In Figure P7.16, the plant, P(s) = 48,500/s² + 2.89s; represents the dynamics of a robotic manipulator joint. The system’s output, C(s), is the joint’s angular position (Low, 2005). The system is controlled in a closed loop configuration as shown with G(s) = K_P + K_I/s, a proportional plus-integral (PI) controller to be discussed in Chapter 9. R(s) is the joint’s desired angular position. D(s) is an external disturbance, possibly caused by improper dynamics modeling, Coulomb friction, or other external forces acting on the joint.

a. Find the system’s type.

b. Show that for a step disturbance input, e_ss = 0 when K_I ≠ 0.

c. Find the value of KI that will result in e_ss = 5% for a parabolic input.

d. Using the value of K_I found in Part c, find the range of K_P for closed-loop stability.

Transcribed Image Text:

D(s) R(s) + C(s) G(s) P(s) FIGURE P7.16