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

Feedback is defined as the process where a portion of theoutput 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 setpoint value. The system error would be equal to the set point minus the outputvalue, 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.comNegative feedback reduces the gain hence produces andimproves system stability. When a small value of the Vout signal is applied tothe inverting negative input terminal through the Rf, then a negative feedbackcontrol is gotten. The Op-amp is required in the circuitry is to amplify the weaksignal gotten from the input because of its connection to the inverting inputof the amplifier and produce a bigger signal as the output. Also, its gain canbe controlled restriction using the negative feedback.

Hence, a portion of thesignal would be fed back (Rf) to the inverting input (Rin). The Op-amp used inthis 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 toother available controllers and it makes the system resistant to randomcomponent values and inputs (Basic Electronics Tutorials, 2018).The PI algorithm is one of the most widely used in theindustry and this is because of its simple structure, cost effectiveness and itis easy to design. It removes steady state error from the system. Thiscontroller is also unable to predict future errors in the system.

Thecontroller 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 timee(t) = controller error (setpoint-measured value)The integral part can have a negative effect on the responsespeed and stability of the whole system. It also integrates the controllererror (e(t)) continuously. For the Ti value/parameter, it is always positiveand when it is used as the denominator as a small value, it allows room forlarger values. CObias and  are the proportional part of the equation,while   is the integral part. If e(t) increases ordecreases, the null value does so instantly and proportionally. DiscussionThis lab exercise includes the designing and building of adigital level control system for a coupled tank system.

The digital controlsystem was used to implement control of the liquid level in the tank system toan accuracy of +/-2mm of the set point and to monitor the flow rate of liquidinto the tank. An interface circuit was first built in the lab using thecircuit diagram given on Unilearn, and it was then tested in the lab ensuringthat the output gotten was of the desired value. The interface circuit willlink the Labjack DAQ and the tank system as required in the diagram that wasgiven on Unilearn. The level sensor in the tank was calibrated twice and thevalues of the voltage (Vh) at each liquid level tested were recorded. This isbecause the average voltage would be calculated from the results gotten fromthe calibration and used in plotting a graph (liquid level versus the averagevoltage (Vh) was the gotten using excel). The A and B values can be calculated manually by finding the gradient andintercept of the graph.

The Aand B valueswere calculated on excel and shown in figure below.