The filtered split-path nonlinear integrator (F-SPANI) is a generic nonlinear controller designed to improve the transient performance of linear (motion) systems in terms of overshoot. The main idea underlying F-SPANI is that the amplitude and phase of an integrator can be tuned using independent filters, resulting in more efficient use of the buffer of the integrator. In this article, a general description of F-SPANI is presented. In addition, a stability analysis result is presented that provides sufficient conditions in the form of linear matrix inequalities (LMIs) for closed-loop stability analysis on the basis of construction of a common quadratic Lyapunov function (CQLF). The ease of the design, implementation, and the potential of the proposed controller are illustrated both in simulations and in experiments on an industrial pick-and-place machine.@en

The performance of fault detection filters relies on a high sensitivity to faults and a low sensitivity to disturbances. The aim of this paper is to develop an approach to directly shape these sensitivities, expressed in terms of minimum and maximum singular values. The developed method offers an alternative solution to the H-/H∞ synthesis problem, building upon traditional multiobjective synthesis results. The result is an optimal filter synthesized via iterative convex optimization and the approach is particularly useful for fault diagnosis as illustrated by a numerical example.@en

Hyperthermia treatment consists of elevating the temperature of the tumor to increase the effectiveness of radiotherapy and chemotherapy. Hyperthermia treatment planning (HTP) is an important tool to optimize treatment quality using pre-treatment temperature predictions. The accuracy of these predictions depends on modeling uncertainties such as tissue properties and positioning. In this study, we evaluated if HTP accuracy improves when the patient is imaged inside the applicator at the start of treatment. Because perfusion is a major uncertainty source, the importance of accurate treatment position and anatomy was evaluated using different perfusion values. Volunteers were scanned using MR imaging without ('planning setup') and with the MR-compatible hyperthermia device ('treatment setup'). Temperature-based quality indicators were used to assess the differences between the standard, apparent and the optimized hyperthermia dose. We conclude that pre-treatment imaging can improve HTP predictions accuracy but also, that tissue perfusion modelling is crucial if temperature-based optimization is applied.@en

Background: During resonance frequency (RF) hyperthermia treatment, the temperature of the tumor tissue is elevated to the range of 39–44°C. Accurate temperature monitoring is essential to guide treatments and ensure precise heat delivery and treatment quality. Magnetic resonance (MR) thermometry is currently the only clinical method to measure temperature noninvasively in a volume during treatment. However, several studies have shown that this approach is not always sufficiently accurate for thermal dosimetry in areas with motion, such as the pelvic region. Model-based temperature estimation is a promising approach to correct and supplement 3D online temperature estimation in regions where MR thermometry is unreliable or cannot be measured. However, complete 3D temperature modeling of the pelvic region is too complex for online usage. Purpose: This study aimed to evaluate the use of proper orthogonal decomposition (POD) model reduction combined with Kalman filtering to improve temperature estimation using MR thermometry. Furthermore, we assessed the benefit of this method using data from hyperthermia treatment where there were limited and unreliable MR thermometry measurements. Methods: The performance of POD–Kalman filtering was evaluated in several heating experiments and for data from patients treated for locally advanced cervical cancer. For each method, we evaluated the mean absolute error (MAE) concerning the temperature measurements acquired by the thermal probes, and we assessed the reproducibility and consistency using the standard deviation of error (SDE). Furthermore, three patient groups were defined according to susceptibility artifacts caused by the level of intestinal gas motion to assess if the POD–Kalman filtering could compensate for missing and unreliable MR thermometry measurements. Results: First, we showed that this method is beneficial and reproducible in phantom experiments. Second, we demonstrated that the combined method improved the match between temperature prediction and temperature acquired by intraluminal thermometry for patients treated for locally advanced cervical cancer. Considering all patients, the POD–Kalman filter improved MAE by 43% (filtered MR thermometry = 1.29°C, POD–Kalman filtered temperature = 0.74°C). Moreover, the SDE was improved by 47% (filtered MR thermometry = 1.16°C, POD–Kalman filtered temperature = 0.61°C). Specifically, the POD–Kalman filter reduced the MAE by approximately 60% in patients whose MR thermometry was unreliable because of the great amount of susceptibilities caused by the high level of intestinal gas motion. Conclusions: We showed that the POD–Kalman filter significantly improved the accuracy of temperature monitoring compared to MR thermometry in heating experiments and hyperthermia treatments. The results demonstrated that POD–Kalman filtering can improve thermal dosimetry during RF hyperthermia treatment, especially when MR thermometry is inaccurate.@en

