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Discrete ∫

Discrete

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.

Direction	ID	Label	Type	Status
→ In	`in`	In	number	Required
→ In	`reset`	Reset	number	Optional
← Out	`out`	Out	number	Output

Parameters	Label	Type	Default
`method`	Integration Method	select	`forward`
`initialCondition`	Initial Condition	number	`0`
`sampleTime`	Sample Time	number	`0.01`

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

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