Transfer Function from State Space Model
The transfer function can be calculated using state space analysis. We will now see the procedure for calculating the transfer function.
The state equations of the LTI system are:
[Tex]\dot{x} = Ax+Bu [/Tex] —- (state equation (1))
[Tex]y=Cx+Du [/Tex] —- (output equation (2))
Applying Laplace Transform on both the sides of equation (1):
sx(s) = Ax(s)+Bu(s)
(sI-A)x(s) = Bu(s)
[Tex]x(s)= \frac{Bu(s)}{sI-A} [/Tex] —(3)
Applying Laplace Transform on both the sides of equation (2):
y(s) = Cx(s)+Du(s) —-(4)
Now, substituting the value of equation 3 into equation 4, we will get:
[Tex]y(s)= C\frac{Bu(s)}{sI-A} + du(s) [/Tex]
[Tex]\frac{y(s)}{u(s)} = \frac{C}{sI-A}B + D [/Tex] — (5)
where,
- A: system matrix (nxn)
- B: input matrix (nxm)
- C: output matrix (pxn)
- D: relevance of output with input matrix
The equation 5 represents the transfer function of the given system. With the help of this equation we can directly calculate the transfer function of the system.
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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