Solved Example on State Space Analysis
Example: Obtain the state space equation of the following differential equation:
[Tex]\frac{2d^3y}{dt^3}+\frac{4d^2y}{dt^2}+\frac{6dy}{dt}+8y=10u(t) [/Tex]
Solution
Triple derivative –> 3 variables
[Tex]x_{1}=y [/Tex]
[Tex]x_{2}=\frac{dy}{dt}=\dot{x_{1}} [/Tex]
[Tex]x_{3}=\frac{d^2y}{dt^2}=\dot{x_{2}} [/Tex]
[Tex]\dot{x_{3}}=\frac{d^3y}{dt^3} [/Tex]
[Tex]\frac{d^3y}{dt^3} = 5u(t)-\dot{\dot{{2y}}}-3\dot{y}-4y [/Tex]
[Tex]\frac{d^3y}{dt^3} = 5u(t)-2x_{3}-3x_{2}-4x_{1} [/Tex]
The final solution is given below:
What is State Space Analysis ?
The State Space analysis applies to the non-linear and time-variant system. It helps in the analysis and design of linear, non-linear, multi-input, and multi-output systems. Earlier the transfer function applied to the linear time-invariant system but with the help of State Space analysis, it is possible to find the transfer function of the non-linear and time-variant systems. In this article, we will study the State Space Model in control system engineering.
Table of Content
- What is the State Space Analysis?
- State Space Model
- Transfer Function from State Space Model
- State Transition Matrix and its Properties
- Controllability and Observability
- Solved Example on State Space Analysis
- Advantages and Disadvantages of State Space Analysis
- Applications of State Space Analysis
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