Turn up the gain to go faster, and at some point the robot starts to shake, then to swing wildly. Feedback can make things worse.
Key idea
A system is stable if its error dies out. Too much gain or too much delay makes it overshoot, then oscillate, and finally diverge. A common hand-tuning order: raise $K_p$ until it oscillates, back off; add $K_d$ to damp; add a little $K_i$ last for the leftover error.
Why it works
Each correction takes time to show up in the measurement. A big correction based on old news overshoots, and the next correction overshoots back. A simple model shows it: if each step corrects $K$ times the error, the new error is $(1 - K)$ times the old. That shrinks only if $0 < K < 2$.
Worked example: Does it settle?
Each step: new error $= (1 - K) \times$ old. With $K = 1.5$ and starting error 8?
- $1 - 1.5 = -0.5$.
- Errors: 8, −4, 2, −1, 0.5…
Answer: Yes: it flips sign each step but shrinks.
Worked example: And with K = 2.5?
Same start.
- $1 - 2.5 = -1.5$.
- Errors: 8, −12, 18, −27…
Answer: No: it grows. Unstable.
Common mistake
Raising the gain to go faster and being surprised when the robot shakes. Faster response and calm response pull against each other.
Safety while tuning. Tune a new controller with the robot on a stand or the arm unloaded, at low power, with the power switch in reach. An unstable loop can swing hard.
The Book Cart in the Science Lab balances a chain of books on a moving cart, a classic hard control problem.