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Questions and Answers
What is the purpose of studying observability?
What is the purpose of studying observability?
- To take derivatives of continuous-time measurements
- To consider an input-free system
- To find the determinants of square matrices
- To obtain information from measurements of outputs and inputs (correct)
In linear algebra, a system of linear algebraic equations with n unknowns has a unique solution if and only if:
In linear algebra, a system of linear algebraic equations with n unknowns has a unique solution if and only if:
- The system matrix is symmetric
- The system matrix has rank n (correct)
- The system matrix is invertible
- The determinants of square matrices are non-zero
How is the observability of a system tested?
How is the observability of a system tested?
- By checking if the system matrix has rank n
- By finding the determinants of square matrices
- By taking derivatives of continuous-time measurements
- By ensuring the completeness of the rank of square matrices (correct)
What indicates that a system under consideration is observable?
What indicates that a system under consideration is observable?
When is a linear continuous-time system controllable?
When is a linear continuous-time system controllable?
How is the completeness of the rank of square matrices tested?
How is the completeness of the rank of square matrices tested?
What concept is the dual of controllability?
What concept is the dual of controllability?
What indicates that a linear continuous-time system is controllable?
What indicates that a linear continuous-time system is controllable?
In linear algebra, when does a system of linear algebraic equations with n unknowns have a unique solution?
In linear algebra, when does a system of linear algebraic equations with n unknowns have a unique solution?
What is the purpose of studying observability in systems?
What is the purpose of studying observability in systems?
What is the purpose of studying observability in systems?
What is the purpose of studying observability in systems?
When is a linear continuous-time system controllable?
When is a linear continuous-time system controllable?
What concept is the dual of controllability?
What concept is the dual of controllability?
How is the observability of a system tested?
How is the observability of a system tested?
What indicates that a system under consideration is observable?
What indicates that a system under consideration is observable?
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Study Notes
Controllability and Observability
- Controllability and observability represent two major concepts of modern control system theory.
- Controllability is necessary to be able to do whatever we want with the given dynamic system under control input.
- Observability is necessary to see what is going on inside the system under observation.
Controllability
- A process G is said to be controllable if every state variable x of G can be affected or controlled in finite time.
- This is achieved by some unconstrainted control signal u(t).
- Controllability means that every state variable x of G can be affected in finite time.
Observability
- A process G is said to be observable if every state variable x of G eventually affects some of the outputs y of the process.
- Observability means that every state variable x of G eventually affects some of the outputs y of the process.
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