Question

A unity feedback system has the characteristic equation shown below. Use the Routh - Hurwitz Stability Criterion to find the range of K for stability. Enter the LOWER bound of this range to two decimal places.

s⁴+10s³+35s²+(50+K)s+(24−2K)=0

Answer 1

To determine the range of K for stability using the Routh-Hurwitz Stability Criterion, create the Routh array and apply the conditions for stability to find the lower bound.

Step-by-step explanation:

To determine the range of K for stability using the Routh-Hurwitz Stability Criterion, we need to create the Routh array using the coefficients of the characteristic equation. The characteristic equation for the unity feedback system is:

s⁴ + 10s³ + 35s² + (50+K)s + (24−2K) = 0

We can create the Routh array as follows:

| 1 35 24-2K
| 10 50+K
| 2K
| 24-2K

Using the Routh array, we can determine the conditions for stability:
- All the elements in the first column (1, 10, and 2K) must be positive for stability.
- The sign changes in the first column cannot exceed one. If they exceed one, it indicates the presence of one or more poles in the right-half of the s-plane, which leads to instability.

By applying these conditions, we can calculate the lower bound of the range of K for stability.