Feedback time e(t) = controller error (set point-measured value)

Feedback is defined as the process where a portion of the
output signal (V or I) is used as an input. For a negative feedback controller,
it allows the input to be controlled so that it will equal the desired set
point value. The system error would be equal to the set point minus the output
value, and the transfer function of the system is the output (set point)
divided by the input. The figure below shows the negative feedback controller;

Figure 1.
Negative feedback control from ElectronicsTutorial.com

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Negative feedback reduces the gain hence produces and
improves system stability. When a small value of the Vout signal is applied to
the inverting negative input terminal through the Rf, then a negative feedback
control is gotten. The Op-amp is required in the circuitry is to amplify the weak
signal gotten from the input because of its connection to the inverting input
of the amplifier and produce a bigger signal as the output. Also, its gain can
be controlled restriction using the negative feedback. Hence, a portion of the
signal would be fed back (Rf) to the inverting input (Rin). The Op-amp used in
this lab was the LM741 Op-amp.

If the input at Vin is positive and this condition occurs,
then the output voltage becomes more negative but at some point it will stabilise.
Negative feedback controller is mostly used because of stability compared to
other available controllers and it makes the system resistant to random
component values and inputs (Basic Electronics Tutorials, 2018).

The PI algorithm is one of the most widely used in the
industry and this is because of its simple structure, cost effectiveness and it
is easy to design. It removes steady state error from the system. This
controller is also unable to predict future errors in the system. The
controller doesn’t continue to compute changes when the error is equal to zero.
 The ideal form of the PI controller is;

 

Where; CObias = null value,

Kc = controller gain,

Ti = controller reset time

e(t) = controller error (set
point-measured value)

The integral part can have a negative effect on the response
speed and stability of the whole system. It also integrates the controller
error (e(t)) continuously. For the Ti value/parameter, it is always positive
and when it is used as the denominator as a small value, it allows room for
larger values. CObias and  are the proportional part of the equation,
while   is the integral part. If e(t) increases or
decreases, the null value does so instantly and proportionally.

 

Discussion

This lab exercise includes the designing and building of a
digital level control system for a coupled tank system. The digital control
system was used to implement control of the liquid level in the tank system to
an accuracy of +/-2mm of the set point and to monitor the flow rate of liquid
into the tank. An interface circuit was first built in the lab using the
circuit diagram given on Unilearn, and it was then tested in the lab ensuring
that the output gotten was of the desired value. The interface circuit will
link the Labjack DAQ and the tank system as required in the diagram that was
given on Unilearn. The level sensor in the tank was calibrated twice and the
values of the voltage (Vh) at each liquid level tested were recorded. This is
because the average voltage would be calculated from the results gotten from
the calibration and used in plotting a graph (liquid level versus the average
voltage (Vh) was the gotten using excel). The A and B values can be calculated manually by finding the gradient and
intercept of the graph. The A
and B values
were calculated on excel and shown in figure below.