Observability Homework Help

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Ideas of Observability Best Taught by Experts from the Industry

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What is Observability?

Rudolf E. Kalman first introduced the idea of observability for linear dynamic systems.When a present state can be identified only by the outputs in fixed time under any possible sequence of state and control trajectories, the system is then said to be in observable condition.

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So, to define it simply, observability meansthe behaviour of the complete system can be determined from output of the system. A system not being observable refers to that situation where the current values cannot be predicted through outputs.

Reasons why things cannot be observed directly:

  • If the state variable has no physical existence as it’s a dummy.
  • If there is no physical accessibility to positions of specific state variables.
  • If there is no proper measuring instrument for these state variables.

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Relations between controllability and observability:

Both controllability and observability are known as the mathematical duals of a system. Their concepts are also quite similar as there is a strong connection between them. For instance, a system will be controllable only when it is observable. The outcomes of the two are same.

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