What is the characteristic equation of a control system?
Practice Questions
Q1
What is the characteristic equation of a control system?
It is derived from the transfer function.
It describes the system's input-output relationship.
It is always a polynomial of degree one.
It determines the system's frequency response.
Questions & Step-by-Step Solutions
What is the characteristic equation of a control system?
Step 1: Understand that a control system can be represented by a transfer function, which is a mathematical representation of the system's output in relation to its input.
Step 2: The transfer function is usually expressed as a ratio of two polynomials: the numerator represents the output and the denominator represents the input.
Step 3: The characteristic equation is obtained by setting the denominator of the transfer function equal to zero.
Step 4: This equation helps us find the values (called poles) that determine the behavior of the system.
Step 5: Analyzing the roots of the characteristic equation allows us to determine if the system is stable or unstable.
