Finding a State-Space Representation for Helicopter Pitch Angle Control

Thread starter Nico Frontmann
Start date Nov 2, 2014
Tags

Control theory Representation Space State State space

In summary, State Space Representation is a mathematical modeling technique used to describe a system's dynamics and behaviors over time. It involves representing a system using state variables and input/output equations. It is important because it allows for the understanding and analysis of complex systems and is useful in designing controllers. Some advantages of using State Space Representation include its compactness and ability to integrate different models, while its limitations include only being applicable to linear systems and requiring advanced mathematical techniques. In real-world applications, it is used in various fields such as control engineering, economics, physics, computer science, and machine learning.

Nov 2, 2014

Nico Frontmann

I need help finding a state-space representation for the given system and locally linearizing it...

Objective is to control the pitch angle theta, as an output, of the helicopter by regulating the rotor angle u, as an input.

This is what I've done, but apparently it isn't correct, and I don't understand why:

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Nov 3, 2014

donpacino

Gold Member

in your A matrix you are saying X3'=9.8*theta-14.3*theta'-0.198*theta.

1. What is State Space Representation?

State Space Representation is a mathematical modeling technique used in control engineering and other fields to describe a system's dynamics and behaviors over time. It involves representing a system using state variables, which are variables that describe the current state of the system, and input/output equations that relate the state variables to the system's inputs and outputs.

2. Why is State Space Representation important?

State Space Representation allows us to understand and analyze the behavior of complex systems. It is particularly useful in control engineering as it allows us to design controllers that can regulate the state variables and achieve desired system performance. It also provides a unified framework for modeling various physical, biological, and social systems.

3. What are the advantages of using State Space Representation?

One advantage of using State Space Representation is that it allows for a more compact and efficient representation of a system compared to other modeling techniques. It also allows for easy integration of different models and subsystems, making it a powerful tool for modeling complex systems. Additionally, it provides a clear and intuitive way to visualize and understand the dynamics of a system.

4. What are the limitations of State Space Representation?

One limitation of State Space Representation is that it can only be used for systems that can be described using linear equations. Therefore, it may not be suitable for modeling highly nonlinear systems. Additionally, it can be computationally intensive and may require advanced mathematical techniques for analysis and design.

5. How is State Space Representation used in real-world applications?

State Space Representation is widely used in various fields, including control engineering, economics, physics, and computer science. It is used for modeling and controlling physical systems such as robots, aircraft, and chemical processes. It is also used in economic models to study market dynamics and in computer science for designing efficient algorithms and data structures. Additionally, State Space Representation is used in machine learning and artificial intelligence for modeling and predicting the behavior of complex systems.