Optimal sign inverting control for time-delayed systems, a concept study with experiments

Abstract

An intriguing control logic, sign inverting control (SIC) is considered for control systems with delayed feedback. It starts with a nominal control law formulated for non-delayed case and simply inverts the sign of the control gains for some surprising benefits when used with the delays. This operation sounds paradoxical as the sign inversion potentially harms the stability of the non-delayed dynamics. However, SIC with large delays may yield some complementary benefits to the nominal control logic from delay robustness perspective. The main question we address in this paper is ‘How to select the nominal control law so that such a contribution can be (a) feasible, (b) optimal in some sense?’ A structured methodology is proposed to achieve this, starting with a linear quadratic regulator based controller. A single scaling factor on the corresponding control gains is used for one-dimensional optimisation. Experimental validation of the concept of this optimal SIC procedure is also reported on a single-axis manipulator.

Keywords:

• SIC
• optimisation
• CTCR
• stability
• delay

Acknowledgement

We would like to thank the reviewers and editor-in-chief for helping to improve the overall quality of the paper with their constructive advice.