Characteristic equation of control system

1. What is a characteristic equation in control system?
2. How do you find the characteristic equation of a system?
3. What is the characteristic equation of an open-loop system?
4. Why is characteristic equation important?

What is a characteristic equation in control system?

The characteristic equation is nothing more than setting the denominator of the closed-loop transfer function to zero. In control theory, there are two main methods of analyzing feedback systems: the transfer function (or frequency domain) method and the state space method.

How do you find the characteristic equation of a system?

The system closed-loop transfer function is YR(s)=KL(s)1+KL(s), where L(s)=b(s)a(s). To compute closed loop poles, we extract characteristic polynomial from closed loop transfer function YR(s) and set it as 0, hence we solve for s according to characteristic equation 1+KL(s)=0.

What is the characteristic equation of an open-loop system?

We can rewrite the open loop transfer function as G(s)H(s)=N(s)/D(s) where N(s) is the numerator polynomial, and D(s) is the denominator polynomial. N(s)= 1, and D(s)= s² + 3 s.

Why is characteristic equation important?

of the characteristic equation are called eigenvalues, and are extremely important in the analysis of many problems in mathematics and physics. The polynomial left-hand side of the characteristic equation is known as the characteristic polynomial.