High-precision motion platforms, such as industrial wire bonders used in semiconductor packaging, face demanding speed and accuracy requirements that challenge the inherent performance limits of Linear Time-Invariant (LTI) control, such as Bode's gain-phase relationship and the waterbed effect. Reset control strategies, particularly the Constant in Gain Lead in Phase (CGLP) architecture, offer a compelling solution by providing broadband phase lead without the gain penalty associated with linear lead filters. However, the inherent nonlinearity of reset elements introduces higher-order harmonics into the control loop. In precision motion control, these harmonics can shift reset timing, induce additional zero-crossings per excitation period, and invalidate the fundamental modeling assumptions of closed-loop sinusoidal-input describing function (HOSIDF) analysis.

To overcome these nonlinear limitations and prevent unreliable reset behavior, this thesis utilizes a shaping filter framework to strategically control the frequency-domain distribution of higher-order harmonics. By suppressing low-frequency harmonic distortion while preserving necessary phase lead around the crossover frequency, the proposed shaping filter formulation keeps zero-crossing proximity metrics within reliable bounds, thereby validating the underlying analytical HOSIDF modeling assumptions. Furthermore, this study investigates and validates the fundamental trade-offs between steady-state tracking precision and transient settling performance in shaped reset systems.

Building upon these theoretical insights, a systematic design guideline is established to synthesize reset controllers with shaping filters tailored to spectral error distributions across distinct motion phases. Following these proposed guidelines, a constraint-compliant reset controller featuring a sixth-order shaping filter was synthesized and evaluated on an industrial wire bonder motion stage. The experimental results demonstrate that the designed controller eliminates low-frequency disturbance energy without compromising closed-loop robustness margins, achieving an average improvement of 10.1% in stationary RMS tracking error and 7.2% in settling time across the complete set of operational references when compared to the state-of-the-art unshaped reset baseline. These findings confirm that performance-oriented nonlinearity distribution successfully reconciles transient speed with high steady-state positioning accuracy in industrial motion systems. ... Read more

Precision engineering applications, such as atomic force microscopes and semiconductor motion stages, demand high accuracy in tracking and disturbance rejection, often limited by the waterbed effect and gain-phase constraints in linear control systems. This thesis introduces nonlinear control designs leveraging Fractional-order Hybrid-Integrator-Gain Systems (FO-HIGS) to overcome these limitations, providing tunable phase lead with reduced higher-order harmonics compared to traditional integer-order HIGS.

Two novel FO-HIGS-based controllers are proposed: (1) An enhanced CgLp filter integrated with PID control to improve low-frequency tracking by compensating phase lag through parameter tuning (e.g., fractional order α and corner frequency), minimizing parasitic nonlinear effects via simulation-based higher-order sinusoidal-input describing function (HOSIDF) analysis and pseudo-sensitivity evaluation. (2) A FO-HIGS-based LPF for superior high-frequency noise attenuation, achieving lower cumulative power spectral density than linear counterparts.

Simulations and experiments on a linear-motor-actuated motion stage validate the designs, demonstrating improved performance in reference tracking and disturbance rejection while maintaining stability. ... Read more

Linear controllers are widely preferred in the industry for controlling motion platforms used in semiconductor and electronics manufacturing machines. However, as production demands for semiconductor devices increase, the performance of linear controllers reaches a plateau due to their intrinsic limitations, making further improvements increasingly difficult. Thus, the reset control has been explored as a potential solution as it can overcome the limitations and it consists of the frequency domain analysis tools.

Past research has shown that the CgLp (Constant in gain, Lead in phase) is the most advanced reset based filter and has shown performance improvements for an industrial machine. The non-linearity of these filters, which gives an advantage over linear filters, also makes their placement within a control loop highly critical. While the inherent non-linearity of these filters provides certain advantages, it can also be detrimental to system performance.

This thesis aims at developing architectures based on sequencing strategies to improve the performance of reset based filters by optimally utilizing the non-linearity. Also, the disadvantages of existing frequency domain analysis methods have been identified. Finally, the method of filtered architecture which can shape the non-linearity of reset based filters have been explored.
... Read more

In response to the precision motion industry's growing demand for higher accuracy, faster, and robustness, the design of conventional linear time-invariant (LTI) controllers has reached its inherent limits, which is the waterbed effect and Bode's gain-phase relationship. To overcome these limitations, a Constant in gain, Lead in phase (CgLp) element has been introduced. This element combines a reset low pass filter with a linear lead element, providing additional phase without affecting the constant gain through the phase characteristics of the reset element.

Previous researches have explored the sequence of first-order reset element(FORE) and Lead element within the CgLp(i.e. FORE-Lead and Lead-FORE CgLp), revealing a trade-off between transient overshoot and steady-state noise suppression. This thesis proposes a tunable CgLp architecture that is capable of achieving performance between FORE-Lead and Lead-FORE CgLp. The tunable CgLp provides compromise transient overshoot and steady-state noise attenuation, offering the possibility of optimizing transient response under a satisfying noise performance.

However, tunable CgLp cannot reduce higher-order harmonics and associated errors. Thus, the second part of this thesis introduces a framework that employs filters to shape nonlinearity. The feasibility of using notch and anti-notch filters to enhance disturbance rejection performance is theoretically analyzed and validated using a mass plant. Design recommendations for this framework are also provided. Nevertheless, tunable CgLp and the nonlinearity shaping architecture can be used in combination, which provides the potential to further enhance the performance of reset control systems. ... Read more