Examples
Examples
Try the starting example
- Plant numerator coefficients
- 1
- Plant denominator coefficients
- 1,3,2
- Negative-feedback gains
- 0,1,3,5
- Gain and closed-loop pole coordinates (JSON)
- [[0,[[-2,0],[-1,0]]],[1,[[-1.5,-0.866025403784],[-1.5,0.866025403784]]],[3,[[-1.5,-1.65831239518],[-1.5,1.65831239518]]],[5,[[-1.5,-2.17944947177],[-1.5,2.17944947177]]]]
Try another scenario
- Plant numerator coefficients
- [2]
- Plant denominator coefficients
- [1, 3, 2]
- Negative-feedback gains
- [0, 1, 3, 5]
- Gain and closed-loop pole coordinates (JSON)
- [[0,[[-2,0],[-1,0]]],[1,[[-1.5,-1.32287565553],[-1.5,1.32287565553]]],[3,[[-1.5,-2.39791576166],[-1.5,2.39791576166]]],[5,[[-1.5,-3.1224989992],[-1.5,3.1224989992]]]]
Calculation method
Calculation method
Gain and closed-loop pole coordinates (JSON)
Negative unity-feedback characteristic polynomial D(s)+K N(s); evaluate numerical roots at supplied gains, not continuous branch tracking.
Symbols and units
- a
- Plant numerator coefficients
- b
- Plant denominator coefficients
- c
- Negative-feedback gains
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- User-supplied measurements and assumptions; Negative unity-feedback characteristic polynomial D(s)+K N(s); evaluate numerical roots at supplied gains, not continuous branch tracking. Supported limits: Finite numeric values bounded to 1e9 magnitude; lists and tables contain 1–100 records unless a stricter bound is stated. Inputs use the units shown. Lists explicitly paired by a method must have matching lengths; independent polynomial coefficient vectors may differ. Respect stated physical, interpolation, policy and computational domain limits. Polynomial degrees are bounded to 6. Higher-degree near-multiple roots with a small derivative relative to coefficient scale are rejected as ill-conditioned; nonconvergent root solves are rejected rather than presented as accurate.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
Background reading; this does not imply endorsement or independent review of SumFizz.