DYNAMIC CORRECTION OF
ERRORS OF MEASURING CONVERTERS
doctor of science S.T. Tikhonchuk,
A.V. Zadereyko
One of the biggest challenges in
creating the automated control systems of complex objects and technological
processes is the task of improving the accuracy of measurements.
When measuring
fast processes should take into account the inertia of the components of the
measuring channel. As a rule, the inertia measurement channel defined inertia
sensor used. Confine correction measurements made using sensors, a mathematical
model which can be represented as a delay element of the first, second or
higher-order transfer function:
W(p) =
1/[(T_{1}p+1)(T_{2}p+1)*...*(T_{n}p+1)], n = 1,2,...,N
(1)
A similar problem occurs whenever
the rate of change of the measured parameter is comparable to the time constant
of the sensor.
The basic approach to solving the
problem of recovering the true parameter values at the input to output values
measured approach is based on the construction of the converter transfer
function implements the inverse of the transfer function of the sensor [1].
This
converter is constructed by incorporating sensor model in a feedback channel
operational amplifier with infinite gain. The transfer function W_{k}(p) = 1/W
(p), as a rule, has a differentiating properties and attempts to build devices
that implement this transfer function are generally not lead to success.
Correction algorithms implementing the transfer function W_{k}(p), obtained by
unstable and moreover, significantly increase measurement errors.
Thus, the
presence of measurement errors, which always have a place in the real
measurement systems do not effectively implement this approach.
This problem can be partially
solved by using the method of regularization. Discussed in relation to the
problem of constructing devices for solving the inverse problem of correcting
the measurements use the regularization method can be reduced to the use of an
operational amplifier with a finite gain.
One possible solution to this problem
is the approach that is implemented in [2], where due to the choice of structure
has been avoided depending on the magnitude of the gain coefficient
regularization.
The most promising approach to improve the accuracy
characteristics of process control systems, is the use of single-device
structures for dynamic correction of sensor errors.
Fig.1. Functional diagram of
the measurement path (+ sensor device dynamic correction)
Figure 1 shows a functional block
diagram of the measurement path (sensor + dynamic correction device) with the
resulting transfer function:
W_{р}(p) = W(p) * W_{у}(p)
(2)
where W(p) - transfer function of
the sensor (1) and W_{y}(p) - transfer function of the dynamic correction unit:
W_{у}(p) =
1/ [W_{а}(p) * К - К + W_{c}-1(p), (3)
where W_{a}(p) = W(p) - kernel
driver with the transfer function is identical to the sensor.
K - static
correction parameter, W_{c}(p) - a correction unit with a transfer function:
n=1
S h_{x} p^{x}
x=0 Wc(p)
= --------------- (4)
n
S f_{x} p^{x}
x=1
Substituting (1) and (4) to (3)
and without loss of generality: tending to the most simple form W_{c}(p), setting
h_{x} = 0 (x = 1, ... , n) on the basis of [3], we obtain:
h_{0}*[(T1_{p}+1)*...*(T_{n}p+1)] W_{у}(p) = ----------------------------------------------------------------- (5)
n
Кh_{0} - Кh_{0} [(T_{1}p+1)*...*(T_{n}p+1)][(T_{n}p+1)] * S f_{x} p^{x}
x=1
The resulting transfer function of
the entire measurement path described by the relation:
h_{0} W_{у}(p) = -------------------------------------------------------------------- (6)
n
Кh_{0} - Кh_{0} [(T_{1}p+1)*...*(T_{n}p+1)][(T_{n}p+1)] * S f^{x} p^{x}
x=1
We write the characteristic
equation (6) as follows:
p^{n} + A_{0 }p^{n-1} + ...
+ A^{n-1} p + A_{n} = 0, (7)
where A_{0}, A_{n-1},
A_{n} - the coefficients of the corresponding powers of
p of
the characteristic equation of the transfer function (6).
To ensure the recovery of the measured signals with minimal distortion, it is
necessary that the roots of the characteristic equation (7) were valid and had
maximum modulus values [4], since the time constants of recovery signals are
determined by the absolute values of the roots of p_{i},
i = 1, ..., n the
characteristic equation.
Source: Authors publication
Published: 16.12.2013 |