In this work, we present a novel data-driven tuning framework for a class of nonlinear controllers, namely those based on the so-called hybrid integrator-gain system (HIGS). In particular, we focus on minimizing the settling time in point-to-point tasks, i.e., the time required for the error to converge and settle within a desired error bound after the task has finished. The proposed approach is based on sampled-data extremum-seeking control and allows simultaneous tuning of both linear and nonlinear parts of the controller, while guaranteeing input-to-state stability based solely on non-parametric frequency-response function data of the plant. These stability properties are guaranteed by a newly developed procedure for the data-driven verification of existing stability criteria. The efficacy of the proposed approach in tuning HIGS-based controllers for improving the settling time is validated extensively with a case study on an industrial wire bonder showing significant improvements in the worst-case settling time compared to LTI control.

This article introduces an output prediction method for a general class of closed-loop reset control systems. The considered type of system consists of a linear time-invariant (LTI) part which is connected in feedback with a reset controller that (partially) resets (a part of) its states when its input is equal to zero. Given some practical assumptions on the reset element’s input signal, the system output can be accurately predicted when the system is subject to a sinusoidal input. One benefit of this approach is that it provides an intuitive frequency-domain representation of the system. Another benefit is that output prediction can be done based solely on a frequency-response function (FRF) of the LTI part of the system. This article also introduces an accurate and computationally efficient algorithm which can – based on the predicted output – compute a closed-loop pseudo-sensitivity. This pseudo-sensitivity represents the ratio between the maximum absolute value of the system’s output and the amplitude of its input, similar to the closed-loop sensitivity functions for LTI systems.

This article introduces output prediction methods for two types of systems containing sinusoidal-input uniformly convergent (SIUC) elements. The first method considers these elements in combination with single-input single-output linear time-invariant (LTI) systems before, after, and in parallel to them. The second method considers a multiple-input multiple-output LTI system where each input is controlled by an SIUC element. The output prediction only requires frequency-response functions of the LTI elements and is fully accurate for sinusoidal inputs.

This work proposes a novel nonlinear Proportional-Integral (PI) controller, which utilizes a generalized first-order reset element. The proposed element can achieve similar magnitude-characteristics as its linear counterpart but with less phase lag at the open-loop crossover frequency (i.e. the control bandwidth), according to a sinusoidal-input describing function (SIDF) analysis. The same can be achieved with an existing reset-based integrator, the Clegg integrator (CI). However, it is known that a Proportional-CI (PCI) element can excessively generate higher-order harmonics of its input, which are neglected in the SIDF-analysis. Furthermore, a PCI can cause a limit cycle when placed in closed-loop with certain types of plants. The novel PI controller proposed in this work can prevent the limit cycle and can reduce the generation of higher-order harmonics, while retaining the beneficial phase advantage that is associated with existing reset-based PI controllers.

In this work, the proportional Clegg integrator (PCI), a resetting proportional-integrator (PI) element, is studied with the aim of improving the performance of an industrial motion stage currently controlled by a linear controller. A novel parallel continuous reset (CR) architecture, based on the PI, is presented, along with frequency-based tuning guidelines, similar to linear time-invariant (LTI) loopshaping techniques. Open-loop higher order sinusoidal input describing functions (HOSIDFs) and pseudo-sensitivities computed through analytically derived approximate closed-loop HOSIDFs were effectively applied to predict steady-state performance. The experimental results, obtained on a wire bonding machine, confirmed that resonance-induced vibrations of the machine's base frame can be suppressed more effectively by adopting a PCI-PID controller compared to the currently used linear controller. The novel structure does not only reduce unwanted excitation of higher order harmonics of the base frame resonance, such as the series CR architecture recently introduced in literature, but also avoids amplification of noise when implemented in practice. With the novel parallel structure, a significant (32%) decrease in the root mean square (rms) of the settling error could be achieved when compared to the linear controller currently used and the series CR reset structure.

In this paper, the higher-order sinusoidal-input describing function (HOSIDF) of the fractional-order hybrid integrator-gain system (HIGS) is derived analytically. The HIGS element, designed as a nonlinear component, aims to overcome limitations inherent in linear control, such as the waterbed effect. The HIGS element has been generalized by replacing the integer-order integrator with a fractional one. Here, a modified version of the fractional-order HIGS (FO-HIGS) is introduced with the aim of shaping the nonlinearity at low frequencies. Additionally, this paper demonstrates that obtaining an analytical solution for the HOSIDF of the FO-HIGS enables us to gain better insight into the tuning of the control architecture.