constraint

Algebraic (differential-algebraic) constraint state solved by the DAE solver.

📝Syntax

Block type: constraint

📥Input Arguments

Parameter	Description
input ports	1 input port(s) declared: the constraint residual g.

📤Output Arguments

Parameter	Description
output ports	1 output port(s) declared: the algebraic state z.

📄Description

Algebraic (differential-algebraic) constraint state solved by the DAE solver.

Module	`nflow_blocks`
Library	Continuous blocks
Type	`constraint`
Label	Constraint

Description

The Constraint block introduces one algebraic state z (its output). It has no derivative of its own; instead the DAE solver adjusts z so that the block's input signal g is driven to zero. Wire the surrounding diagram so the input computes the constraint residual g(z, x) = 0 (typically using the block's own output z), and the solver holds the system on that manifold.

This block is only meaningful under the differential-algebraic solver: set the model's solver to dae. Under any other solver, or in generated C / Rust code, it is rejected with a clear message (there is no explicit lowering for a differential-algebraic system).

Ports

Input(s)

Port	Role	Side	Position
Port_1	The constraint residual g, driven to zero.	left	x=0, y=40

Output(s)

Port	Role	Side	Position
Port_1	The algebraic state z the solver determines.	right	x=80, y=40

Parameters

Parameter	Default value
`InitialCondition`	0

The initial condition is only an initial guess for z; the solver refines it to a consistent value with IDACalcIC.

Block Characteristics

Block type	constraint
Family	Continuous blocks
Rendered size	80 x 80
Phases	INIT, OUTPUT, DERIVATIVE
Internal state or history	one algebraic (mass-0) state
Signal data type	double numeric values

Equation or Rule

$$0 = g(z, x),\qquad y = z$$

Implementation Sources

Manifestmodules/nflow_blocks/libraries/continuous/library.json

{
  "id": "builtin.continuous",
  "title": "Continuous",
  "version": "1.0.0",
  "format": "nflow-2",
  "metadata": {
    "author": "Allan CORNET",
    "created": "2026-03-21",
    "tool": "Nelson nflow"
  },
  "comment": "Blocks for continuous-time systems",
  "license": "LGPL-3.0",
  "builtin": true,
  "blocks": [
    {
      "type": "integrator",
      "label": "Integrator",
      "icon": "integrator.svg",
      "phases": [
        "INIT",
        "OUTPUT",
        "UPDATE"
      ],
      "width": 80,
      "height": 80,
      "inputs": [
        {
          "x": 0,
          "y": 40,
          "side": "left"
        }
      ],
      "outputs": [
        {
          "x": 80,
          "y": 40,
          "side": "right"
        }
      ],
      "defaultParams": {
        "InitialCondition": 0,
        "ExternalReset": "none",
        "InitialConditionSource": "internal",
        "LowerSaturationLimit": "-inf",
        "UpperSaturationLimit": "inf"
      },
      "render": {
        "type": "math",
        "useRectElement": true,
        "bodyClass": "block-body integrator-body",
        "mathGroupClass": "integrator-math",
        "formula": "\\frac{1}{s}"
      }
    },
    {
      "type": "tf",
      "label": "Transfer Fn",
      "icon": "tf.svg",
      "phases": [
        "INIT",
        "OUTPUT",
        "ALGEBRAIC",
        "UPDATE"
      ],
      "width": 85,
      "height": 80,
      "inputs": [
        {
          "x": 0,
          "y": 40,
          "side": "left"
        }
      ],
      "outputs": [
        {
          "x": 85,
          "y": 40,
          "side": "right"
        }
      ],
      "defaultParams": {
        "Numerator": [
          3
        ],
        "Denominator": [
          1,
          3
        ]
      },
      "render": {
        "type": "math",
        "bodyClass": "block-body",
        "mathGroupClass": "tf-math",
        "formula": "\\frac{N(s)}{D(s)}"
      }
    },
    {
      "type": "delay",
      "label": "Delay",
      "icon": "delay.svg",
      "phases": [
        "INIT",
        "OUTPUT",
        "UPDATE"
      ],
      "width": 80,
      "height": 80,
      "inputs": [
        {
          "x": 0,
          "y": 40,
          "side": "left"
        }
      ],
      "outputs": [
        {
          "x": 80,
          "y": 40,
          "side": "right"
        }
      ],
      "defaultParams": {
        "DelayTime": 0.1
      },
      "render": {
        "type": "math",
        "bodyClass": "block-body",
        "mathGroupClass": "delay-math",
        "formula": "e^{-sT}"
      }
    },
    {
      "type": "stateSpace",
      "label": "State-Space",
      "icon": "stateSpace.svg",
      "phases": [
        "INIT",
        "OUTPUT",
        "UPDATE"
      ],
      "width": 160,
      "height": 80,
      "inputs": [
        {
          "x": 0,
          "y": 40,
          "side": "left"
        }
      ],
      "outputs": [
        {
          "x": 160,
          "y": 40,
          "side": "right"
        }
      ],
      "defaultParams": {
        "A": 1,
        "B": 1,
        "C": 1,
        "D": 0,
        "InitialCondition": 0
      },
      "render": {
        "type": "math",
        "bodyClass": "block-body",
        "mathGroupClass": "state-space-math",
        "formula": "\\dot{x}=Ax+Bu",
        "textSize": "16px"
      }
    },
    {
      "type": "lpf",
      "label": "LPF",
      "icon": "lpf.svg",
      "phases": [
        "INIT",
        "OUTPUT",
        "UPDATE"
      ],
      "width": 80,
      "height": 80,
      "inputs": [
        {
          "x": 0,
          "y": 40,
          "side": "left"
        }
      ],
      "outputs": [
        {
          "x": 80,
          "y": 40,
          "side": "right"
        }
      ],
      "defaultParams": {
        "Cutoff": 1
      },
      "render": {
        "src": "lpf.svg",
        "type": "image"
      }
    },
    {
      "type": "hpf",
      "label": "HPF",
      "icon": "hpf.svg",
      "phases": [
        "INIT",
        "OUTPUT",
        "UPDATE"
      ],
      "width": 80,
      "height": 80,
      "inputs": [
        {
          "x": 0,
          "y": 40,
          "side": "left"
        }
      ],
      "outputs": [
        {
          "x": 80,
          "y": 40,
          "side": "right"
        }
      ],
      "defaultParams": {
        "Cutoff": 1
      },
      "render": {
        "src": "hpf.svg",
        "type": "image"
      }
    },
    {
      "type": "derivative",
      "label": "Derivative",
      "icon": "derivative.svg",
      "phases": [
        "INIT",
        "OUTPUT",
        "UPDATE"
      ],
      "width": 80,
      "height": 80,
      "inputs": [
        {
          "x": 0,
          "y": 40,
          "side": "left"
        }
      ],
      "outputs": [
        {
          "x": 80,
          "y": 40,
          "side": "right"
        }
      ],
      "defaultParams": {},
      "render": {
        "type": "math",
        "useRectElement": true,
        "bodyClass": "block-body",
        "mathGroupClass": "derivative-math",
        "formula": "\\frac{d}{dt}"
      }
    },
    {
      "type": "pid",
      "label": "PID",
      "icon": "pid.svg",
      "phases": [
        "INIT",
        "OUTPUT",
        "UPDATE"
      ],
      "width": 80,
      "height": 80,
      "inputs": [
        {
          "x": 0,
          "y": 40,
          "side": "left"
        }
      ],
      "outputs": [
        {
          "x": 80,
          "y": 40,
          "side": "right"
        }
      ],
      "defaultParams": {
        "P": 1,
        "I": 0,
        "D": 0,
        "N": 0,
        "LowerSaturationLimit": "-inf",
        "UpperSaturationLimit": "inf"
      },
      "render": {
        "type": "math",
        "bodyClass": "block-body",
        "mathGroupClass": "pid-math",
        "formula": "\\mathsf{PID}"
      }
    },
    {
      "type": "constraint",
      "label": "Constraint",
      "icon": "constraint.svg",
      "phases": [
        "INIT",
        "OUTPUT",
        "DERIVATIVE"
      ],
      "width": 80,
      "height": 80,
      "inputs": [
        {
          "x": 0,
          "y": 40,
          "side": "left"
        }
      ],
      "outputs": [
        {
          "x": 80,
          "y": 40,
          "side": "right"
        }
      ],
      "defaultParams": {
        "InitialCondition": 0
      },
      "render": {
        "type": "math",
        "bodyClass": "block-body",
        "mathGroupClass": "constraint-math",
        "formula": "g=0"
      }
    }
  ]
}

