This dissertation focuses on the frequency response analysis and design of Linear Time- Invariant systems (LTI) reset feedback control systems for precision motion applications. In the precision motion industry, there is a growing demand for control systems that deliver higher positioning resolution, faster response, and enhanced stability. However, inherent limitations in linear controllers, such as the “waterbed effect” and the Bode phase gain trade-off, limit their performance, posing challenges in meeting these evolving requirements.

Reset feedback control has emerged as an effective solution to address the limitations of linear control systems in precision motion applications. The practical implementation of control strategies relies on reliable analysis methods. Among these, frequency response analysis stands out as an effective and widely utilized method across industries. However, existing frequency response analysis methods for both open-loop and closed-loop reset control systems face challenges, including accuracy limitations and restrictions to specific control system structures. The first category of contributions in this dissertation addresses these challenges by introducing frequency response analysis methods for open-loop and closed-loop Single-Input and Single-Output (SISO) LTI reset control systems within a generalized control system structure. Moreover, to further realize the potential of reset control, the second category of contributions focuses on proposing novel reset control designs to enhance system performance. The content is organized into nine chapters…
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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.

This paper presents a controller design approach aimed at optimizing the tracking capability of a freeform optical surface tracking system. It is shown that the second-order disturbance caused by the non-linearity in the system's spring and the changes in surface height is by far the biggest contributor to the tracking error. To reduce this error the paper proposes a position dependent spring force compensation, aiming to use the measurable non-linearity in the spring to effectively linearize the system. Thereafter, it is shown that the tracking error is mainly caused by the change in surface height and an unknown disturbance acting around the bandwidth. Since the change in surface height is known, a feedforward control structure is used to suppress the effect of this disturbance. Following this modification, the unknown disturbance becomes dominant. To suppress the effect of this disturbance a so called 'Constant in Gain Lead in Phase' controller is added that decreases the magnitude of the sensitivity function in the active frequency range of the disturbance, without increasing the sensitivity's magnitude at other frequencies. The proposed controller modifications are all experimentally validated on a freeform optical surface measurement machine through the evaluation of the tracking error during a tilted flat measurement.

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.

High-precision mechatronic equipment often benefits from or even needs vibration isolation to function within specification. Examples of such equipment include metrology devices, space instrumentation and lithography assemblies. Vibration isolation is often the function of the mounting between the equipment and the floor or rest of the machine. An important factor for vibration isolation is the stiffness of this mount. High stiffness mounts result in high force disturbance rejection, at the cost of sensitivity to indirect disturbances. So-called ultra hard mount systems take advantage of ultra high stiffness to offer superior position stability in the presence of force disturbances. However, this also leads to an emphasized sensitivity to indirect disturbances. Active vibration control can be used to overcome this. Feedback is used to dampen the resonance mode of the mounting system. Feedforward is used to lower the transmissibility, resulting in reduced sensitivity to indirect disturbances. This has been successfully implemented on less stiff hard mount systems in the past, but the techniques remained unexplored on ultra hard mount systems. This research focusses on the experimental implementation of existing active vibration control techniques on an ultra hard mount system. It was found that the closed loop behaviour of piezo-based ultra hard mount systems are well predictable. Furthermore, it was found that good damping performance can be achieved by various methods, reducing the output vibrations up to 60%. Using straightforward stiffness compensation feedforward, the influence of indirect disturbances was shown to be reduced significantly. A reduction of 94% in the effect of indirect disturbances was realized using disturbance feedforward when compared to the uncontrolled case. This work shows that ultra hard mounts can be used in applications where strong direct disturbance rejection is required, even in the presence of indirect disturbances using a combined feedback and feedforward approach.

