Local PD Feedback Control

 

Most of the feedback algorithms used in the current control system are digital implementation of a proportional plus derivative (PD) control. In industrial robots, a local PD feedback control law is applied at each joint independently. The advantages of using a PD controller are the following:

• Very simple to implement.
• Does not require the identification of robot parameters.
• Suitable for real-time control since it has very few computations compared to the complicated nonlinear dynamic equations.
• The behavior of the system can be controlled by changing the feedback gains.

On the other hand, there are some disadvantages of using a PD controller instead of the dynamic equations such as:

• High update rate is required to achieve reasonable accuracy.
• Dynamic equations should be used to simulate the robot manipulator behavior
• There is always trade-off between static accuracy and the overall system stability.
• Using local PD feedback law at each joint independently does not consider the couplings of dynamics between robot links.

Some ideas have been suggested to enhance the usability of the local PD feedback law for trajectory tracking. One idea is to add a lag-lead compensator using frequency response analysis [5]. Another method is to build an inner loop stabilizing controller using a multivariable PD controller, and an outer loop tracking controller using a multivariable PID (proportional, integral, and derivative) controller [52].

In general, using a local PD feedback controller with high update rates can give an acceptable accuracy for trajectory tracking applications. It was proved that using a linear PD feedback law is useful for positioning and trajectory tracking [21].