Controllability and Observability in Power Systems
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Questions and Answers

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:

  • 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?

  • 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?

    <p>Rank O = 2 ≠ 0</p> Signup and view all the answers

    When is a linear continuous-time system controllable?

    <p>When the system matrix has full rank</p> Signup and view all the answers

    How is the completeness of the rank of square matrices tested?

    <p>Finding their determinants</p> Signup and view all the answers

    What concept is the dual of controllability?

    <p>Observability</p> Signup and view all the answers

    What indicates that a linear continuous-time system is controllable?

    <p>Completeness of the rank of the controllability matrix</p> Signup and view all the answers

    In linear algebra, when does a system of linear algebraic equations with n unknowns have a unique solution?

    <p>When the system matrix has rank n</p> Signup and view all the answers

    What is the purpose of studying observability in systems?

    <p>To represent the dual concept of controllability</p> Signup and view all the answers

    What is the purpose of studying observability in systems?

    <p>To analyze the system's controllability</p> Signup and view all the answers

    When is a linear continuous-time system controllable?

    <p>When the controllability matrix has full rank</p> Signup and view all the answers

    What concept is the dual of controllability?

    <p>Observability</p> Signup and view all the answers

    How is the observability of a system tested?

    <p>By checking if the observability matrix has full rank</p> Signup and view all the answers

    What indicates that a system under consideration is observable?

    <p>When the rows of the observability matrix are linearly independent</p> Signup and view all the answers

    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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    Test your knowledge on the concepts of controllability and observability in power systems. Explore the important aspects of control system theory related to power dynamics.

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