System analysis and robustness

Software is increasingly embedded in a variety of physical contexts. This imposes new requirements on tools that support the design and analysis of systems. For instance, modeling embedded and cyberphysical systems needs to blend discrete mathematics, which is suitable for modeling digital components, with continuous mathematics, used for modeling physical components. This blending of continuous and discrete creates challenges that are absent when the discrete or the continuous setting are considered in isolation. We consider robustness, that is, the ability of an analysis of a model to cope with small amounts of imprecision in the model. Formally, we identify analyses with monotonic maps between complete lattices (a mathematical framework used for abstract interpretation and static analysis) and define robustness for monotonic maps between complete lattices of closed subsets of a metric space.</p

Stochastic Satbility and Performance Robustness of Linear Multivariable Systems

Stochastic robustness, a simple technique used to estimate the robustness of linear, time invariant systems, is applied to a single-link robot arm control system. Concepts behind stochastic stability robustness are extended to systems with estimators and to stochastic performance robustness. Stochastic performance robustness measures based on classical design specifications are introduced, and the relationship between stochastic robustness measures and control system design parameters are discussed. The application of stochastic performance robustness, and the relationship between performance objectives and design parameters are demonstrated by means of example. The results prove stochastic robustness to be a good overall robustness analysis method that can relate robustness characteristics to control system design parameters

Unifying robustness analysis and system ID

A unified systems analysis framework is presented, which includes conventional robustness analysis, model validation, and system identification as special cases and thus shows them to be instances of the same fundamental problem. A concrete version of this framework is developed for the linear case, based on a generalized structured singular value. This unification forms the basis for the use of common computational tools and and a more natural interplay between modeling, identification, and robustness analysis

Bond graph based sensitivity and uncertainty analysis modelling for micro-scale multiphysics robust engineering design

Components within micro-scale engineering systems are often at the limits of commercial miniaturization and this can cause unexpected behavior and variation in performance. As such, modelling and analysis of system robustness plays an important role in product development. Here schematic bond graphs are used as a front end in a sensitivity analysis based strategy for modelling robustness in multiphysics micro-scale engineering systems. As an example, the analysis is applied to a behind-the-ear (BTE) hearing aid. By using bond graphs to model power flow through components within different physical domains of the hearing aid, a set of differential equations to describe the system dynamics is collated. Based on these equations, sensitivity analysis calculations are used to approximately model the nature and the sources of output uncertainty during system operation. These calculations represent a robustness evaluation of the current hearing aid design and offer a means of identifying potential for improved designs of multiphysics systems by way of key parameter identification

Robustness analysis of a nucleic acid controller for a dynamic biomolecular process using the structured singular value

In the field of synthetic biology, theoretical frameworks and software tools are now available that allow control systems represented as chemical reaction networks to be translated directly into nucleic acid-based chemistry, and hence implement embedded control circuitry for biomolecular processes. However, the development of tools for analysing the robustness of such controllers is still in its infancy. An interesting feature of such control circuits is that, although the transfer function of a linear system can be easily implemented via a chemical network of catalysis, degradation and annihilation reactions, this introduces additional nonlinear dynamics, due to the annihilation kinetics. We exemplify this problem for a dynamical biomolecular feedback system, and demonstrate how the structured singular value (μ) analysis framework can be extended to rigorously analyse the robustness of this class of system. We show that parametric uncertainty in the system affects the location of its equilibrium, and that this must be taken into account in the analysis. We also show that the parameterisation of the system can be scaled for experimental feasibility without affecting its robustness properties, and that a statistical analysis via Monte Carlo simulation fails to uncover the worst-case uncertainty combination found by μ-analysis.</p

Multivariable Inferential Feed-Forward Control

Two multivariable inferential feed-forward control strategies are proposed in this paper. In the first strategy, the effects of disturbances on the primary process variables are inferred from uncontrolled secondary process variables that are measured on-line. In the second approach, the effects of disturbances on the primary process variables are inferred from the manipulated variables for those controlled secondary process variables that have fast dynamics. The proposed strategies are particularly useful in situations where some disturbances cannot be easily and quickly measured. Robustness analysis of the inferential feed-forward controllers and the selection of appropriate secondary measurements are discussed. Structured singular value analysis is used in assessing the robustness of the inferential feed-forward control systems. The performance characteristics of the two inferential feed-forward control systems are demonstrated by application to a simulated methanol-water separation column. In the first system, the effects of disturbances in feed composition (and feed rate) are inferred from tray temperatures, whereas in the second system, the disturbance effects are inferred from inventory manipulations. Nonlinear dynamic simulation results demonstrate the superior performance of these strategies. Robustness analysis shows that using multiple tray temperatures can improve the robustness of the inferential feed-forward controller, and this conclusion is confirmed by simulation