Discrete

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

\begin{aligned} &\text{Forward Euler:} && y[n] = y[n-1] + T \cdot u[n-1] \\ &\text{Backward Euler:} && y[n] = y[n-1] + T \cdot u[n] \\ &\text{Trapezoidal:} && y[n] = y[n-1] + \frac{T}{2} (u[n] + u[n-1]) \end{aligned}

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

Examples

Zie de ingebouwde voorbeelden in de handleiding voor een demonstratie van dit blok.