StoryLine

Terminology

  • Block: a technology that produces, consumes, converts, stores or transports energy

  • Controller: a technology that control a block or a group of blocks

  • Location: a site

  • Node: a combination of blocks, controllers and a location

Terminology - 2

  • modular time integration / multi-framing / multi-rate (and multi-method) integration /// modular simulation

  • clocked discretized continuous-time

  • communication step size control

  • algebraic loops / cyclic dependencies

  • time-based block diagrams

  • coupled system with direct feed-through

  • sequential modular time integration methods (for coupled multi-body system models)

  • classical monolithic simulation techniques

  • coupling strategies (coupling mechanism) and partitioning

  • block oriented representation: \(u_{j}\rightarrow\boxed{\dot{x_{j}}=f_{j}(x_{j},u_{j})}\rightarrow y_{j}=g_{j}(x_{j},u_{j})\)

  • sampling points: \(T_{n}\) (Kubler 2000)

  • macro steps: \(T_{n}\rightarrow T_{n+1}\) (Kubler 2000)

  • sampling rate: \(H_{n}=T_{n+1}-T_{n}\) (Kubler 2000)

Subsystem

\begin{equation} \left\{\begin{array}[]{ll}\dot{x_{j}}(t)=f_{j}(x_{j}(t),u_{j}(t),u_{ex}(t))\\ y_{j}(t)=g_{j}(x_{j}(t),u_{j}(t))\\ \end{array}\right.\\ \end{equation}
\begin{equation} u_{j}(t)=c_{j}(y_{1}(t),...,y_{j-1}(t),y_{j+1}(t),...,y_{r}(t)),j\in[1,r]\\ \end{equation}
\begin{equation} \left\{\begin{array}[]{ll}\dot{x}(t)=f(x(t),u(t),u_{ex}(t))\\ y(t)=g(x(t),u(t)),u(t)=c(y(t))\\ \end{array}\right.\\ \end{equation}