It is often required that identified models exhibit certain stability and dissipativity properties, e.g., passivity or ℓ2-gain. The aim of this article is to develop an unconstrained parametrization of linear parameter-varying (LPV) input–output (IO) discrete-time (DT) models that guarantees stability/dissipativity by construction, i.e., the model is stable/dissipative for any choice of model parameters. To achieve this, it is shown that any quadratically stable/dissipative DT-LPV-IO model can be generated by a mapping of transformed coefficient functions that are constrained to the unit ball. The unit ball is reparameterized through a Cayley transformation, resulting in a fully unconstrained parameterization. These results immediately apply to linear time-varying IO models. In the linear time-invariant case, an unconstrained parameterization of all stable/dissipative DT transfer functions is obtained. The unconstrained parametrization enables, among others, the use of neural network coefficient functions in LPV system identification while guaranteeing stability and dissipativity.

Hard-to-model, often nonlinear dynamics limit the tracking performance of physical-model-based feedforward control in medical interventional X-ray (IX) systems. In this article, these unknown dynamics are compensated using a physics-guided neural network (PGNN) feedforward controller. The PGNN consists of a parallel combination of a physical model describing the equations of motions of the IX and a feedforward neural network. To ensure that the neural network compensates only for the dynamics not included in the physical model, the neural network output in the subspace spanned by the physical model is penalized through regularization. As a result, the physical model serves as a baseline for performance, and the neural network contribution can be monitored or disabled. The PGNN feedforward controller is validated on an experimental IX setup, illustrating its superior performance over a physical-model-based feedforward controller.

Increasingly stringent performance requirements for motion systems necessitate explicit control of the flexible dynamic behavior. The aim of this paper is to present an approach to identify spatio-temporal models of overactuated mechatronic systems with a limited number of spatially distributed sensors. The proposed approach exploits the modal modeling framework and exploits the symmetry in modal models to enhance the spatial resolution of the identified spatially-sampled modal models. Spatio-temporal models are identified by updating prior finite element method-based models based on the identified extended modal models. The experimental results illustrate the effectiveness of the proposed approach for the identification of complex position-dependent mechanical systems.

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.

Next-generation deformable mirrors are envisaged to exhibit low-frequency flexible dynamics and to contain a large number of spatially distributed actuators due to increasingly stringent performance requirements. The increasingly complex system characteristics necessitate identifying the flexible dynamic behavior for design validation and next-generation control. The aim of this paper is to develop a unified approach for the identification of mechanical systems with a large number of spatially distributed actuators and a limited number of sensors. A frequency domain-based approach using local modeling techniques is developed. The modal modeling framework is employed to analyze the design and create outputs that were not measured. The proposed approach is applied to an experimental deformable mirror case study that illustrates the effectiveness of the proposed approach.

Fine positioning stages based on piezoceramic materials have found widespread success in various applications due to their attractive features. However, the inherent hard nonlinear behavior of piezoelectric actuators complicates modeling, control, and synchronization processes. In this study, adopting an input–output perspective, we propose and experimentally verify a model-free control and synchronization technique for these stages. Specifically, our approach introduces a model-free trajectory generator that adjusts the desired trajectory using position measurement data to minimize tracking errors. We validate this technique using a representative precision motion system, consisting of a planner stage and a uni-axial fine stage, under step-and-scan trajectories commonly employed in wafer scanners. Remarkably, despite its simplicity, the proposed design procedure can be seamlessly extended to other robotics and automation applications.

Identifying structured discrete-time linear time/parameter-varying (LPV) input-output (IO) models with global stability guarantees is a challenging problem since stability for such models is only implicitly defined through the solution of matrix inequalities (MI) in terms of the model's coefficient functions. In this letter, a structured linear IO model class is developed that results in a quadratically stable model for any choice of coefficient functions, enabling identification using standard optimization routines while guaranteeing stability. This is achieved through transforming the MI-based stability constraints in a necessary and sufficient manner, such that for any choice of transformed coefficient functions the MIs are satisfied. The developed stable LPV-IO model is employed in simulation to estimate the parameter-varying damping of mass-damper-spring system with stability guarantees, while a standard LPV-IO model results in an unstable estimate.

