Question

A transfer function of control system does not have pole-zero cancellation. Which one of the following statements is true?

• A. System is neither controllable nor observable.
• B. System is completely controllable and observable.
• C. System is observable but uncontrollable.
• D. System is controllable but unobservable.

Hint:

When analyzing control systems, ensure you examine both controllability and observability, especially in the context of pole-zero cancellation. A system must be both for efficient control and monitoring.

Answer 1

The Correct Option is B

A system without pole-zero cancellation usually satisfies the conditions for controllability and observability. This implies the system is both controllable and observable, and no cancellation occurs between poles and zeros. Hence, the system would be completely controllable and observable.