Continuous

Integrator Block

Integrates input signal over time using Trapezoidal rule for numerical accuracy

Description

The Integrator block computes the time integral (accumulated sum) of an input signal. It is the inverse operation to the Derivative block and is essential for accumulating signals, computing areas, and implementing the I-term in PID controllers.

Mathematical Model

Continuous:  y(t) = y₀ + ∫₀ᵗ u(τ) dτ
Discrete:    y[n] = y[n-1] + (Δt/2) × (u[n] + u[n-1])  (Trapezoidal rule)

Parameters

initialCondition

Starting value of the accumulator at t=0.

Type: number
Default: 0
Tooltip: Starting value for the integrator

lowerLimit

Minimum output value (saturation).

Type: number
Range: -1e9 to 1e9
Default: -100000
Tooltip: Minimum output value (saturation)

upperLimit

Maximum output value (saturation).

Type: number
Range: -1e9 to 1e9
Default: 100000
Tooltip: Maximum output value (saturation)

reset (optional)

Reset trigger input. Set > 0 to reset output to initial condition.

Type: number
Required: false
Tooltip: Set > 0 to reset output to initial condition

Reset Behavior

The integrator has an optional reset input port:

When reset > 0, the output is forced to the initialCondition value
Integration is skipped during the reset step
After reset, previous_input is set to the current input value to prevent a large trapezoidal step on the next integration step
On the first step after reset is released, integration resumes cleanly from the initial condition
Multiple consecutive resets hold the output at initialCondition

Examples

Constant Integration (1 second)

Constant input (value=2) integrated over 1 second produces linearly increasing output (0 to 2).

Velocity from Acceleration

Accelerometer signal (constant 5 m/s²) integrated to produce velocity (0 to 5 m/s over 1 sec).

Remarks

Inverse of Derivative: Complementary operation (Integrator + Derivative ≈ identity with delay)
Trapezoidal Rule: More accurate than Euler for smooth signals
I-term in PID: Essential for eliminating steady-state error
Saturation: Prevents integrator windup when output hits limits. Once saturated, the accumulated value is clamped; it can still decrease (or increase) when the input reverses.
Initial Condition: Set non-zero to start accumulation from different point