Abstract
Servo-control is a common control problem that typically involves a system characterized by torque input and angular position output. A direct-drive robot, for example, is a coupled and typically nonlinear servo-control problem. One means of closed-loop control of a servo-system is proportional-derivative (PD) control. PD control is passive in character and thus stable, and since it can be easily implemented in analog form, the stability is not compromised by computational time delays. A significant issue in implementing PD control on a servo-system is the selection of the control gains. Linearizing a nonlinear servo-system and utilizing linear analysis methods suggests best performance is achieved at maximum possible gain. Maximum gain, however, drives the actuators into saturation, which renders the system nonlinear and the linear analysis invalid. This paper investigates the effect of actuator saturation on servo-system tracking performance by formulating a frequency-based equivalent to the linear system -3dB bandwidth. The proposed method utilizes a series of band-limited pseudo-random tracking inputs to characterize the “bandwidth” of a nonlinear system. Numerical analysis based on this method shows that, for a servo-system that exhibits actuator saturation, the optimal tracking performance is not achieved at maximum gain. Instead, performance improves up to a given gain, then begins to recede as the gain is increased further. The analysis also shows that avoiding actuator saturation to ensure linear behavior significantly sacrifices system performance. The performance characterization scheme is illustrated by an example of a servo system with actuator saturation. The methodology is also compared with linear analysis techniques, and the two shown to be well-correlated for a linear system.
