Automated Reset Controller Design in the Frequency Domain

Abstract

The speed and precision required in the precision motion industry is an ever-growing challenge. Linear control offers intuitive frequency-domain controller design methods that are based on a frequency response function (FRF) of the plant, which is obtained solely from measurement data. Unsurprisingly, linear controllers account for over 90% of the controllers currently used in the industry. However, as linear controllers are subject to inherent performance limitations such as Bode's gain-phase relationship and the waterbed effect, research on nonlinear control solutions to overcome these limitations is ubiquitous. Reset control first showed up in 1958 with the Clegg integrator (CI). According to a sinusoidal-input-describing-function analysis, the CI provides reduced phase lag compared to a linear integrator, suggesting Bode's gain-phase relationship can be overcome and consequently allowing for performance surpassing that of linear control systems. The drawbacks of the CI are the possible emergence of limit cycles and the excitation of high-frequent modes of the system originating from higher-order harmonics of the CI's input caused by discontinuities in the control signal. The generalised-first-order-reset-element-based integrator (GFbI) is the only reset element that can prevent the emergence of limit cycles and can reduce the generation of higher-order harmonics, whilst retaining the advantageous reduced phase lag the CI provides and allowing for closed-loop controller design based on a plant FRF while taking the effects of higher-order harmonics into account, matching design methods of linear controllers. Optimally tuning a reset controller is a complex and time-consuming task. Moreover, established tuning rules are still lacking. This work facilitates designing a reset controller containing a GFbI element by providing two contributions to utilise the potential of the GFbI element to improve upon linear control. The first is a comparative study on the effect of the controller element sequence, aimed at reducing the negative consequences of the higher-order harmonics generated by the reset element. The second is the proposal of an FRF-based optimisation algorithm utilising frequency-domain performance prediction methods to automatically tune a reset controller containing a GFbI element to adhere to the imposed constraints and maximise the benefit gained from the nonlinear element. Validation using a simulated and physical wire bonder showed the algorithm successfully tuned four different reset controllers using two different sequences. The performance of the tuned reset controllers was compared to that of equally-well-tuned linear controllers. In the first use case with the goal of suppressing a dominant vibration in the error signal, the median root-mean-square error was reduced by 16.245%. In the second use case, the goal was to improve the settling time, which was achieved by a median of 9.791%. The best results were achieved using a sequence in which the higher-order harmonics were avoided from passing through the lead filter in open loop, mitigating amplification thereof. The proposed tuning algorithm proved able to tune reset controllers containing a GFbI element such that the performance of linear control based on frequency-domain performance prediction metrics was surpassed, where two use cases confirmed the predicted performance increase through time-domain simulations and experiments on a physical setup.