Actuators and Sensors

Actuators are assumed only on the boundary sides of the geometrical object - not inside the object. It is possible to place more than one actuator on one boundary side. So, boundary sides with actuators are subdivided in partitions of equal size. In each partition we can specify wheter one actuator is assumed or not. It is not possible to specify more than one actuator per partition. If for instance 5 actuators are assumed on boundary :south then 5 partitions are created.

Spatial Characterization

The n-th actuator has inside its partition the radially symmetric spatial characterization

\[b_{n}(x) = m_{n} \exp(-M_{n} ~ \lVert x-x_{c}\rVert^{2~\nu_{n}})\]

with

• scaling $m \in [0,1]$
• curvature matrix $M \in \mathbb{R}^3$,
• power $\nu \in \{1,2,3, \cdots\}$ and
• central point $x_{c}$ of the partition.

The central point of each partition is calculated internally, all other values have to be fixed. In many situations curvature matrix $M$ can be assumed as a scaled identity matrix, for example $M = 54 ~ I_{3 \times 3}$.

Quick Overview

HeatRods have single points as boundary sides:

• only 1 actuator per side is possible
• no partitions
• spatial characterization $b$ is only a number

HeatPlates have four boundary sides as 1-dimensional lines:

• more than 1 actuator per side is possible
• partitions are 1-dimensional intervals
• spatial characterization $b_{n}(x)$ is 1-dimensional function

HeatCuboidss have six boundary sides as 2-dimensional areas:

• more than 1 actuator per side is possible
• partitions are 2-dimensional intervals
• spatial characterization $b_{n}(x)$ is 2-dimensional function, $x=(x_{1},x_{2})$

Sensors

measure(temperatures :: Vector{<:Real}, character :: Vector{<:Real})

measure(temperatures :: Matrix{<:Real}, character :: Vector{<:Real})