Butterworth Pattern-Based Integral Resonant Controller Design for Nanopositioning Systems with Internal Delay

Control systems capable of damping resonant modes while ensuring stability have been a major field of development as the requirements for high scanning speeds and precision become more widespread in modern engineering applications. Integral Resonant Control (IRC) is a promising approach that offers simplicity, ease of design and robustness. The ideal IRC controller displays the Butterworth pattern. Unfortunately, due to the inherent internal time delays of the systems, if not accounted for during the design stage, real-world experimental trials show deviation from the Butterworth pattern and the emergence of highly resonant behaviour. This paper showcases what effect not accounting for time delays during the design procedure has on a system as well as offers a novel design methodology to reach as close as possible to the closed-loop Butterworth filter pattern within the IRC scheme in the presence of known time delays using the 1st order Pade approximation. The mathematical explanation for why the Butterworth pattern cannot be achieved is also explained. The proposed approach is compared to existing methodologies, demonstrating its effectiveness and superior performance in nanopositioning applications. Through simulations and experimental trials on a nanopositioning platform, it is shown that accounting for time delays during design significantly enhances the system's performance and reduces tracking error. The presented methodology offers a practical solution for enhancing the precision of positioning systems with inherent time delays.