Disturbance Rejection and Feedforward Control

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Core Idea

Disturbance rejection capability depends on where the disturbance enters the plant relative to the feedback path. Feedback alone cannot reject disturbances before they affect output. Feedforward control (estimating disturbances and applying compensating input) can reject measured disturbances without feedback delay. Combined feedback-feedforward architectures offer superior disturbance attenuation.

Explainer

From your study of the feedback configuration, you know that a closed-loop controller measures output, computes an error, and adjusts input to drive that error toward zero. This is a powerful paradigm, but it has a structural limitation: feedback can only correct an error *after it appears in the output*. If a disturbance enters the plant, the loop must first detect the resulting output deviation, then correct it—incurring both detection delay and correction time. For slow or small disturbances this is acceptable; for fast or large ones, the correction arrives too late to prevent significant performance degradation.

The entry point of a disturbance relative to the feedback loop determines how well feedback can handle it. A disturbance entering at the plant input—before the main process—causes output deviations that the feedback loop must work backward to correct; high loop gain is required to keep these deviations small. A disturbance entering between two cascaded stages will propagate through only the downstream portion before the sensor catches it—better, but still reactive. The key insight is that feedback is inherently reactive: it waits for consequences before acting, and no amount of loop gain eliminates the latency between a disturbance occurring and the corrective action arriving.

Feedforward control breaks this reactive constraint by measuring the disturbance directly and applying a compensating input simultaneously—before the disturbance has time to affect the output. If the disturbance is measurable and the plant's response is known, the feedforward controller can ideally cancel the disturbance completely. In a building heating system, an outdoor temperature sensor can trigger increased heating *before* the indoor temperature begins to drop, rather than waiting for the thermostat to detect an error. The feedforward compensator acts as an inverse plant model: it pre-computes what correction is needed and injects it without waiting for feedback.

Pure feedforward's limitation is its dependence on an accurate plant model. Model errors, unmeasured disturbances, and parameter drift leave residual errors that feedforward cannot address. This is where the combined feedforward-feedback architecture achieves the best of both worlds: feedforward provides fast, anticipatory rejection of the *measured* disturbance, while feedback corrects the residuals that feedforward cannot eliminate due to modeling imperfection. The two mechanisms are complementary—feedforward handles what is measurable and modeled; feedback handles what is not—and their combination is the standard approach in high-performance industrial control wherever disturbances can be sensed directly.

Practice Questions 5 questions

Prerequisite Chain

Counting to 10Counting to 20Understanding ZeroThe Number ZeroCounting to FiveOne-to-One CorrespondenceCombining Small Groups Within 5Addition Within 10Addition Within 20Two-Digit Addition Without RegroupingTwo-Digit Addition with RegroupingAddition Within 100Repeated Addition as MultiplicationMultiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Two-Digit by One-Digit DivisionDivision with RemaindersRemainders and Quotients in DivisionDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueReading and Writing DecimalsComparing and Ordering DecimalsAdding and Subtracting DecimalsMultiplying DecimalsDividing DecimalsDividing FractionsMixed Number ArithmeticOrder of OperationsInteger Order of OperationsVariable ExpressionsCombining Like TermsOne-Step EquationsTwo-Step EquationsSolving Multi-Step EquationsEquations with Variables on Both SidesAngle Pairs: Complementary, Supplementary, and VerticalParallel Lines and TransversalsCorresponding AnglesAlternate Interior AnglesTriangle Angle Sum TheoremExterior Angle TheoremTriangle Inequality TheoremSimilar Triangles: AA SimilaritySimilar Triangles: SSS and SAS SimilarityProportions in Similar TrianglesRight Triangle Trigonometry IntroductionTrigonometric Ratios ReviewRadian MeasureConverting Between Degrees and RadiansThe Unit CircleGraphing Sine and CosineGraphing Tangent and Reciprocal Trigonometric FunctionsDerivatives of Trigonometric FunctionsAntiderivativesIterated Integrals and Fubini's TheoremDouble Integrals in Cartesian CoordinatesDouble Integrals over Rectangular RegionsDouble Integrals in Polar CoordinatesDouble Integrals: Definition and SetupIterated Integrals and Fubini's TheoremDouble Integrals over Rectangular RegionsDouble Integrals over General RegionsApplications of Double Integrals: Area, Mass, and MomentsTriple Integrals in Cartesian CoordinatesTriple Integrals in Cylindrical and Spherical CoordinatesChange of Variables and the Jacobian DeterminantApplications of Triple Integrals: Volume and MassVector Fields and Their RepresentationsLine Integrals of Vector FieldsGreen's TheoremSurface Integrals and Flux of Vector FieldsSurface Integrals and Flux of Vector FieldsDivergence Theorem: Flux and OutflowDivergence TheoremElectric FluxGauss's LawConductors in Electrostatic EquilibriumCapacitance and CapacitorsDielectricsDielectric Constant and Relative PermittivityElectric Field Inside Dielectric MaterialsDielectric Materials and PolarizationDielectric Susceptibility and PermittivityEnergy Density in Electric FieldsElectric Current and Current DensityElectrical Resistance and ResistivityOhm's Law and Circuit ElementsElectromotive Force (EMF) and BatteriesKirchhoff's Circuit Laws: Voltage and CurrentDC Circuit Network Analysis MethodsTransient Response in RC CircuitsRC CircuitsLC and RLC CircuitsAC Circuits: FundamentalsImpedance and ReactanceAC Power and ResonanceElectromagnetic WavesFrequency-Dependent Permittivity and DispersionElectromagnetic Waves in Anisotropic MediaBirefringence and DichroismWave Plates: Quarter-Wave and Half-Wave PlatesCircular and Elliptical Polarization ProductionPolarization States: Linear, Circular, and EllipticalLinear Superposition of WavesSuperposition Principle in ElectrostaticsElectric Field Lines and VisualizationElectric Potential and Potential EnergyElectric Potential and VoltageIdeal Voltage and Current SourcesSeries, Parallel, and Combined Resistor NetworksVoltage Divider Principle and ApplicationsKirchhoff's Voltage and Current LawsNodal Analysis MethodLinearity, Superposition, and ScalingAC Steady-State Circuit AnalysisAC Circuit Analysis Using PhasorsAC Power AnalysisResonance in RLC CircuitsFrequency Response and Bode PlotsBode Plot Stability AnalysisNyquist Stability CriterionGain and Phase MarginsPID ControllersLead and Lag CompensatorsLead Compensator DesignCompensator Realization: Active and Passive NetworksLead-Lag Compensation Design and ImplementationCompensation Design: Cascade vs. Feedback Control TradeoffsCascade and Feedforward ControlDisturbance Rejection and Feedforward Control

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