A reset integral controller is discussed that induces improved low-frequency disturbance rejection properties under double integrator control without giving the unwanted increase of overshoot otherwise resulting from adding an extra linear integrator. To guarantee closed-loop stability, a (conditional) reset condition is used that restricts the input-output behavior of the dynamic reset element to a [0,α]-sector with α a positive (finite) gain. As a result, stability can be guaranteed on the basis of a circle criterion-like argument and checked through (measured) frequency response data. Both stability and performance of the control design will be discussed via measurement results obtained from a wafer stage system of an industrial wafer scanner.@en

The analysis of incremental stability typically involves measuring the distance between any two solutions of a given dynamical system at the same time instant, which is problematic when studying hybrid dynamical systems. Indeed, hybrid systems generate solutions defined with respect to hybrid time instances (that consists of both the continuous time elapsed and the discrete time, which is the number of jumps experienced so far), and two solutions of the same hybrid system may not be defined at the same hybrid time instant. To overcome this issue, we present novel definitions of incremental stability for hybrid systems based on graphical closeness of solutions. As we will show, defining incremental asymptotic stability with respect to the hybrid time yields a restrictive notion, such that we also investigate incremental asymptotic stability notions with respect to the continuous time only or the discrete time only, respectively. In this manner, two (effectively dual) incremental stability notions are attained, called jump- and flow incremental asymptotic stability. To present Lyapunov conditions for these two notions, in both cases, we resort to an extended hybrid system and we prove that the stability of a well-defined set for this extended system implies incremental stability of the original system. We can then use available Lyapunov conditions to infer the set stability of the extended system. Various examples are provided throughout this paper, including an event-triggered control application and a bouncing ball system with Zeno behavior, that illustrate incremental stability with respect to continuous time or discrete time, respectively.@en

The analysis of incremental stability typically involves measuring the distance between any two solutions of a given dynamical system at the same time instant, which is problematic when studying hybrid dynamical systems. Indeed, hybrid systems generate solutions defined with respect to hybrid time instances (that consists of both the continuous time elapsed and the discrete time, which is the number of jumps experienced so far), and two solutions of the same hybrid system may not be defined at the same hybrid time instant. To overcome this issue, we present novel definitions of incremental stability for hybrid systems based on graphical closeness of solutions. As we will show, defining incremental asymptotic stability with respect to the hybrid time yields a restrictive notion, such that we also investigate incremental asymptotic stability notions with respect to the continuous time only or the discrete time only, respectively. In this manner, two (effectively dual) incremental stability notions are attained, called jump- and flow incremental asymptotic stability. To present Lyapunov conditions for these two notions, in both cases, we resort to an extended hybrid system and we prove that the stability of a well-defined set for this extended system implies incremental stability of the original system. We can then use available Lyapunov conditions to infer the set stability of the extended system. Various examples are provided throughout this paper, including an event-triggered control application and a bouncing ball system with Zeno behavior, that illustrate incremental stability with respect to continuous time or discrete time, respectively.@en