Conventional and state-of-the-art Coil-based Hybrid Reluctance Actuators (CB-HRAs) for precision motion control are well-regarded for their high force generation but notorious for Joule heat dissipation. This coil-based heat generation problem compromises the quality and effectiveness of precision engineering applications, especially in vacuum, space and cryogenic environments. This research focuses on exploring and advancing the capabilities of the Hybrid Tunable Reluctance Actuator (HTRA) as a novel alternative for coil-less, contactless and high-force actuation. The working principle is based on reluctance tuning, i.e. changing the actuator’s internal properties to generate contactless magnetic force on a mover. This research develops methodologies to design, classify, and evaluate optimal force-generating HTRAs using analytical and numerical magnetic models. In symphony with this process, novel concepts and mathematical statements in reluctance tuning are created to explain key results and establish standard design principles for generic HTRAs. The resulting optimal HTRA design is analytically evaluated against CB-HRAs to benchmark and confirm the potential of HTRAs in force generation and power dissipation for different actuation forms. The research further progresses into numerically modeling key nonlinear magnetic effects to refine the HTRA’s design. Subsequently, numerically-verified multibody dynamical models are developed to accurately simulate inherently nonlinear and complex HTRAs, while ensuring these models can be generally extrapolated. The proof-of-concept is obtained on a manufactured HTRA setup, followed by experimental validations of the multibody dynamical models through system identification. Finally, the first linear control system for an HTRA is synthesized based on real-time data to explore its achievable bandwidths, position reference tracking abilities, and other closed-loop performance parameters using feedback, feedforward and delay compensation techniques.

The increasing demand for microchips has driven the search for new control techniques in industry. While linear controllers dominate industrial control due to their simplicity and effectiveness, they face inherent limitations such as the waterbed effect and Bode’s gain-phase trade-offs. To address these challenges, this research explores the potential of nonlinear control, specifically reset control, to improve upon linear controllers. Reset control was used, since the sensitivity function of the reset controller can directly be constructed using the frequency response function of the plant. This thesis introduces a method for incorporating a reset based filter that improves upon linear control through closed-loop frequency domain shaping(pseudo-sensitivity).

In this study we introduce the following: an introduction and shaping method of a modified constant gain and lead in phase (CGLP) element. Which is achieved by adding gain in parallel with the generalized first order reset element (GFORE) to limit high-frequency nonlinear behavior. Furthermore a process for frequency-domain shaping of the added filter that can be implemented with an existing linear controller. Lastly, the thesis demonstrates how to solve pseudo-sensitivity constraint violations and shows the effectiveness of direct pseudo-sensitivity shaping for improving time-domain response.

Validation using both a simulated and an industrially used wirebonder, confirmed that the reset-based controller significantly outperformed optimized linear controller, with a 39.50% decrease in mean settling time and a 40.30% decrease in mean root-mean-square error (RMSE). This research shows the potential of reset control in industrial applications.

Reluctance actuators boast a high motor constant in small air-gap applications when compared to Lorentz actuators. Inherent non-linearities in the F-I relation limit force predictability. Replacing conventional current control with flux control can greatly improve force predictability. Traditionally, hall sensors or hysteresis modelling are employed for accurate flux estimation. This thesis proposes a calibration strategy and control architecture for hybrid flux estimation. The novel control architecture is implemented on a test set-up at MI-Partners. The flux estimator consists of a high pass filtered sense coil and a low pass filtered current probe for integration drift correction. Through comparison of force estimation errors due to magnetic hysteresis, (analog) integration drift and integration errors the optimal crossover frequency was calculated to be 13 mHz. The hybrid control architecture is capable of force prediction accuracy on par with hall control. Simulated positioning accuracy even shows an improvement of 13%, simulations show an improvement in maximum error from 423  micrometer to 369 micrometer. A positioning accuracy improvement of up to 332% over a similar current controlled system has been demonstrated.

This thesis explores the use of reset control to improve disturbance rejection in systems subjected to wideband noise. In the high-tech industry, there is a continuous push for improved performance, particularly in achieving fast and stable motion with nanometer-level precision. Linear controllers, though industry-standard, are constrained by limitations such as Bode's gain-phase relation. Reset control offers a promising alternative, but its behaviour under wideband disturbances remains unexplored. However, such excitation is common in the context of active vibration isolation. The wide-spectrum excitation may result in dominant slow or excessive resetting, depending on the system. In both cases, the behaviour of the reset element will be different than designed. Also, the traditional method of Describing Function (DF) will not sufficiently represent the reset element's behaviour under such conditions, as it is defined for single sinusoidal excitation. This thesis studies the Power Spectral Density (PSD) of the reset triggering signal of the reset element to understand the resetting behaviour. The method of Best Linear Approximation (BLA) is applied to enable the analysis of the reset element in frequency domain. Furthermore, a novel method is developed to shape the reset triggering signal, to achieve the desired behaviour of the reset element at the frequency of interest. Both simulations and experiments showed the feasibility of the method in achieving the desired behaviour of the reset element. Depending on the properties of the system, this will result in improvement of the disturbance rejection.