state space modeling

Discussion in 'Homework Help' started by tulips_006, Feb 24, 2012.

1. tulips_006 Thread Starter New Member

Jul 24, 2010
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hi to all... i need help in state space modeling of this block diagram.. problem is i can separate the state variables from each other.. state variables are "i" "v" and "y"... can any one tell me what to do?

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2. steveb Senior Member

Jul 3, 2008
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Those are the state variables because they are the outputs of integrators. Hence, the state equations (which are equations for the derivatives of the state variables) are found at the input to those integrators. You will want to express each state derivative as a function of the state variables and the input variables.

3. tulips_006 Thread Starter New Member

Jul 24, 2010
4
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thanks steveb for replying... actually i m writing the equation for the derivatives. but problem comes where i have to separate the variable to write them in matrix form. i cant separate them so i dont know how to write them in matrix form...

my equations are

i' = [(-iR + u)(y/k)] + [(iv)/y]
v' = -[ (k/m)*(i/y)^2] +g
y' = v

as u can see all the variables are quite tangled. to write them in matrix form i have to separate each variable with its cofficients... and i dont know how

4. steveb Senior Member

Jul 3, 2008
2,431
469
Ah, you are trying to fit your equations into a linear state space model. The issue is that your system is a nonlinear system. Are you sure that you have to put it in matrix form?

If you do, then you are being asked to linearize the equations. There are methods to do this. They are not difficult methods, but they are not so easy to describe. Before going down this path, I want to make sure that you have a clear understanding of what your assigned question is really asking.

In general, a nonlinear state-space system can't be put into a matrix form (unless you linearize it), and there is nothing wrong with describing a nonlinear state space system the way you wrote it.

5. tulips_006 Thread Starter New Member

Jul 24, 2010
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the question was to represent it into state space model. when i was getting this result i was thinking that it might not be linear thats why i cant write it in matrix form... if i have to linearize this.. what methods do i have to use? u can just name them or write some basic intro. i can research more it my self... thanks again for helping

6. steveb Senior Member

Jul 3, 2008
2,431
469
First, let's look at how you phrased the question: "... represent it into a state space model". Strictly, those equations you wrote are a state space model. Particularly, it is a nonlinear state space model, but still it is a state space model. For some reason, the terminology can be vague and many people mean a "linear" state space model when they say "state space model". Hence, I'm still confused on what you are really being asked.

However, I leave the above issue for you to figure out, and I'll assume that you are trying to develop a linear state space model. Linear state space models require linear first order differential equations for the state variables. Hence, you need to linearize your nonlinear equations. The technique for doing this is to establish a steady state operating point (called a DC Q-point in circuit theory) and to allow any variations to be small signals (called AC signals in circuit theory) around that operating point.

This allows you to sove the DC problem independently, using the nonlinear equations with all time derivatives set to zero. Then you can write a set of linear state space equations for the AC variables.

This technique sounds confusing at first and it looks confusing when written in a general form, as it is in text books. But, the actual application of the method is quite simple and straightforward. I've attached my own description, which I've written up for others in the past. Also, the following book describes this technique formally. I don't think the explanation is any more clear or detailed than what I've provided, but the book is a very good control theory book if you are looking one.

"Modern Control Engineering" by Ogata

• Linearization.pdf
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Last edited: Feb 24, 2012
7. tulips_006 Thread Starter New Member

Jul 24, 2010
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thank u so much for ur kind reply actually i m also not quite sure if i have to linearize it for my assignment or not... but in case if i have to i should know a little bit about it again very thankful to u