QUESTION 2. [Total marks 20] The Laplace transfer function of the control signal
ID: 2081192 • Letter: Q
Question
QUESTION 2. [Total marks 20] The Laplace transfer function of the control signal U(s) is in relation to the feed- back error E(s): 1. Derive the velocity form of the PI controller (i.e expression of the derivative of the control signal). 17 marks] 2. Assuming that the sampling interval is At, from the velocity form, derive the implementation equation that will calculate the actual output of the PI controller at sample time ti. [7 marks] 3. Assuming that the control signal is limited to unin and w write down the implementation equations for PI controller with anti-wind-up scheme. [6 marks]Explanation / Answer
(1) v(s)= velocity= Laplace of v(t)
V(t)= du/dt
Using lapace property of derivative;
Laplace of dy/dt =s*y(s),
Hence Laplace du/dt= su(s)= kc(s+1/t1)*E(s).
Hence v(s)=s*u(s)=kc(s+1/t1)*E(s).