--%>
Assignment Help - homework help

Non linear dynamic model equation to linear equation

Could you please show the steps from non linear dynamic model equation to linear equation?

E

Expert

Verified

We'll show one step as this linearization is automatically carried out in MATLAB.

Consider the part F(h) = CAs(2gh)1/2

To linearize we'll represent this part or F(h) as Taylor series expansion around steady state stock height hs.

F(h) = F(hs) + (dF/dh)hs(h – hs) + ... higher order terms in (h – hs)

dF/dh = CAs(1/2)(2g)1/2 h-1/2

(dF/dh)s = CAs(1/2)(2g)1/2 hs-1/2 

F(h) = F(hs) + (dF/dh)hs(h – hs)
       
F(h) = F(hs) + (CAs(1/2)(2g)1/2 hs-1/2)(h – hs)

F(h) = F(hs) + K'h h'
where K'h is a constant and h' is the deviation variable in h.

Of course we have to linearize the first term also in the same way, Taylor series expansion, then we can collect the h' and P'vd.    

   Related Questions in Programming Languages

  • Q : Define the term Peripheral devices

    Define the term Peripheral devices: It is the devices attached to a computer, like disk drives, printers, mice, and so forth.

    		•
  • Q : How XML web services integrate two

    How can XML web services integrate two legacy distributed systems, one based on Corba and one based on Java RMI?

    		•
  • Q : Define Short-circuit operator

    Short-circuit operator: It is an operator in which only as a lot of operands are computed as are required to determine the final outcome of the operation. The logical-and (&&) and logical-or (||) operators are most general illustration, though

    		•
  • Q : Requirement of Timer control in AJAX

    Explain the requirement of a Timer control in the AJAX.

    		•
  • Q : Explain Magic number Magic number : It

    Magic number: It is a constant value with significance within a specific context. For example, the value 12 could mean numerous different things - the number of hrs you have worked today, the number of dollars you are payable by a friend, and so forth

    		•
  • Q : Swapping system What action of the

    What action of the swapping system does in case it identifies the illegal page for the swapping?

    		•
  • Q : Write a program that prints out 20

    Write a program that prints out 20 random cards form a standard deck of 52 cards. Make sure the program prints out different sets of cards from one run to the next.

    		•
  • Q : Explain Switch statement Switch

    Switch statement: It is a selection statement in which the value of an arithmetic expression {expression!arithmetic} is compared for the match alongside different case labels. When no match is found, the optional default label is chosen For example:

    		•
  • Q : What is Server Server : Something which

    Server: Something which gives a service. The Web server delivers resources to its clients, for example. Whenever the server is an object, this is the recipient of messages from its object clients.

    		•
  • Q : Explain Abstract Windowing Toolkit

    Abstract Windowing Toolkit: The Abstract Windowing Toolkit (AWT) offers a collection of classes which simplify the creation of applications with the GUI (graphical user interfaces). Such are to be found in the java.awt packages. Included are classes f

    		•