Discrete Time Integrator

The Discrete-Time Integrator block implements discrete-time integration or accumulation of the input signal. The block can integrate or accumulate using the Forward Euler, Backward Euler, and Trapezoidal methods. In integration mode,  is the block’s sample time. In accumulation mode, . The block’s sample time determines when the block’s output signal is computed.

•     Forward Euler method:  is approximated by .

The output signal at step  is defined by

Let .

At first step, .

At second step, .

At k-th step, .

•     Backward Euler method:  is approximated by .

The output signal at step  is defined by

Let .

At first step, .

At second step, .

At k-th step, .

•     Trapezoidal method:  is approximated by .

Let .

If  is fixed, the block uses the following steps.

At first step, .

At second step,

At k-th step,

If  is variable, the block uses the following steps.

At first step, .

At second step, .

At k-th step,  

Dialog box

Figure 1  Discrete Time Integrator dialog box

Parameters