Stability Checks: Characteristic Roots in Real and Imaginary Parts, a Stable Flag & a Gain Sweep
This lesson is part of the course
In this lesson
You sweep the controller gain from 0 to 8, compute the coefficients and the discriminant of s² + a·s + b, the real and imaginary parts of the roots in separate columns and flag each gain as stable or unstable.
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Lessons in this course
- Open vs Closed Loop: A Toy Heater, a Disturbance Step & Sensitivity to a Gain Change Locked
- First-Order Systems: A Step Table, 63 % at One Time Constant & Settling at About 4τ Locked
- Second-Order Systems: Damping Ratio, Natural Frequency, Overshoot, Peak & Settling Time Locked
- Proportional Control: Closed-Loop Gain, Steady-State Error & Speed vs Error for Four Gains Locked
- Dead Time & Sampling: Delaying the Input by d Steps, Sample Period & When a Loop Starts to Oscillate Locked
- Stability Checks: Characteristic Roots in Real and Imaginary Parts, a Stable Flag & a Gain Sweep Locked
- Frequency Response: Magnitude in Decibels, Phase, Corner Frequency, Parts in Series & Margins Locked
- Capstone – Tuning Table & Comparison: P vs PI Settings, Simulated Responses, Overshoot & Summed Absolute Error Locked