The analysis of incremental stability properties typically involves measuring the distance between any pair of solutions of a given dynamical system, corresponding to different initial conditions, at the same time instant. This approach is not directly applicable for hybrid systems in general. Indeed, hybrid systems generate solutions that are defined with respect to hybrid times, which consist of both the continuous time elapsed and the discrete time, that is the number of jumps the solution has experienced. Two solutions of a hybrid system do not a priori have the same time domain, and we may therefore not be able to compare them at the same hybrid time instant. To overcome this issue, we invoke graphical closeness concepts. We present definitions for incremental stability depending on whether incremental asymptotic stability properties hold with respect to the hybrid time, the continuous time, or the discrete time, respectively. Examples are provided throughout the paper to illustrate these definitions, and the relations between these three incremental stability notions are investigated. The definitions are shown to be consistent with those available in the literature for continuous-time and discrete-time systems.@en

In this paper, we introduce the split-path nonlinear integrator (SPANI) as a novel nonlinear filter designed to improve the transient performance of linear systems in terms of overshoot, while preserving good rise-time and settling behavior. In particular, this nonlinear controller targets the well-known trade-off induced by integral action, which removes steady-state errors due to constant external disturbances, but deteriorates transient performance in terms of increased overshoot. The rationale behind the proposed SPANI filter is to ensure that the integral action has, at all times, the same sign as the closed-loop error signal, which, as we will show, enables a reduction in overshoot thereby leading to an overall improved transient performance. The resulting closed-loop dynamics is modeled by a hybrid dynamical system, for which we provide sufficient Lyapunov-based conditions for stability. Furthermore, we illustrate the effectiveness, the design and the tuning of the proposed controller in a benchmark simulation study of an industrial pick-and-place machine.@en

In this paper, we introduce the split-path nonlinear integrator (SPANI) as a novel nonlinear filter designed to improve the transient performance of linear systems in terms of overshoot, while preserving good rise-time and settling behavior. In particular, this nonlinear controller targets the well-known trade-off induced by integral action, which removes steady-state errors due to constant external disturbances, but deteriorates transient performance in terms of increased overshoot. The rationale behind the proposed SPANI filter is to ensure that the integral action has, at all times, the same sign as the closed-loop error signal, which, as we will show, enables a reduction in overshoot thereby leading to an overall improved transient performance. The resulting closed-loop dynamics is modeled by a hybrid dynamical system, for which we provide sufficient Lyapunov-based conditions for stability. Furthermore, we illustrate the effectiveness, the design and the tuning of the proposed controller in a benchmark simulation study of an industrial pick-and-place machine.@en

In this paper, we introduce the split-path nonlinear integrator (SPANI) as a novel nonlinear filter designed to improve the transient performance of linear systems in terms of overshoot, while preserving good rise-time and settling behavior. In particular, this nonlinear controller targets the well-known trade-off induced by integral action, which removes steady-state errors due to constant external disturbances, but deteriorates transient performance in terms of increased overshoot. The rationale behind the proposed SPANI filter is to ensure that the integral action has, at all times, the same sign as the closed-loop error signal, which, as we will show, enables a reduction in overshoot thereby leading to an overall improved transient performance. The resulting closed-loop dynamics is modeled by a hybrid dynamical system, for which we provide sufficient Lyapunov-based conditions for stability. Furthermore, we illustrate the effectiveness, the design and the tuning of the proposed controller in a benchmark simulation study of an industrial pick-and-place machine.@en

In this paper, we introduce the split-path nonlinear integrator (SPANI) as a novel nonlinear filter designed to improve the transient performance of linear systems in terms of overshoot, while preserving good rise-time and settling behavior. In particular, this nonlinear controller targets the well-known trade-off induced by integral action, which removes steady-state errors due to constant external disturbances, but deteriorates transient performance in terms of increased overshoot. The rationale behind the proposed SPANI filter is to ensure that the integral action has, at all times, the same sign as the closed-loop error signal, which, as we will show, enables a reduction in overshoot thereby leading to an overall improved transient performance. The resulting closed-loop dynamics is modeled by a hybrid dynamical system, for which we provide sufficient Lyapunov-based conditions for stability. Furthermore, we illustrate the effectiveness, the design and the tuning of the proposed controller in a benchmark simulation study of an industrial pick-and-place machine.@en

