State space system model - hard and really fast - PLEASE

In summary, a state space system model is a mathematical representation of a physical system that takes into account both the system's internal state variables and inputs and outputs. It is used in control engineering and is considered "hard" and "really fast" if it accurately captures the dynamics of a complex system and can provide real-time predictions and responses. Some benefits of using a state space system model include the ability to analyze and predict system behavior, design and tune controllers, and optimize performance. This model is commonly used in practical applications such as aerospace and automotive engineering, robotics, and process control.
  • #1
jamesponty
6
0
State space system model - hard and really need help fast - PLEASE!

Hi,

Just found this site (a little too late I fear!). I have an assignment due tomorrow and I can not solve the last part of it. We are able to source information from anywhere to complete the assignment and you guys are my last hope! I have been trying for two days straight now and can't figure out the last section.

I have a system model digram which I have saved as an image and placed here: (It's just too big to add as an attachment)
http://www.megaupload.com/?d=03HUNNYJ [Broken]
(Close the popup and wait for the timer to count down then you can download the picture)

I have to represent this system in terms of the state space variables outlined on the sheet. I can create state equations for the current and the motor's angular velocity but I can't get the third state space equation. ie. derivitve of Tension = ?

I have worked out the the derivitive of the Tension = K(vw-vs) but don't know where to go from there.

This is a fairly hard problem and I don't know if this is the right section to place it but I am hoping someone could help me?!

Thanks
Jamesponty
 
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  • #2


Dear Jamesponty,

I understand your frustration and urgency in completing your assignment. I am always here to help and I am happy to assist you with your problem.

First of all, let me assure you that this is indeed the right section to ask for help with a state space system model. Many scientists and engineers frequent this forum and are well-equipped to provide you with the necessary guidance.

Now, onto your problem. From the system model diagram, it seems that the third state space variable is the tension in the rope. In order to represent this in terms of the state equations, we need to consider the forces acting on the rope.

As you have correctly deduced, the derivative of tension is equal to K(vw-vs), where K is a constant and vw is the velocity of the weight and vs is the velocity of the motor. This means that the tension in the rope is directly proportional to the difference in velocities between the weight and the motor.

In order to represent this in a state equation, we need to consider the forces acting on the rope. The tension in the rope is caused by the weight pulling down on one end and the motor pulling up on the other end. This can be represented as follows:

Tension = Weight force - Motor force

We can then use the known equations for weight and motor force (F=mg and F=Kvs respectively) to substitute in for the forces and get the following state equation:

d(Tension)/dt = mg - Kvs

This represents the derivative of tension in terms of the other state variables (vs in this case). I hope this helps you to complete your assignment. If you need any further clarification, please do not hesitate to ask.

Best of luck with your assignment!
 
  • #3


Hi Jamesponty,

I understand that you are facing a difficult problem with your assignment and need help with the state space system model. State space models are mathematical representations of a physical system that describe the relationship between the input, output, and internal state variables of the system. They are commonly used in engineering and scientific fields to analyze and control complex systems.

In order to solve your problem, it is important to carefully analyze the system model diagram you have provided. Try to identify all the state variables and their relationships. From your description, it seems like you have already identified two state equations for the current and motor's angular velocity. However, you are having trouble with the third state space equation for the derivative of tension.

To find this equation, you will need to use the relationship between the voltage and the current in the system. Remember that the derivative of tension is equal to the current, multiplied by the resistance. Therefore, your third state equation can be written as the derivative of tension equals the current multiplied by the resistance.

I understand that this may be a challenging problem, but I encourage you to keep trying and break it down into smaller parts. You can also consult your textbook or other resources for more guidance. Additionally, seeking help from a tutor or your instructor may also be beneficial. I wish you the best of luck in solving your assignment and completing it on time.
 

1. What is a state space system model?

A state space system model is a mathematical representation of a physical system that describes how the system's state changes over time. It is commonly used in control engineering and can be used to design controllers that can regulate the behavior of a system.

2. How is a state space system model different from other models?

A state space system model differs from other models in that it takes into account both the internal state variables of a system and its inputs and outputs. This allows for a more comprehensive representation of the system's behavior.

3. What makes a state space system model "hard" and "really fast"?

A state space system model can be considered "hard" and "really fast" if it accurately captures the dynamics of a complex system and can provide real-time predictions and responses. This requires advanced mathematical techniques and efficient algorithms.

4. What are the benefits of using a state space system model?

A state space system model offers several benefits, including the ability to analyze and predict the behavior of a system, design and tune controllers to regulate the system's behavior, and simulate different scenarios to optimize system performance.

5. How is a state space system model used in practical applications?

A state space system model is used in a wide range of practical applications, such as aerospace and automotive engineering, robotics, and process control. It can be used to design and control systems, predict and prevent failures, and optimize system performance.

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