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1) The below circuit has an output 10 times the difference between the 2 input signals. Show how this could be realised using 2 Operational Amplifiers and 5 Resistors, and provide values of the resistors

415_Operational Amplifiers.jpg

2) For a Proportional plus Derivative Controller, construct the shape of the output waveform for the triangular waveform shown, if the input rises and falls at the rate of 4 units per minute, where Proportional Band is 20% and the Derivative Action time is 0.1 Minutes

758_Proportional plus Derivative Controller.jpg

3.

324_Proportional Only Gain.jpg

a) For the above graph where the Proportional Only Gain was 4, calculate the required settings of a PID Controller using the Quarter Amplitude Response Method

b) If for the above the Proportional Only Gain was 6 estimate the settings of a PID Controller using the Ultimate Cycle Method

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