Siep Weiland

Pepijn B. Cox, Siep Weiland, Roland Tóth

This paper deals with the certification problem for robust quadratic stability, robust state convergence, and robust quadratic performance of linear systems that exhibit bounded rates of variation in their parameters. We consider both continuous-time (CT) and discrete-time (DT) parameter-varying systems. In this paper, we provide a uniform method for this certification problem in both cases and we show that, contrary to what was claimed previously, the DT case requires a significantly different treatment compared to the existing CT results. In the established uniform approach, quadratic Lyapunov functions, that are affine in the parameter, are used to certify robust stability, robust convergence rates, and robust performance in terms of linear matrix inequality feasibility tests. To exemplify the procedure, we solve the certification problem for $\mathscr{L}_2$-gain performance both in the CT and the DT cases. A numerical example is given to show that the proposed approach is less conservative than a method with slack variables.

Daming Lou, Siep Weiland

In this paper, a parametric model order reduction (pMOR) technique is proposed to find a simplified system representation of a large-scale and complex thermal system. The main principle behind this technique is that any change of the physical parameters in the high-fidelity model can be updated directly in the simplified model. For deriving the parametric reduced model, a Krylov subspace method is employed which yields the relevant subspaces of the projected state. With the help of the projection operator, first moments of the low-rank model are set identical to the correspondent moments of the original model. Additionally, a prior upper bound of the error induced by the approximation is derived.

Dhruv Khandelwal, Siep Weiland, Amol Khalate

This paper presents a methodology for model based robust fault diagnosis and a methodology for input design to obtain optimal diagnosis of faults. The proposed algorithm is suitable for real time implementation. Issues of robustness are addressed for the input design and fault diagnosis methodologies. The proposed technique allows robust fault diagnosis under suitable conditions on the system uncertainty. The designed input and fault diagnosis techniques are illustrated by numerical simulation.

Fei Chen, Sofie Haesaert, Alessandro Abate et al.

The analysis of industrial processes, modelled as descriptor systems, is often computationally hard due to the presence of both algebraic couplings and difference equations of high order. In this paper, we introduce a control refinement notion for these descriptor systems that enables analysis and control design over related reduced-order systems. Utilising the behavioural framework, we extend upon the standard hierarchical control refinement for ordinary systems and allow for algebraic couplings inherent to descriptor systems.

Samarth Toolhally, Joeri Roelofs, Siep Weiland et al.

In inkjet printing, optimal paper moisture is crucial for print quality, achieved through hot-air impingement in the fixation unit. This paper presents a modular digital twin of the fixation unit, modeling the thermo-fluidic drying process and monitoring its spatio-temporal performance. The novel approach formulates the digital twin as an infinite-dimensional state estimator that infers fixation states from limited sensor data, while remaining robust to disturbances. Modularity is achieved through a graph-theoretic model, where each node represents thermo-fluidic dynamics in different sections of the fixation unit. Evaporation is modeled as a nonlinear boundary effect coupled with node dynamics via Linear Fractional Representation. Using the Partial Integral Equation (PIE) framework, we develop a unified approach for stability, input-output analysis, simulation, and rapid prototyping, validated with operational data from a commercial printer. An $\mathcal{H}_{\infty}$-optimal Luenberger state estimator is then synthesized to estimate thermal states from available sensor data, enabling real-time monitoring of spatio-temporal thermal effects on paper sheets.

Ming Li, Zhiyong Sun, Siep Weiland

This paper revisits a classical challenge in the design of stabilizing controllers for nonlinear systems with a norm-bounded input constraint. By extending Lin-Sontag's universal formula and introducing a generic (state-dependent) scaling term, a unifying controller design method is proposed. The incorporation of this generic scaling term gives a unified controller and enables the derivation of alternative universal formulas with various favorable properties, which makes it suitable for tailored control designs to meet specific requirements and provides versatility across different control scenarios. Additionally, we present a constructive approach to determine the optimal scaling term, leading to an explicit solution to an optimization problem, named optimization-based universal formula. The resulting controller ensures asymptotic stability, satisfies a norm-bounded input constraint, and optimizes a predefined cost function. Finally, the essential properties of the unified controllers are analyzed, including smoothness, continuity at the origin, stability margin, and inverse optimality. Simulations validate the approach, showcasing its effectiveness in addressing a challenging stabilizing control problem of a nonlinear system.