P10.32 When a motor drives a flexible structure, the structure’s natural frequencies, as compared to the bandwidth of the servodrive, determine the contribu

tion of the structural flexibility to the errors of the resulting motion. In current industrial robots, the drives are often relatively slow, and the structures are relatively rigid, so that overshoots and other er

rors are caused mainly by the servodrive. However, depending on the accuracy required, the structural deflections of the driven members can become sig

nificant. Structural flexibility must be considered the major source of motion errors in space structures and manipulators. Because of weight restrictions in space, large arm lengths result in flexible structures.

Furthermore, future industrial robots should require lighter and more flexible manipulators.

To investigate the effects of structural flexibil

ity and how different control schemes can reduce unwanted oscillations, an experimental apparatus was constructed consisting of a DC motor driving a slender aluminum beam. The purpose of the ex

periments was to identify simple and effective con

trol strategies to deal with the motion errors that occur when a servomotor is driving a very flexible structure [13].

The experimental apparatus is shown in Figure P10.32(a), and the control system is shown in Figure P10.32(b). The goal is that the system will have a Kυ 

of 100.

(a) When G s c( ) = K, determine K and ob

tain the Bode plot. Find the phase margin and gain margin.

(b) Using the Nichols chart, find ωr p , M ω, and ωB.

(c) Select a compensator so that the phase margin is P M. . ≥ 35° and find ωr p , M ω, and ωB for the compensated system.