DiscreteIntegrator Block

Discrete-time integrator (accumulator). Supports forward Euler, backward Euler, and trapezoidal methods.

# DiscreteIntegrator Block

Description

Discrete-time integrator that accumulates the input signal over time. Equivalent to a running sum scaled by the sample time.

Mathematical Model

Forward Euler:  y[n] = y[n-1] + T · u[n-1]
Backward Euler: y[n] = y[n-1] + T · u[n]
Trapezoidal:    y[n] = y[n-1] + T · (u[n] + u[n-1]) / 2

where y[n] is the current output, u[n] the current input, and T the sample time.

Parameters

method

Integration method:

• forward: Forward Euler — uses previous input value
• backward: Backward Euler — uses current input value
• trapezoidal: Trapezoidal rule — averages current and previous input

initialCondition

Starting value of the accumulator.

sampleTime

Discrete sample period (seconds).

Remarks

• Forward Euler: Simplest method but can be unstable for fast dynamics; suitable for mild integration
• Backward Euler: Implicit method — more stable for stiff systems; recommended for control loops
• Trapezoidal: Best accuracy for smooth signals; matches Tustin/bilinear transform for filter design
• Reset: The integrator can be reset by changing the initialCondition parameter at runtime
• Windup: In feedback control loops, the integrator may wind up if the output is saturated; use anti-windup strategies

See Also

• Integrator: Continuous-time integrator
• DiscreteDerivative: Discrete-time derivative (inverse operation)