Closed forms of stabilizing sets are generally only available for linearized systems. An innovative numerical strategy to estimate stabilizing sets of PI or PID controllers tackling (uncertain) nonlinear systems is proposed. The stability of the closed-loop system is characterized by the sign of the largest Lyapunov exponent (LLE). In this framework, the bottleneck is the computational cost associated with the solution of the system, particularly including uncertainties. To overcome this issue, an adaptive surrogate algorithm, the Monte Carlo intersite Voronoi (MiVor) scheme, is adopted to pertinently explore the domain of the controller parameters and classify it into stable/unstable regions from a low number of nonlinear estimations. The result of the random analysis is a stochastic set providing probability information regarding the capabilities of PI or PID controllers to stabilize the nonlinear system and the risk of instabilities. The minimum of the LLE is proposed as tuning rule of the controller parameters. It is expected that using a tuning rule like this results in PID controllers producing the highest closed-loop convergence rate, thus being robust against model parametric uncertainties and capable of avoiding large fluctuating behavior. The capabilities of the innovative approach are demonstrated by estimating robust stabilizing sets for the blood glucose regulation problem in type 1 diabetes patients.

This study explores reduced-order modeling for analyzing time-dependent diffusion-deformation of hydrogels. The full-order model describing hydrogel transient behavior consists of a coupled system of partial differential equations in which the chemical potential and displacements are coupled. This system is formulated in a monolithic fashion and solved using the finite element method. We employ proper orthogonal decomposition as a model order reduction approach. The reduced-order model performance is tested through a benchmark problem on hydrogel swelling and a case study simulating co-axial printing. Then, we embed the reduced-order model into an optimization loop to efficiently identify the coupled problem’s material parameters using full-field data. Finally, a study is conducted on the uncertainty propagation of the material parameter.

This work presents a comparative review and classification between some well-known thermodynamically consistent models of hydrogel behavior in a large deformation setting, specifically focusing on solvent absorption/desorption and its impact on mechanical deformation and network swelling. The proposed discussion addresses formulation aspects, general mathematical classification of the governing equations, and numerical implementation issues based on the finite element method. The theories are presented in a unified framework demonstrating that, despite not being evident in some cases, all of them follow equivalent thermodynamic arguments. A detailed computational analysis is carried out where Taylor–Hood elements are employed in the spatial discretization to satisfy the inf-sup condition and to prevent spurious numerical oscillations. The resulting discrete problems are solved using the FEniCS platform through consistent variational formulations, employing both monolithic and staggered approaches. We conduct benchmark tests on various hydrogel structures, demonstrating that major differences arise from the chosen volumetric response of the hydrogel. The significance of this choice is frequently underestimated in the state-of-the-art literature but has been shown to have substantial implications on the resulting hydrogel behavior.

This paper presents the robust control of Three-Leg Split-Capacitor Shunt Active Power Filters (TLSC SAPFs) by means of structured $H\infty$ controllers for reactive, unbalanced, and harmonic compensation and the DC-link bus voltage regulation. Robust controller synthesis is performed based on the TLSC SAPF dynamical model including power losses in passive elements. Before the control implementation, a systematic procedure for the nonlinear controllability verification of the converter and its quantification using the set-theoretic approach is presented. Controllability verification serves to accurately design the SAPF’s operation region. Thus, a Voltage Oriented Control (VOC) structure is implemented by using two different approaches to determine the PI controller parameters: (1) the traditional Pole-Placement method (PP-PI) and (2) the $H\infty$-PI structured synthesis approach, which leads to PI robust controllers. From the latter approach, two sets of parameters are obtained. The first set considers the nominal model ($H\infty$-PI), and the second one explicitly accounts for the model parametric uncertainties ($H\infty$-uPI). An optimization procedure is presented for obtaining the optimal $H\infty$-PI and $H\infty$-uPI controller parameters where four complementary constrains are defined to establish a trade-off between the controllers performance and robustness. The enforcement of constraints is later evaluated for each of three PI controllers obtained. This work aims to establish a common ground for the comparison of robust control strategies applied to TLSC APFs; therefore, the TLSC SAPF compensation performance is measured and compared with the performance indices: integral of the absolute error ($IAE$), integral of the time-weighted absolute error ($ITAE$), integral of the absolute control action ($IUA$), and maximum sensitivity ($M_s$).