Question

Given the characteristic equation s³+6s²+11s+12, use the RH method to determine if the system is stable and if not, how many poles are in the right hand half plane.

Answer 1

Using the Routh-Hurwitz method on the characteristic equation s³+6s²+11s+12, there are no sign changes in the first column of the Routh array. This indicates that there are no poles in the right-hand half-plane and the system is stable.

Step-by-step explanation:

To determine if a system represented by the characteristic equation s³+6s²+11s+12 is stable, we can use the Routh-Hurwitz (RH) method. The RH method involves creating the Routh array and checking the number of sign changes in the first column, which indicate the number of poles in the right-hand half-plane (RHP). A system is stable only when all poles are in the left-hand half-plane (LHP).

For the given characteristic equation, we construct the Routh array as follows:

• Row 1: s³ coefficients: 1 and 11
• Row 2: s² coefficients: 6 and 12
• Row 3: s¹ coefficient: Using the formula (6*11 - 12*1) / 6 = 66/6 = 11
• Row 4: s° coefficient: The constant term, which is 12

Now, we look at the sign of the first column:

• s³: 1 (positive)
• s²: 6 (positive)
• s¹: 11 (positive)
• s°: 12 (positive)

Since there are no sign changes in the first column, there are no poles in the RHP, indicating that the system is stable.