INTE – Controlled integrator

Block SymbolLicensing group: STANDARD

Function Description
The INTE block implements a controlled integrator with variable integral time constant ti and two indicators of the output signal level (ymin a ymax). If $RUN = on$ and $R1 = off$ then

y(t)=1Ti∫t0u(τ)dτ+C,<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow> <mi>y</mi><mrow><mo class="MathClass-open">(</mo><mrow><mi>t</mi></mrow><mo class="MathClass-close">)</mo></mrow> <mo class="MathClass-rel">=</mo> <mfrac><mrow><mn>1</mn></mrow> <mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfrac><msubsup><mrow><mo class="MathClass-op"> ∫ <!--nolimits--></mo><!--nolimits--></mrow><mrow><mn>0</mn></mrow><mrow><mi>t</mi></mrow></msubsup><mi>u</mi><mrow><mo class="MathClass-open">(</mo><mrow><mi>τ</mi></mrow><mo class="MathClass-close">)</mo></mrow><mi>d</mi><mi>τ</mi> <mo class="MathClass-bin">+</mo> <mi>C</mi><mo class="MathClass-punc">,</mo> </mrow></math>

where $C = y 0$ . If $RUN = off$ and $R1 = off$ then the output y is frozen to the last value before the falling edge at the RUN input signal. If $R1 = on$ then the output y is set to the initial value y0. The integration uses the trapezoidal method as follows

yk=yk−1+TS2Ti(uk+uk−1),<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow> <msub><mrow><mi>y</mi></mrow><mrow><mi>k</mi></mrow></msub> <mo class="MathClass-rel">=</mo> <msub><mrow><mi>y</mi></mrow><mrow><mi>k</mi><mo class="MathClass-bin">−</mo><mn>1</mn></mrow></msub> <mo class="MathClass-bin">+</mo> <mfrac><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow> <mrow><mn>2</mn><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfrac><mrow><mo class="MathClass-open">(</mo><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>k</mi></mrow></msub> <mo class="MathClass-bin">+</mo> <msub><mrow><mi>u</mi></mrow><mrow><mi>k</mi><mo class="MathClass-bin">−</mo><mn>1</mn></mrow></msub></mrow><mo class="MathClass-close">)</mo></mrow><mo class="MathClass-punc">,</mo> </mrow></math>

where $T_{S}$ is the block execution period. If $T_{i} = 0$ , the block realize summation by following equation

y k = y k - 1 + u k . <math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow> <msub><mrow><mi>y</mi></mrow><mrow><mi>k</mi></mrow></msub> <mo class="MathClass-rel">=</mo> <msub><mrow><mi>y</mi></mrow><mrow><mi>k</mi><mo class="MathClass-bin">-</mo><mn>1</mn></mrow></msub> <mo class="MathClass-bin">+</mo> <msub><mrow><mi>u</mi></mrow><mrow><mi>k</mi></mrow></msub><mo class="MathClass-punc">.</mo> </mrow></math>

If $T_{i} < 0$ , the block behaviour is undefined.

Consider using the SINT block, whose simpler structure and functionality might be sufficient for elementary tasks.

Inputs

u	Analog input of the block	Double (F64)
RUN	Enable execution	Bool
	off .. Integration stopped on ... Integration running
R1	Block reset, initialization of the integrator output to y0	Bool
y0	Initial output value	Double (F64)
ti	Integral time constant	Double (F64)

Outputs

y	Integrator output	Double (F64)
Q	Running integration indicator	Bool
LY	Lower level indicator ( $y < ymin$ )	Bool
HY	Upper level indicator ( $y > ymax$ )	Bool

Parameters

ymin	Lower level definition $⊙$ -1.0	Double (F64)
ymax	Upper level definition $⊙$ 1.0	Double (F64)
SAT	Limit output if level limit is reach	Bool

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