10 research outputs found
LPVcore: MATLAB toolbox for LPV modelling, identification and control
Get PDFThis paper describes the LPVcore software package for MATLAB developed to model, simulate, estimate and control systems via linear parameter-varying (LPV) input-output (IO), state-space (SS) and linear fractional (LFR) representations. In the LPVcore toolbox, basis affine parameter-varying matrix functions are implemented to enable users to represent LPV systems in a global setting, i.e., for time-varying scheduling trajectories. This is a key difference compared to other software suites that use a grid or only LFR-based representations. The paper contains an overview of functions in the toolbox to simulate and identify IO, SS and LFR representations. Based on various prediction-error minimization methods, a comprehensive example is given on the identification of a DC motor with an unbalanced disc, demonstrating the capabilities of the toolbox. The software and examples are available on www.lpvcore.net
Large-Scale H<sub>2</sub> Optimization for Thermo-Mechanical Reliability of Electronics
Get PDFOptimization of transient models is required in several domains related to thermo-mechanical reliability of electronics, such as Prognostic Health Monitoring (PHM) and design optimization. A novel framework for efficient (local) parameter optimization of transient models in the H2 norm is proposed. The optimization is feasible for large-scale transient models because it approximates the gradient using physics-based model order reduction (MOR), in contrast to existing approaches that typically use data-driven surrogate models such as neural networks. To demonstrate the framework an optimal fixed-order virtual sensor for PHM of a Ball Grid Array (BGA) is numerically determined.</p
Stable Sparse Operator Inference for Nonlinear Structural Dynamics
Get PDFStructural dynamics models with nonlinear stiffness appear, for example, when analyzing systems with nonlinear material behavior or undergoing large deformations. For complex systems, these models become too large for real-time applications or multi-query workflows. Hence, model reduction is needed. However, the mathematical operators of these models are often not available since, as is common in industry practice, the models are constructed using commercial simulation software. In this work, we propose an operator inference-based approach aimed at inferring, from data generated by the simulation model, reduced-order models (ROMs) of structural dynamics systems with stiffness terms represented by polynomials of arbitrary degree. To ensure physically meaningful models, we impose constraints on the inference such that the model is guaranteed to exhibit stability properties. Convexity of the optimization problem associated with the inference is maintained by applying a sum-of-squares relaxation to the polynomial term. To further reduce the size of the ROM and improve numerical conditioning of the inference, we also propose a novel clustering-based sparsification of the polynomial term. We validate the proposed method on several numerical examples, including a representative 3D Finite Element Model (FEM) of a steel piston rod
Stochastic Optimization of Large-Scale Parametrized Dynamical Systems
Get PDFMany relevant problems in the area of systems and control, such as controller
synthesis, observer design and model reduction, can be viewed as optimization
problems involving dynamical systems: for instance, maximizing performance in
the synthesis setting or minimizing error in the reduction setting. When the
involved dynamics are large-scale (e.g., high-dimensional semi-discretizations
of partial differential equations), the optimization becomes computationally
infeasible. Existing methods in literature lack computational scalability or
solve an approximation of the problem (thereby losing guarantees with respect
to the original problem). In this paper, we propose a novel method that
circumvents these issues. The method is an extension of Stochastic Gradient
Descent (SGD) which is widely used in the context of large-scale machine
learning problems. The proposed SGD scheme minimizes the norm
of a (differentiable) parametrized dynamical system, and we prove that the
scheme is guaranteed to preserve stability with high probability under
boundedness conditions on the step size. Conditioned on the stability
preservation, we also obtain probabilistic convergence guarantees to local
minimizers. The method is also applicable to problems involving non-realizable
dynamics as it only requires frequency-domain input-output samples. We
demonstrate the potential of the approach on two numerical examples:
fixed-order observer design for a large-scale thermal model and controller
tuning for an infinite-dimensional system.Comment: 19 pages, 10 figure
Stable sparse operator inference for nonlinear structural dynamics
No full textStructural dynamics models with nonlinear stiffness appear, for example, when analyzing systems with nonlinear material behavior or undergoing large deformations. For complex systems, these models become too large for real-time applications or multi-query workflows. Hence, model reduction is needed. However, the mathematical operators of these models are often not available since, as is common in industry practice, the models are constructed using commercial simulation software. In this work, we propose an operator inference-based approach aimed at inferring, from data generated by the simulation model, reduced-order models (ROMs) of structural dynamics systems with stiffness terms represented by polynomials of arbitrary degree. To ensure physically meaningful models, we impose constraints on the inference such that the model is guaranteed to exhibit stability properties. Convexity of the optimization problem associated with the inference is maintained by applying a sum-of-squares relaxation to the polynomial term. To further reduce the size of the ROM and improve numerical conditioning of the inference, we also propose a novel clustering-based sparsification of the polynomial term. We validate the proposed method on several numerical examples, including a representative 3D Finite Element Model (FEM) of a steel piston rod.</p
Stochastic optimization of large-scale parametrized dynamical systems
No full textMany problems in systems and control, such as controller synthesis and observer design, can be viewed as optimization problems involving dynamical systems: For instance, maximizing closed-loop performance in the controller synthesis setting. When the system includes large-scale, sparse state–space models, the optimization becomes computationally challenging. Existing methods in literature lack computational scalability or only solve an approximate version of the problem. We propose a method to locally minimize the H2 norm of a differentiable parametrized dynamical system that resolves these issues. We do this by estimating the gradient of the H2 norm using samples of the frequency response function, which can be obtained efficiently for large-scale, sparse state–space models. We prove that the scheme is guaranteed to preserve stability with high probability under boundedness conditions on the step size used in the optimization. We also obtain probabilistic guarantees that our method converges to a local minimizer. The method is applicable to problems involving non-realizable or infinite-dimensional dynamics. We demonstrate the effectiveness of the approach on two numerical examples.</p
