General Method for Uncertainty Evaluation of Safety Integrity Level (SIL) Calculations

PresentationThe IEC 61511 standard requires a verification calculation that a proposed design for a safety instrumented function (SIF) achieves the desired safety integrity level (SIL). The evaluation of the safety integrity level of a new or existing safety instrumented system requires detailed calculations based on the failure rates of the device and the planned maintenance/testing cycle for the system. The failure rates of the devices are often taken from standard failure rate tabulations of equipment. The maintenance and testing plans are developed based on plant experience. All of the data used in the SIL calculations are uncertain. This paper develops a general method for uncertainty analysis of the SIL calculations. The general method is based on the application of probability theory - variance contribution analysis (VCA) – to the equations presented in ISA TR 84.00.02-2115. An example is worked to demonstrate the methodology

Fault Tree Uncertainty Analysis

PresentationFault tree analysis (FTA) is a widely used methodology in the process industries. FTA is used for the development of failure mechanisms, computation of failure frequencies and the determination of the probability of failure on demand of safety systems. Much of the data used in a FTA study are uncertain. For example, the failure rate of a pump is often not known with great precision. Likewise the failure rates of instrumentation are often known only within some defined limits. The common practice, used by analysts in the quantification of a fault tree, is to use the most likely or best guess as to the needed failure rate data. The use of best guess values as data inputs to the quantification of a fault tree creates uncertainty in the computed results. This paper presents a general methodology for the determination of the impact of uncertainty on the results of a fault tree study. The general methodology is based on the mathematics of propagation of error and variance contribution analysis. An example is presented to illustrate the application of the fault tree uncertainty analysis methodology to a real world problem

Interpreting the iISS Small-Gain Theorem as Transient Plus ISS Small-Gain Regulation

International audienceThis paper addresses the problem of establishing stability of interconnections of integral input-to-state stable (iISS) systems. Recently, the small-gain theorem for input-tostate stable (ISS) systems has been extended to the class of iISS systems. It has been also proved that at least one of the two iISS subsystems comprising a feedback interconnection needs to be ISS with respect to the state of the other subsystem for guaranteeing the iISS of the overall system. This paper shows that making use of this necessary condition enables to provide more insight on the iISS small gain theorem by giving an alternative proof of this result from the perspective of transient plus ISS small-gain regulation

Revisiting the iISS small-gain theorem through transient plus ISS small-gain regulation

International audienceRecently, the small-gain theorem for input-to-state stable (ISS) systems has been extended to the class of integral input-to-state stable (iISS) systems. Feedback connections of two iISS systems are robustly stable with respect to disturbance if an extended small-gain condition is satisfied. It has been proved that at least one of the two iISS subsystems needs to be ISS for guaranteeing globally asymptotic stability and iISS of the overall system. Making use of this necessary condition for the stability, this paper gives a new interpretation to the iISS small gain theorem as transient plus ISS small-gain regulation. The observation provides useful information for designing and analyzing nonlinear control systems based on the iISS small-gain theorem

Distributed Synchronization of Heterogeneous Oscillators on Networks With Arbitrary Topology

Many network applications rely on the synchronization of coupled oscillators. For example, such synchronization can provide networked devices with a common temporal reference necessary for coordinating actions or decoding transmitted messages. In this paper, we study the problem of using distributed control to achieve phase and frequency synchronization of a network of coupled heterogeneous nonlinear oscillators. Not only do our controllers guarantee zero-phase error in steady state under arbitrary frequency heterogeneity, but they also require little knowledge of the oscillator nonlinearities and network topology. Furthermore, we provide a global convergence analysis, in the absence of noise and propagation delay, for the resulting nonlinear system whose phase vector evolves on the n-torus

Self-Healing First-Order Distributed Optimization with Packet Loss

We describe SH-SVL, a parameterized family of first-order distributed optimization algorithms that enable a network of agents to collaboratively calculate a decision variable that minimizes the sum of cost functions at each agent. These algorithms are self-healing in that their convergence to the correct optimizer can be guaranteed even if they are initialized randomly, agents join or leave the network, or local cost functions change. We also present simulation evidence that our algorithms are self-healing in the case of dropped communication packets. Our algorithms are the first single-Laplacian methods for distributed convex optimization to exhibit all of these characteristics. We achieve self-healing by sacrificing internal stability, a fundamental trade-off for single-Laplacian methods.Comment: arXiv admin note: substantial text overlap with arXiv:2104.0195

Self-Healing First-Order Distributed Optimization

In this paper we describe a parameterized family of first-order distributed optimization algorithms that enable a network of agents to collaboratively calculate a decision variable that minimizes the sum of cost functions at each agent. These algorithms are self-healing in that their correctness is guaranteed even if they are initialized randomly, agents drop in or out of the network, local cost functions change, or communication packets are dropped. Our algorithms are the first single-Laplacian methods to exhibit all of these characteristics. We achieve self-healing by sacrificing internal stability, a fundamental trade-off for single-Laplacian methods.Comment: Corrected equation (40) by changing "min" to "max", results unaffecte

Human-Multirobot Collaborative Mobile Manipulation: the Omnid Mocobots

The Omnid human-collaborative mobile manipulators are an experimental platform for testing control architectures for autonomous and human-collaborative multirobot mobile manipulation. An Omnid consists of a mecanum-wheel omnidirectional mobile base and a series-elastic Delta-type parallel manipulator, and it is a specific implementation of a broader class of mobile collaborative robots ("mocobots") suitable for safe human co-manipulation of delicate, flexible, and articulated payloads. Key features of mocobots include passive compliance, for the safety of the human and the payload, and high-fidelity end-effector force control independent of the potentially imprecise motions of the mobile base. We describe general considerations for the design of teams of mocobots; the design of the Omnids in light of these considerations; manipulator and mobile base controllers to achieve useful multirobot collaborative behaviors; and initial experiments in human-multirobot collaborative mobile manipulation of large, unwieldy payloads. For these experiments, the only communication among the humans and Omnids is mechanical, through the payload.Comment: 8 pages, 10 figures. Videos available at https://www.youtube.com/watch?v=SEuFfONryL0. Submitted to IEEE Robotics and Automation Letters (RA-L