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

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.