Ensuring stability of discrete-time (DT) linear parameter-varying (LPV) input-output (IO) models estimated via system identification methods is a challenging problem as known stability constraints can only be numerically verified, e.g., through solving Linear Matrix Inequalities. In this paper, an unconstrained DT-LPV-IO parameterization is developed which gives a stable model for any choice of model parameters. To achieve this, it is shown that all quadratically stable DT-LPV-IO models can be generated by a mapping of transformed coefficient functions that are constrained to the unit ball, i.e., a small-gain condition. The unit ball is then reparameterized through a Cayley transformation, resulting in an unconstrained parameterization of all quadratically stable DT-LPV-IO models. As a special case, an unconstrained parameterization of all stable DT linear time-invariant transfer functions is obtained. Identification using the stable DT-LPV-IO model with neural network coefficient functions is demonstrated on a simulation example of a parameter-varying mass-damper-spring system.

Flexible dynamics in motion systems lead to inherent spatio-temporal system behavior. The aim of this paper is to develop an unified approach for the identification of modal models of spatio-temporal overactuated systems. The approach exploits the modal modeling framework and the overactuated setting to enhance the estimation of the spatial system behavior. The proposed approach is applied in an experimental case study. The case study considers an experimental overactuated stage and illustrates the effectiveness of the proposed approach.

The performance of a feedforward controller is primarily determined by the extent to which it can capture the relevant dynamics of a system. The aim of this paper is to develop an input-output linear parameter-varying (LPV) feedforward parameterization and a corresponding data-driven estimation method in which the dependency of the coefficients on the scheduling signal are learned by a neural network. The use of a neural network enables the parameterization to compensate a wide class of constant relative degree LPV systems. Efficient optimization of the neural-network-based controller is achieved through a Levenberg-Marquardt approach with analytic gradients and a pseudolinear approach generalizing Sanathanan-Koerner to the LPV case. The performance of the developed feedforward learning method is validated in a simulation study of an LPV system showing excellent performance.

Tracking performance of physical-model-based feedforward control for interventional X-ray systems is limited by hard-to-model parasitic nonlinear dynamics, such as cable forces and nonlinear friction. In this paper, these nonlinear dynamics are compensated using a physics-guided neural network (PGNN), consisting of a physical model, embedding prior knowledge of the dynamics, in parallel with a neural network to learn hard-to-model dynamics. To ensure that the neural network learns only unmodelled effects, the neural network output in the subspace spanned by the physical model is regularized via an orthogonal projection-based approach, resulting in complementary physical model and neural network contributions. The PGNN feedforward controller reduces the tracking error of an interventional X-ray system by a factor of 5 compared to an optimally tuned physical model, successfully compensating the unmodeled parasitic dynamics.

An increasing trend in the use of neural networks in control systems is being observed. The aim of this paper is to reveal that the straightforward application of learning neural network feedforward controllers with closed-loop data may introduce parameter inconsistency that degrades control performance, and to provide a solution. The proposed method employs instrumental variables to ensure consistent parameter estimates. A nonlinear system example reveals that the developed instrumental variable neural network (IVNN) approach asymptotically recovers the optimal solution, while pre-existing approaches are shown to lead to inconsistent estimates.

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.

In high-precision motion systems, set-point tracking often comes with the problem of overshoot, hence poor settling behavior. To avoid overshoot, PD control (thus without using an integrator) is preferred over PID control. However, PD control gives rise to steady-state error in view of the constant disturbances acting on the system. To deal with both overshoot and steady-state error, a sliding mode controller with saturated integrator is studied. For large servo signals the controller is switched to PD mode as to constrain the integrator buffer and therefore the overshoot. For small servo signals the controller switches to PID mode as to avoid steady-state error. The tuning of the switching parameters will be done automatically with the aim to optimize the settling behavior. The sliding mode controller will be tested on a high-precision motion system.