G(s)=(c)/(s^(2)+2\\\\zeta \\\\omega _(n)s+\\\\omega _(n)^(2)),(7-7)

\ The design should satisfy the following specifications:\ Fastest response with no overshoot.\ The closed loop undamped natural frequency

\\\\omega _(n)=16ra(d)/(s)

.\ No set point bias

(b_(SP)=0)

.\ Use the parameters

K

and

\\\\tau

, obtained in the DC motor modeling experiment, for your\ calculations. Before arriving at the lab you must do the following:\ Derive a formula for

k_(p)

and

k_(l)

using eqns. 7-6 and 7-7.\ Calculate

k_(P)

and

k_(l)

according to the design specs.\ Derive a formula for the gain

c

.\ b- Design a PI controller with set point bias. Use the results in part (a) and find the set\ point bias to eliminate one of the poles of the system in eq. 7-6. Thus the complete system\ will be reduced to a first order response. Find the gain in this case.

a- Design a PI controller for the DC motor trainer investigated in DC motor modeling experiment. In this design we shall set the parameters of the controller to give the system a transfer function of the form: 2 Automatic Control Lab. Experiment 7 University L Loue bjen for Technology Loplogill G(s)=s2+2ns+n2c The design should satisfy the following specifications: - Fastest response with no overshoot. - The closed loop undamped natural frequency n=16rad/s. - No set point bias (bSP=0). Use the parameters K and , obtained in the DC motor modeling experiment, for your calculations. Before arriving at the lab you must do the following: - Derive a formula for kp and kl using eqns. 7-6 and 7-7. - Calculate kP and kl according to the design specs. - Derive a formula for the gain c. b- Design a PI controller with set point bias. Use the results in part (a) and find the set point bias to eliminate one of the poles of the system in eq. 7-6. Thus the complete system will be reduced to a first order response. Find the gain in this case