Class ControlSystems

java.lang.Object

org.episteme.natural.engineering.control.ControlSystems

public class ControlSystems
extends Object

Control systems analysis. Modernized to use typed Quantities for Time and Frequency.

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	ControlSystems.PIDController	PID controller output. u(t) = Kp*e + Ki*∫e*dt + Kd*de/dt Operating on abstract mathematical signals (Real).

Method Summary

Modifier and Type	Method	Description
static Real	firstOrderMagnitude(Real K, Quantity<Frequency> omega, Quantity<Frequency> omegaCutoff)	Bode magnitude for first-order system.
static Quantity<Angle>	firstOrderPhase(Quantity<Frequency> omega, Quantity<Frequency> omegaCutoff)	Bode phase for first-order system.
static Real	firstOrderStepResponse(Real K, Quantity<Time> tau, Quantity<Time> t)	First-order system step response. y(t) = K * (1 - e^(-t/Ï„))
static Real	gainMargin(Real gainAtPhaseCrossover)	Gain margin in dB.
static Quantity<Dimensionless>	overshoot(Real zeta)	Overshoot percentage.
static Quantity<Time>	peakTime(Quantity<Frequency> wn, Real zeta)	Peak time for second-order underdamped system. tp = π / wd
static Quantity<Angle>	phaseMargin(Quantity<Angle> phaseAtCrossover)	Phase margin from open-loop gain and phase at crossover.
static Quantity<Time>	riseTime(Quantity<Frequency> wn, Real zeta)	Rise time estimate for second-order system. tr ≈ (π - φ) / wd
static Real	secondOrderStepResponse(Quantity<Frequency> wn, Real zeta, Quantity<Time> t)	Second-order system step response (underdamped).
static Quantity<Time>	settlingTime(Quantity<Frequency> wn, Real zeta)	Settling time (2% criterion). ts ≈ 4 / (ζ * ωn)
static Real	steadyStateError(Real Kp)	Steady-state error for type 0 system with step input. ess = 1 / (1 + Kp)

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

firstOrderStepResponse

public static Real firstOrderStepResponse(Real K,
 Quantity<Time> tau,
 Quantity<Time> t)

First-order system step response. y(t) = K * (1 - e^(-t/Ï„))

secondOrderStepResponse

public static Real secondOrderStepResponse(Quantity<Frequency> wn,
 Real zeta,
 Quantity<Time> t)

Second-order system step response (underdamped).

riseTime

public static Quantity<Time> riseTime(Quantity<Frequency> wn,
 Real zeta)

Rise time estimate for second-order system. tr ≈ (π - φ) / wd

peakTime

public static Quantity<Time> peakTime(Quantity<Frequency> wn,
 Real zeta)

Peak time for second-order underdamped system. tp = π / wd

overshoot

public static Quantity<Dimensionless> overshoot(Real zeta)

Overshoot percentage. %OS = 100 * e^(-ζπ / sqrt(1-ζ²))

settlingTime

public static Quantity<Time> settlingTime(Quantity<Frequency> wn,
 Real zeta)

Settling time (2% criterion). ts ≈ 4 / (ζ * ωn)

steadyStateError

public static Real steadyStateError(Real Kp)

Steady-state error for type 0 system with step input. ess = 1 / (1 + Kp)

phaseMargin

public static Quantity<Angle> phaseMargin(Quantity<Angle> phaseAtCrossover)

Phase margin from open-loop gain and phase at crossover.

gainMargin

public static Real gainMargin(Real gainAtPhaseCrossover)

Gain margin in dB.

firstOrderMagnitude

public static Real firstOrderMagnitude(Real K,
 Quantity<Frequency> omega,
 Quantity<Frequency> omegaCutoff)

Bode magnitude for first-order system. |G(jω)| = K / sqrt(1 + (ω/ωc)²)

firstOrderPhase

public static Quantity<Angle> firstOrderPhase(Quantity<Frequency> omega,
 Quantity<Frequency> omegaCutoff)

Bode phase for first-order system. φ = -arctan(ω/ωc)