The comparison between time-varying hybrid trajectories is crucial for tracking, observer design and synchronisation problems for hybrid systems with state-triggered jumps. In this paper, a generic distance function is designed that can be used for this purpose. The so-called “peaking phenomenon”, which occurs when using the Euclidean distance to compare two hybrid trajectories, is circumvented by taking the hybrid nature of the system explicitly into account. Based on the proposed distance function, we define the stability of a trajectory and present sufficient Lyapunov-type conditions for hybrid system with state-triggered jumps. A constructive Lyapunov function design is presented for hybrid systems with affine flow and jump maps and a jump set that is a hyperplane. The stability conditions can then be verified using linear matrix conditions. Finally, for this class of systems, we present a tracking controller that asymptotically stabilises a given hybrid reference trajectory and we illustrate our results with an example.@en

The comparison between time-varying hybrid trajectories is crucial for tracking, observer design and synchronisation problems for hybrid systems with state-triggered jumps. In this paper, a generic distance function is designed that can be used for this purpose. The so-called “peaking phenomenon”, which occurs when using the Euclidean distance to compare two hybrid trajectories, is circumvented by taking the hybrid nature of the system explicitly into account. Based on the proposed distance function, we define the stability of a trajectory and present sufficient Lyapunov-type conditions for hybrid system with state-triggered jumps. A constructive Lyapunov function design is presented for hybrid systems with affine flow and jump maps and a jump set that is a hyperplane. The stability conditions can then be verified using linear matrix conditions. Finally, for this class of systems, we present a tracking controller that asymptotically stabilises a given hybrid reference trajectory and we illustrate our results with an example.@en

The comparison between time-varying hybrid trajectories is crucial for tracking, observer design and synchronisation problems for hybrid systems with state-triggered jumps. In this paper, a generic distance function is designed that can be used for this purpose. The so-called “peaking phenomenon”, which occurs when using the Euclidean distance to compare two hybrid trajectories, is circumvented by taking the hybrid nature of the system explicitly into account. Based on the proposed distance function, we define the stability of a trajectory and present sufficient Lyapunov-type conditions for hybrid system with state-triggered jumps. A constructive Lyapunov function design is presented for hybrid systems with affine flow and jump maps and a jump set that is a hyperplane. The stability conditions can then be verified using linear matrix conditions. Finally, for this class of systems, we present a tracking controller that asymptotically stabilises a given hybrid reference trajectory and we illustrate our results with an example.@en

The comparison between time-varying hybrid trajectories is crucial for tracking, observer design and synchronisation problems for hybrid systems with state-triggered jumps. In this paper, a generic distance function is designed that can be used for this purpose. The so-called “peaking phenomenon”, which occurs when using the Euclidean distance to compare two hybrid trajectories, is circumvented by taking the hybrid nature of the system explicitly into account. Based on the proposed distance function, we define the stability of a trajectory and present sufficient Lyapunov-type conditions for hybrid system with state-triggered jumps. A constructive Lyapunov function design is presented for hybrid systems with affine flow and jump maps and a jump set that is a hyperplane. The stability conditions can then be verified using linear matrix conditions. Finally, for this class of systems, we present a tracking controller that asymptotically stabilises a given hybrid reference trajectory and we illustrate our results with an example.@en

The recently introduced Split-Path Nonlinear Integrator (SPANI) is designed to improve the transient performance of linear (motion) systems in terms of overshoot. The SPANI was shown to be an effective nonlinear controller to improve transient performance by enforcing the same sign in the integrator action and the error. However, to avoid (fast) switching in the control input in steady-state, conservatism had to be introduced in the SPANI design, thereby limiting the performance. In this paper, this conservatism is removed by introducing a new design, called the Filtered Split-Path Nonlinear Integrator (F-SPANI). This design is based on the inclusion of an additional filter in the phase path, which enables the full potential behind the main idea of the SPANI. The ease of the design and implementation and the potential of the proposed controller are illustrated both in simulation and in experiments on a motion system.@en