what is observability in control system
Answers
Answer:
In control theory, observability is a measure of how well internal states of a system can be inferred from knowledge of its external outputs. ... A dynamical system designed to estimate the state of a system from measurements of the outputs is called a state observer or simply an observer for that system
Explanation:
Observability of a control system is the ability of the system to determine the internal states of the system by observing the output in a finite time interval when input is provided to the system. It is another crucial property of the control system as it shows the behavioural approach of the control system.
It is also proposed by R. Kalman, the one who proposed controllability.
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Observability
Observability of a control system is the ability of the system to determine the internal states of the system by observing the output in a finite time interval when input is provided to the system. It is another crucial property of the control system as it shows the behavioural approach of the control system.
It is also proposed by R. Kalman, the one who proposed controllability.
Observability in control system
For a better understanding of the term observability, let us understand it in terms of a question.
Suppose for the applied input to a control system and if we can measure the output of the system for that particular input in the finite time. Then, can you predict the initial state of the system by having the knowledge of the input and output?
If yes, then the system is observable.
In the previous article, we have studied about controllability. Both controllability and observability are duals of each other. As the two are duals thus it is necessary to give you an idea about controllability.
So, basically, in a control system, controllability is the ability of the system to change the initial state to a definite state by the application of input in a finite amount of time. Contrastingly, observability reverses the procedure by determining the internal states from the achieved output. This facilitates the determination of the behaviour of the system. Therefore, the above discussion concludes, that a system is observable if for a possible sequence of state vectors, with the use of output Y(t), every state is determined completely, in a finite time.
It is noteworthy here that if few of the states are not practically determined then the system is not completely observable.
This shows, that it will lead to providing behavioural characteristics of the overall system from the output of that system.
So, if the system is not observable, then each and every state will not be determined even if the output is known. This somewhat represents that the internal states of the system are itself unknown to the controller.