DUBLIN INSTITUTE OF TECHNOLOGY
Kevin Street, Dublin 8.
School Of Control Systems and Electrical Engineering
Solution SheetPage 1 of 7
Course/Year / DT009 Year 3 / ExaminationSitting / Semester 1
2005/2006
Subject / Control and Automation Minor
Examiner / Gavin Duffy
Question No. / 1
(i) Open loop - simple, inexpensive. Result of output not measured. Good knowledge of system required [2]
Suitable example[2]
Closed loop - more complicated but better. Output is measured and compared against setpoint to give an error. [2]
Suitable example[2]
(ii) Integral control -[2]
Remembers past history of the error and is used to remove the offset of a proportional controller[2]
Integral windup – a very large cumulative integral result occurs when the error cannot be corrected (e.g. faulty instrument, valve). [4]
(iii) Ultimate cycle - set controller to P control only; increase gain until oscillations develop; stop increasing gain when system becomes unstable [3]
Process reaction curve - place controller in manual mode; set output to a constant value and allow system to reach a steady state; make a step change in the output and record the process variable response with time [3]
Disadvantage of ultimate cycle is that operates on the borderline of instability - this could cause damage to plant and/or personnel [2]
(iv) Step 1 is Self Test – check for errors in hardware/software
Step 2 is Input Scan – Reads input values from input cards to the memory
Step 3 is Execute Logic – each ladder in program is executed and outputs are updated
Step 4 is Output Scan – Writes output values from memory to output cards[8]
(v) Types of pushbuttons: Start is normally open or press to close switch – done this way so that if wire breaks motor can’t start. Stop is normally closed or press to open switch – done this way so that if wire breaks the motor stops (it’s the same as pressing stop button). [4]
Ladder logic – two ways of doing this.
Option 1 is as follows:
Option 2:
Option 1 or 2[4]
Question No. / 2(a)
(i) Convert to frequency domain as follows: Starting with:
Applying the Laplace transform to this equation gives:
[2]
The transfer function which is the output over the input is now easily determined:
[3]
(ii) We can replace the input TJ(s) in the Laplace transformed equation above with a/s, the Laplace transform of a step input of magnitude a. The equation now becomes:
[5]
(iii) Check the tables to find
[2]
In the above equation, b = 1/ and Ka is a constant so remains unchanged. Therefore:
[3]
(b)
Above code[6]
Comments[4]
Noise is reduced by using the averaged value from the card instead of the present value. [3]
This requires changing the buffer memory address to read the data from the averaged value and also requires sending down a number of averages to the buffer memory address for this information. [2]
Question No. / 3(i) Convert the system into a single block to give the equation below:
the overall output over input = transfer function[4]
the static gain is above the line[4]
the time constant is the constant in the s term[4]
(ii)
i.e. proportional gain = 3[5]
At steady state we have:
Therefore, the error is 10% of the input.[5]
(iii) Proportional offset is the steady state error observed when using proportional control.[2]
It can be removed by adding integral action. The integral term acts on the integral of the error and removes any steady state error. [2]
(iv) Yes. A high gain may result in overshoot and undershoot oscillations which may not die off. This causes instability. [4]
Question No. / 4(i) Block Diagram[9]
(ii) Error = SP – PV (PV = Temp in this case).[2]
When error is positive, heater is On. When error is negative, heater is Off.[2]
(iii) Advantages – cheap, easy to implement, simple, digital output instead of analog[2]
Disadvantages – can’t have PV exactly at setpoint. Frequent switching of output[2]
(iii) Add a deadband or hysteresis. Reduces frequency of switching on and off.[4]
(iv)
[6]
[3]