G(j)
lG-(jco)) I


log scale


-1 slope


; scale


-3 slope


Figure 8.2. Bode diagram of the open-loop position control system.


dropping far below unity. An increase in low-frequency gain of the system would decrease

steady-state error, improve control accuracy in the low frequency range, and increase steady-

state and low-frequency closed-loop stiffness. Therefore, the controllers were required to give

an increase in the low-frequency system gain while providing the ability to adjust the gain of

the resonant peak for guaranteed stability and maximum system response rate.

 Two methods were considered best for increasing the low-frequency gain: introduction of

lag compensation in the loop and addition of velocity feedback in a minor loop (Merritt, 1967).

The properties of a lag compensator alone would allow a definite increase in the low-frequency

response of the joint, but it would also result in an undesirable decrease in the higher frequency

response time. Therefore, a lead compensator was needed to counteract the effects of the lag

compensator at higher frequencies. The lead compensator would also increase the system

bandwidth and response speed and reduce the overshoot. All of these results were desired of

the controllers for the manipulator. Therefore, lag-lead compensators were selected for each