Trapezoidal Integration
The FixPt Integrator: Trapezoidal realization is a
masked subsystem that performs discrete-time integration using the Trapezoidal
method. For this method, integration is approximated by the z-domain
transfer function
where Ts is the sampling period. The transfer
function yields the difference equation
where k is the time step, y(k)
is the current output, y(k - 1) is the output from the previous
time step, u(k) is the current input, and u(k -
1) is the input from the previous time step.
Parameters and Dialog Box
-
Sample time
-
The time interval, Ts, between samples
-
Base data type
-
The processor's base data type
-
Accumulator data type
-
The processor's accumulator data type
Model Design Review
A brief review of the model design is given below.
The design criteria reflect these rules.
-
The gains involve multiplications which are a size-growing operation. In
most cases, it is desirable for gain and input to use the word size given
by the Base data type or smaller. The output can be left at the
Accumulator data type for extra precision in subsequent operations.
Alternatively, if the output were stored to RAM, or used by a size-growing
operation, it could be reduced to the Base data type.
-
The FixPt Sum block converts inputs to the output data type before performing
the actual addition. Given this order of operation, using the Accumulator
data type often gives better precision.
-
The FixPt Conversion block forces the output to the Base data type
before storage in RAM (i.e., before input to the unit delay). Casting the
output in the feedforward part of the realization prevents subsequent operations
from being burdened with a large data type.
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