A New Repetitive Control Framework for Robot Manipulators: Optimal Controller Design and Stability Analysis
Geun Il Song, Dohyeok Kwak, Taewan Kim, Oe Ryung Kang, Jung Hoon Kim, Wookyong Kwon
AI summary
Problem
Existing repetitive control frameworks for robot manipulators lack rigorous optimal synthesis and tractable stability analysis for the inherent time-delay, often resulting in conservative designs and suboptimal tracking performance.
Approach
The authors reformulate the repetitive control system as a delay-feedback model and use linear matrix inequalities to synthesize an H∞ optimal controller that minimizes tracking error energy, alongside a monodromy operator-based stability proof.
Key results
- Delay-feedback system representation for repetitive control
- LMI-based H∞ optimal controller synthesis
- Monodromy operator-based exponential stability condition
- Experimental reduction of tracking error and torque energy vs. LQR and CC-filter
Why it matters
Enables robot control engineers to design provably stable, optimal repetitive controllers that enhance tracking precision and energy efficiency for periodic industrial tasks.
Abstract
This paper provides a new repetitive control framework for robot manipulators with periodic reference sig- nals. We first take the inverse dynamics (ID) approach to a robot manipulator to transform its nonlinear input/output behavior into an equivalent linear time-invariant (LTI) system, for which the conventional repetitive control strategy is employed. To facilitate an optimal controller synthesis and an associated stability analysis, we next derive the so-called delay-feedback system. We then provide a linear matrix inequality (LMI)-based optimal controller synthesis procedures for minimizing the H∞ norm from the disturbance to the tracking error. We next established operator-theoretic stability assertions in terms of the monodromy operator. In particular, a necessary and sufficient condition for the exponential stability of the delay-feedback system is derived. Finally, experiment comparisons are given to demonstrate the overall developed arguments.