1 / 6

Multivariable Linearization

Multivariable Linearization. Solution of the Dilution Problem with more variables. Problem Description. Consider the following Dilution problem: The inflow concentration c in [kg/m 3 ] of A is time varying The flowrate F [m 3 /s] is NOT constant

irina
Download Presentation

Multivariable Linearization

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. BAE 3023 Multivariable Linearization Solution of the Dilution Problem with more variables

  2. Problem Description BAE 3023 • Consider the following Dilution problem: • The inflow concentration cin [kg/m3] of A is time varying • The flowrate F [m3/s] is NOT constant • The material A in the fluid is not reduced by reaction or other means in the tank • The Tank is well mixed • Find the outflow concentration cout [kg/m3] of A

  3. Equation for multi-variable linearization BAE 3023 A mass balance for component A can be written Inflow rate of A - Outflow rate of A = Accumulation rate of A Note that the product Fc is non-linear, so we must linearize the terms. For the multivariable case, Taylor’s Series truncated to first order terms is: Consider the function: f(F,c)=Fc

  4. Application of multi-variable linearization BAE 3023 The linearized differential equation becomes: Transforming, the equation becomes:

  5. Use of Superposition BAE 3023 The transfer function for cout /cin where F is constant is: The transfer function for cout / F where cin is constant is:

  6. Block Diagram for multi-variable case BAE 3023 Because the system is linear, the effects of Cin and F on Cout can be summed to calculate the total effect on Cout:

More Related