (usually for small deviations from a nominal operating point) approximations of the nonlinear system and that the results obtained with linearized models provide a simplified picture of the actual system behavior.
Because [x21 − (x21 )0 ] = x2 − x1 , Eq. 11) where (x2 − x1 ) is the deflection of the spring is from its initial free length. When the spring is nonlinear, it does not have truly constant stiffness k, and it is advisable to employ a nonlinear symbol designation and a nonlinear function to describe it, as follows: FNLS = fNL (x2 − x1 ). 4. 2 Find the response (in terms of force Fk and deflection x1 ) of the spring shown in Fig. /s step change in input velocity from zero, starting from its free length at t = 0.
Step 2. Step 3. Step 4. Step 5. Derive the nonlinear model. Determine the normal operating point. Introduce incremental variables. Linearize all nonlinear terms by use of Taylor’s series expansion. Arrange the linearized equation into a final form. This five-step procedure is applied in the following example. 8 In the mechanical system shown in Fig. 5 x. 27. 8. 1 N. SOLUTION This problem is solved following the five-step linearization process introduced earler in this section. Step 1. 5 x = Fi .