Runtimemodules/nflow_blocks/src/cpp/continuous/constraint.cpp

//=============================================================================
// Copyright (c) 2016-present Allan CORNET (Nelson)
//=============================================================================
// This file is part of Nelson.
//=============================================================================
// LICENCE_BLOCK_BEGIN
// SPDX-License-Identifier: LGPL-3.0-or-later
// LICENCE_BLOCK_END
//=============================================================================
// Algebraic constraint block. Declares one ALGEBRAIC state z
// (its output); the DAE solver drives the block's input g -> 0, so z is defined
// implicitly by the equation g(z, x) = 0 the surrounding diagram builds. OUTPUT
// emits z = x[xOffset]; DERIVATIVE writes the residual g (the block input) into
// the xdot slot, which the solver-loop residual assembly reads as the algebraic
// residual because this state's id = 0 (BlockMetadata::algebraicState). There is
// no fixed-step / discrete meaning; the block only works under the `dae` solver.
//=============================================================================
#include "SimEngineTypes.hpp"
#include "BlockRegistry.hpp"
#include "FieldNames.hpp"
#include "NFlowBlockDescriptor.hpp"
#include "continuous_blocks.hpp"
//=============================================================================
namespace Nelson {
namespace NFlow {
    //=============================================================================
    bool
    handleConstraint(SimCtx& ctx, const Block& b, Phase phase)
    {
        auto& st = getState(ctx, b.nid);
        if (phase == Phase::INIT) {
            nflow::BlockDescriptor bd(b, ctx.variables);
            st.scalar = bd.paramDouble(nflow::kInitial, 0.0); // initial guess for z
            st.output = st.scalar;
            return false;
        }
        if (phase == Phase::OUTPUT) {
            const double* xs = blockX(ctx, b.nid);
            setOutput(ctx, b.nid, xs ? xs[0] : st.scalar);
            return false;
        }
        if (phase == Phase::DERIVATIVE) {
            // The algebraic residual IS the block's input g; store it in the xdot
            // slot so the DAE residual assembly picks it up (id = 0 -> r = g).
            double* xdot = blockXdot(ctx, b.nid);
            if (xdot) {
                xdot[0] = getInput(ctx, b.nid, 0, 0.0);
            }
            return false;
        }
        return false;
    }
    //=============================================================================
} // namespace NFlow
} // namespace Nelson
//=============================================================================

🔗See Also

integrator stateSpace

🕔Version History

Version	Description
1.0.0	initial version

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