Frequency response of discrete-time robot systems--Limitations of PD controllers and improvements by lag-lead compensation

The feedback algorithm widely employed in the various current control strategies is a digital implementation of a conventional proportional plus derivative (PD) control. For dynamic control of robots, this algorithm can be shown to lead to unsatisfactory trade-offs between static accuracy, system stability, insensitivity to model structure inaccuracies and high frequency noise rejection. These trade-offs become even more serious as sampling rate decreases. To reduce these trade-offs, a more realistic discrete time system model of a robot arm and a more sophisticated feedback compensator are required. In this paper, a discrete time system model of a robot arm is derived and limitations of PD controllers are shown. They are consistent with our simulation and experimental results. Also a Lag-lead compensator is designed by a frequency-response analysis based on this model, along with the algorithm for realizing this compensator. Simulations and tests are conducted, which show encouraging results in reducing the trade-offs.