A robotic manipulator together with a cascade PI

Chapter 8, Problem 59

(choose chapter or problem)

A robotic manipulator together with a cascade PI controller (used to improve steady-state response and discussed in Chapter 9) has a transfer function (Low, 2005)

G(s) = \(\left(K_p+\frac{K_1}{s}\right) \frac{48,500}{s^2+2.89 s}\)

Assume the robot's joint will be controlled in the configuration shown in Figure P8.3.

a. Find the value of \(K_I\) that will result in \(e_{s s}\) = 2% for a parabolic input.

b. Using the value of \(K_I\) found in Part a, plot the root locus of the system as a function of \(K_P\).

c. Find the value of \(K_P\) that will result in a real pole at -1. Find the location of the other two poles.

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