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About this document
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- 9 pages
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- Control Systems, Engineering, Mathematics
This document explains the concept of state space representation in control engineering. It defines state variables and discusses their importance in representing the state of a system. It is useful for understanding how to model and analyze systems with multiple inputs and outputs.
What's inside
- Definition of state space representation
- Importance of state variables
- State space vs. frequency domain approach
- State variables in linear systems
- General state-space representation of linear systems
Who it is for: Students of control engineering, systems analysis, and related fields. (Undergraduate)
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Summary
State space representation is a mathematical way to model physical systems in control engineering. Students learn how to use it to work with systems that have multiple inputs and outputs.
State variables and block diagrams
Internal state variables are the fewest system variables that can show the whole state of the system. The number of state variables is usually the same as the order of the system's defining differential equation. Block diagrams show the state space equations.
Linear systems and their matrices
Linear systems with multiple inputs, outputs and state variables can be written in matrix form. The matrices are time-variant or time-invariant. The state vector, output vector and input vector are defined.
Stability, controllability and observability
The stability of a continuous-time LTI system can be studied from the eigenvalues of the state matrix. Controllability and observability are dual concepts. A system is controllable if a certain matrix has full rank. A system is observable if another matrix has full rank.
Feedback and examples
Feedback can be added to a state space model. Two examples are given: a moving object and a pendulum. The moving object example uses Newton's laws of motion. The pendulum example is a nonlinear system.
Key terms
- state space representation
- A mathematical model of a physical system using state variables.
- state variables
- The fewest system variables that can show the whole state of the system.
- controllability
- A measure of how well inputs can change the internal state of a system.
- observability
- A measure of how well internal states can be inferred from external outputs.
- transfer function
- The ratio of the output to the input of a system.
- eigenvalues
- Values that show the stability of a system in state space representation.
Questions this document helps with
- What are state variables in a system?
- How do you check if a system is controllable?
- What is the transfer function of a system?
Summary written with AI from the document's text.
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