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Questions and Answers
What is the dual concept of controllability?
What is the dual concept of controllability?
- Controllability
- Unobservability
- Uncontrollability
- Observability (correct)
How is observability studied?
How is observability studied?
- By using only discrete-time measurements
- By considering an input-free system (correct)
- By introducing random inputs
- By using only continuous-time measurements
What does the rank of the system matrix indicate?
What does the rank of the system matrix indicate?
- The completeness of the system
- The uniqueness of the solution to the system of linear algebraic equations (correct)
- The consistency of the system
- The number of unknowns in the system
How is the observability of a system tested using the rank of a matrix?
How is the observability of a system tested using the rank of a matrix?
What condition ensures that a linear continuous-time system is controllable?
What condition ensures that a linear continuous-time system is controllable?
What condition ensures that a linear continuous-time system is observable?
What condition ensures that a linear continuous-time system is observable?
How is the completeness of the rank of square matrices tested for observability?
How is the completeness of the rank of square matrices tested for observability?
What concept is considered as the dual of controllability?
What concept is considered as the dual of controllability?
What condition ensures that a linear continuous-time system is controllable?
What condition ensures that a linear continuous-time system is controllable?
What does the rank of the system matrix indicate?
What does the rank of the system matrix indicate?
Which method is used to achieve prescribed steady-state response to selected input commands in optimal control system design?
Which method is used to achieve prescribed steady-state response to selected input commands in optimal control system design?
What concept is used to analyze the behavior of feedback control systems utilizing state variables?
What concept is used to analyze the behavior of feedback control systems utilizing state variables?
What aspect of power systems does the concept of Voltage Control primarily address?
What aspect of power systems does the concept of Voltage Control primarily address?
Which theorem is used to analyze the stability of control systems by considering a comparison function and its derivative along the trajectory of the system's state equation?
Which theorem is used to analyze the stability of control systems by considering a comparison function and its derivative along the trajectory of the system's state equation?
Which method is utilized to represent the range of possible transfer functions of a feedback control system as the system's parameters vary?
Which method is utilized to represent the range of possible transfer functions of a feedback control system as the system's parameters vary?
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Study Notes
Controllability and Observability
- Controllability and observability are two major concepts in modern control system theory.
Controllability
- A system is controllable if every state variable can be affected or controlled in finite time by some unconstrained control signal.
- The system must be able to be controlled to achieve desired outcomes.
Observability
- A system is observable if every state variable eventually affects some of the outputs of the process.
- The system must be able to be observed to understand its internal behavior.
Importance of Controllability and Observability
- Controllability is necessary to make the system do what we want.
- Observability is necessary to see what is going on inside the system.
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