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x(t): Setpoint
y(t): Controlled Variable
yR(t): Measured Variable
e(t): Error
V1 and V2: Linear Gain Factors
| | e(t) = x(t) - yR(t) | (1)
| | y(t) = V1e(t) = V1[x(t) - yR(t)] | (2)
| | yR(t) = V2y(t) | (3)
| | y(t) = V1x(t) - V1V2y(t) | Recursive Solution (4)
| | y(t) = V1x(t) / [1 + V1V2] | Equifinal Solution (5)
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References:
Dietrich, J. W. (1999-2003). Subtractive 0th order linear feedback control. Medizinische Kybernetik | Medical Cybernetics. http://www.medizinische-kybernetik.de/ips/fc0.html (21 Jul. 2003).
Röhler, R. (1973). Biologische Kybernetik. Stuttgart, B. G. Teubner.
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x(t): Setpoint
y(t): Controlled Variable
yR(t): Measured Variable
z(t): Load (Sum of all Disturbance Variables)
e(t): Error
V1 and V2: Linear Gain Factors
| | e(t) = x(t) - yR(t) | (1)
| | yS(t) = V1e(t) = V1[x(t) - yR(t)] | (2)
| | y(t) = yS(t) + z(t) = V1[x(t) - yR(t)] + z(t) | (3)
| | yR(t) = V2y(t) | (4)
| | y(t) = V1x(t) - V1V2y(t) + z(t) | Recursive Solution (5)
| | y(t) = [V1x(t) + z(t)] / [1 + V1V2] | Equifinal Solution (6)
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References:
Dietrich, J. W. (1999-2003). Subtractive 0th order linear feedback control. Medizinische Kybernetik | Medical Cybernetics. http://www.medizinische-kybernetik.de/ips/fc0l.html (21 Jul. 2003).
Röhler, R. (1973). Biologische Kybernetik. Stuttgart, B. G. Teubner.
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x(omega): Setpoint
y(omega): Controlled variable
yR(omega): Measured variable
z(omega): Load (Sum of all disturbance variables)
e(omega): Error
V1 and V2: Linear gain factors
omega: Angular Frequency of signal
alpha, beta: Time constants
| | e(omega) = x(omega) - yR(omega) | (1)
| | yS(omega) = V1 e(omega) = V1[x(omega) - yR(omega)] | (2)
| | y(omega) = alpha / (omega + beta) * [yS(omega) + z(omega)] | (3)
| | yR(omega) = V2y(omega) | (4)
| | y(omega) = alpha / (omega + beta) * V1x(omega) - V1V2y(omega) + z(omega) | Recursive Solution (5)
| | y(omega) = [alpha V1x(omega) + alpha z(omega)] / [omega + beta + alpha V1V2] | Equifinal Solution (6)
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References:
Dietrich, J. W. (1999-2003). Subtractive 1st order linear feedback control. Medizinische Kybernetik | Medical Cybernetics. http://www.medizinische-kybernetik.de/ips/fc1l.html (27 Jun. 2004).
Röhler, R. (1973). Biologische Kybernetik. Stuttgart, B. G. Teubner.
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x(t): Setpoint
y(t): Controlled variable
yR(t): Measured variable
z(t): Load (Sum of all disturbance variables)
e(t): Error
V1 and V2: Linear gain factors
| | e(t) = x(t) / yR(t) | (1)
| | yS(t) = V1 e(t) = V1 x(t) / yR(t) | (2)
| | y(t) = yS(t) + z(t) = V1 x(t) / yR(t) + z(t) | (3)
| | yR(t) = V2y(t) | (4)
| | y(t) = V1x(t) / [V2y(t)] + z(t) | Recursive Solution (5)
| | y(t)1,2 = z(t)/2 +/- sqrt[V22 z(t)2 + 4 V1 V2 x(t)]/[2 V2] | Equifinal Solution (6)
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Reference:
Dietrich, J. W. (1999-2003). Quotient 0th Order feedback control with load. Medizinische Kybernetik | Medical Cybernetics. http://www.medizinische-kybernetik.de/ips/qfc0l.html (27 Jun. 2003).
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x(t): Input Signal
y(t): Output Signal
alpha: Gain Factor for Input Signal
beta: Clearance Exponent
y: Steady State Solution
Y(omega): Response to periodic input signals
yD: Deleted information
| | dy/dt = alpha x(t) - beta y(t) | (1)
| | y = alpha x(t) / beta | (2)
| | Y(omega) = alpha / (omega + beta) X(omega) | (3)
| | t1 = 1/beta | (4)
| | yD = y0[1 - exp(-beta t)] | (5)
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Reference:
Dietrich, J. W. (2000). "Signal Storage in Metabolic Pathways: The ASIA Element." kybernetiknet 1 (3, 2000): 1-9.
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 | xr(t): Input Signal
yr(t): Output Signal
| | yr(t) = xr(t) - [xr-1(t) + xr+1(t)] | (1)
| y(t)=Bx(t)
| Vector Form (2)
| | B = ( | 1 | -1 | ... | 0 | ) | | -1 | 1 | ... | 0 | | 0 | -1 | ... | 0 | | ... | ... | ... | ... | | 0 | 0 | ... | 1 |
| Connection Matrix (3) |
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