1. Routh Stability Group Oxygen  Jennifer Gehle Brian Murray Razili Stanke-Koch

2. Routh Stability Governing Polynomial Creating the Array Determining Stability

3. Governing Equation Generated from experimental data Based on the control type (PID) Typically a polynomial

4. Creating the Array General Polynomial: S = ax 3 + bx 2 + cx + d Row 1: ac Row 2: bd Row 3: Row 4:

5. Determining Stability Moving down Column 1 Count number of sign changes If number of sign changes is > 1, system is unstable

6. Example! S = 10x 3 + 5x 2 + 8x + 2 Row 1:108 Row 2:52 Row 3:4 Row4:2 Is this system stable?

7. YES!

8. Example! S = 10x 3 + 5x 2 + 8x + 2 Row 1:108 Row 2:52 Row 3:4 Row4:2 Is this system stable?

9. Control Parameters & Stability S = 24x 3 + 7x 2 + 4x + (2 - Kc) Row 1:244 Row 2:7(2 - Kc) Row 3: Row 4:(2 - Kc) Is this system stable?

10. Depends on Controller Gain! Choose a value of Kc that will make the system stable