Controllability and Observability
Controllability
The system is controllable when the desired output is obtained by applying the specific controlled input. It is the ability to control the state of the system. The controllability of the system can be checked using the Kalam Test. The given below is the condition for the controllability:
Q0 = [B AB A2B ….. An-1B]
If the determinant of Q0 is not equal to 0 then the system is controllable.
[Tex]|Q_{0}| \neq0 [/Tex] —- (system is controllable)
|Q0| = 0 —– (system is un-controllable)
Observability
It is the system’s ability to measure or observe the system state. If the internal state of the system is determined using the input and output signals during a finite interval of time then the system is said to be observable. The observability of the system can be checked using the Kalam Test. The given below is the condition for the observability:
Q0 = [CT ATCT ….. (AT)n-1CT]
Note: AT,CT means transpose of the respective matrix
If the determinant of Q0 is not equal to 0 then the system is controllable.
[Tex]|Q_{0}| \neq0 [/Tex] —- (system is observable)
|Q0| = 0 —– (system is not observable)
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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