PID Controllers¶
Åström, K. J., & Hägglund, T. (1995). PID Controllers: Theory, Design, and Tuning.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Latency
- The lever for managing latency is almost always to shorten the loop, hide the delay behind prediction or buffering, or design the controller to expect that its information is stale, rather than to enlarge the system or push it harder.
This sourceInstrument Society of America. Canonical control-tuning reference: shows that loops with significant dead time must be detuned, predicted, or restructured, grounding the loop-shortening/prediction levers for managing delay-induced instability.
- The lever for managing latency is almost always to shorten the loop, hide the delay behind prediction or buffering, or design the controller to expect that its information is stale, rather than to enlarge the system or push it harder.
Domain-specific¶
- Derivative
- Differential and integral calculus / real analysis — the home theory: the difference-quotient limit, differentiability classes, Taylor expansion, Newton's method, and the f′ = 0 / sign-of-f″ optimization conditions, extended to many variables via the gradient, Jacobian, and Fréchet derivative. Classical mechanics — rate of a rate: velocity as the time-derivative of position and acceleration as its derivative, so Newton's second law F = m d²x/dt² is a second-order differential equation. Economics — quantities at the margin: marginal cost, revenue, and utility as exact derivatives of the corresponding totals rather than finite differences. Optimization theory — critical points and their type: f′(x) = 0 isolating candidates and f″(x) (or the Hessian) classifying minima, maxima, and saddle points, single- and multi-variable. Control engineering — the rate term: the D-term of a PID controller acting on the derivative of the error signal
This sourceThe derivative (D) term of a PID controller as acting on the time-derivative of the error signal, with its filtering and noise caveats.
- Differential and integral calculus / real analysis — the home theory: the difference-quotient limit, differentiability classes, Taylor expansion, Newton's method, and the f′ = 0 / sign-of-f″ optimization conditions, extended to many variables via the gradient, Jacobian, and Fréchet derivative. Classical mechanics — rate of a rate: velocity as the time-derivative of position and acceleration as its derivative, so Newton's second law F = m d²x/dt² is a second-order differential equation. Economics — quantities at the margin: marginal cost, revenue, and utility as exact derivatives of the corresponding totals rather than finite differences. Optimization theory — critical points and their type: f′(x) = 0 isolating candidates and f″(x) (or the Hessian) classifying minima, maxima, and saddle points, single- and multi-variable. Control engineering — the rate term: the D-term of a PID controller acting on the derivative of the error signal
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