electric engineering – control principles

electric engineering – control principles
Task
1. Use fundamental electrical principles to derive a mathematical model for the above circuit? [ 10 marks ]
2. Show how the model can be manipulated into the form of the standard 2nd order transfer function in terms of time constant and damping ratio. Derive subsidiary models for system constants? [ 10 marks ]
3. Apply a 12V input as a step change to the transfer function and convert the result into an expression for Vout in the time domain? [ 10 marks ]
4. For values of R = 100 ? , C = 20 µF and L = 2.0H produce a graph of Vout against time using an appropriate scale to show response time.? , comment on the graph? [ 10 marks ]
5. For the component values given what is the value of peak overshoot and settling time to within 5% of final value? [ 4 marks ]
6. Design a controller using a combination of proportional, Integral or derivative control that you consider appropriate. [10 marks ]
7. Using your controller in series with the process show how the output peak overshot and settling time can be improved.
8. How did you arrive at parameters for your controller settings