Solving State-Variable Models Homework

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In summary, the problem includes two parts where the first part has two output functions, ##y_1## and ##y_2##, while the second part only takes into account ##y_1##. The solution for part a.) involves a matrix equation with two output components, while the solution for part b.) only has one output component. The confusion stemmed from not fully reading and understanding the problem before attempting to solve it.
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LostMechE901
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Homework Statement


Capture.JPG


Homework Equations


##\dot{x} = Ax + Bu## - Input Function
##y = Cx + Du## - Output Function

The Attempt at a Solution


I'm having trouble with the output functions specifically ..
In a.) the correct solution for the output is: \begin{align} & y_1 = x_1 \\ & y_2 = x_2 \\ & \begin{bmatrix} y_1 \ \\ y_2 \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} + \begin{bmatrix} 0 \\ 0 \end{bmatrix} u \end{align}

Now for part b.) the solution is ..

: \begin{align} y_1 & = x_1 \\ y & = \begin{bmatrix} 1 \\ 0 \end{bmatrix}x + \begin{bmatrix} 0 \\ 0 \end{bmatrix} u \end{align}

I don't understand why part a.) has two outputs ##y_1## and ##y_2## whereas part b.) only takes into account ##y_1##. What am I failing to understand conceptually? **I figured it out, apparently I can't read -.-**
 

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LostMechE901 said:
**I figured it out, apparently I can't read -.-**
That's why the template is so good: formulating the problem requires reading (not photographing) it first :rolleyes:
 

1. What is a state-variable model?

A state-variable model is a mathematical representation of a system that tracks changes in multiple variables over time. It is often used in fields such as economics, engineering, and physics to study the behavior of complex systems.

2. How do you solve a state-variable model?

To solve a state-variable model, you first need to specify the variables and their relationships in the form of differential equations. Then, you can use numerical or analytical methods to solve the equations and obtain the values of the variables at different points in time.

3. What are the advantages of using state-variable models?

State-variable models allow for a more comprehensive understanding of how a system works, as they take into account the interactions between different variables. They also allow for the prediction of future behavior and the identification of key factors that influence the system.

4. What are some common applications of state-variable models?

State-variable models are used to study a wide range of systems, from simple physical systems like pendulums to complex economic systems like stock markets. They are also commonly used in fields such as biology, ecology, and psychology to understand the behavior of living organisms and social systems.

5. Are there any limitations to using state-variable models?

State-variable models are based on simplifying assumptions and may not accurately capture all aspects of a system. They also require a lot of data and mathematical expertise to develop and solve. Additionally, they may not be useful for predicting long-term behavior or accounting for unexpected events or changes in the system.

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