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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What is the State Space Analysis?

State Space Analysis is the graphical tool that is used to analyze and design the linear, non-linear, time-variant, time-invariant multi-input, multi-output system. It is used to describe the behavior of LTI systems. It describes the internal state of the system. There are various key components of the state space analysis which are as follows:...

State Space Model

The single-input and single output continuous time LTI system is described by the differential equation which is given below:...

Transfer Function from State Space Model

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State Transition Matrix and its Properties

State Transition Matrix...

Controllability and Observability

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Solved Example on State Space Analysis

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Advantages and Disadvantages of State Space Analysis

There are some list of Advantages and Disadvantages of State Space Analysis given below :...

Applications of State Space Analysis

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Conclusion

The article deals with the State Space Analysis model which is used in the control system. It is useful to find the transfer function of the non-linear, time-variant, multi-input, and multi-output systems. It provides an easy way for the system analysis. In this article, we have studied the concept of state space analysis, the calculation of the transfer functions, its application, advantages, and disadvantages....

FAQs on State Space Analysis in Control System

1. How does the controllability impact the designing of the system?...

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