Last updated: 2021-06-25
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Knit directory:
VSA_altitude_hold/
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This notebook characterises data generated by the simulation of the classically implemented altitude hold controller. We need to understand the properties of the signals in order to design VSA implementations of them.
The values to be characterised are all the real scalars corresponding to the nodes in the data flow diagram for Design 01.
The data is generated from runs of the classically implemented simulation.
The data files are stored in the data directory.
The data is supplied as CSV files, each file corresponding to a different run of the simulation.
Each run of the simulation corresponds to a set of starting conditions and parameters.
The only starting condition that varies between runs is the initial altitude. In effect, the multicopter is dropped from some height, with the motors stopped and the drone must command the motors to attain the target altitude.
The name of each data file contains the values of all the parameters. In this work the target altitude is always constant at 5 metres, but more generally this should be treated as a demand which can vary with time.
Each row of the data file corresponds to a point in time and successive rows correspond to successive points in time. (This is a discrete time simulation with fixed time steps.)
Each file contains 500 time steps.
Each columns of the data file corresponds to a node of the data flow diagram.
Only a subset of the nodes are supplied (the nodes in rectangular boxes in the DFD supplied by Simon Levy) and the values of the other nodes can be reconstructed mathematically.
The values supplied from the input files are recorded to three decimal places, so there is scope for approximation error due to the limited precision.
Where a node value is supplied from the input file use that value and can also be mathematically reconstructed from upstream values, us the input value (rather than the reconstructed value) as input to downstream calculations. This is to avoid propagating approximation errors.
Read the data from the simulations and mathematically reconstruct the values of the nodes not included in the input files.
# function to clip value to a range
clip <- function(
x, # numeric
x_min, # numeric[1] - minimum output value
x_max # numeric[1] - maximum output value
) # value # numeric - x constrrained to the range [x_min, x_max]
{
x %>% pmax(x_min) %>% pmin(x_max)
}
# function to extract a parametr value from the file name
get_param <- function(
file, # character - vector of file names
regexp # character[1] - regular expression for "param=value"
# use a capture group to get the value part
) # value # numeric - vector of parameter values
{
file %>% str_match(regexp) %>%
subset(select = 2) %>% as.numeric()
}
# read the data
d_wide <- fs::dir_ls(path = here::here("data"), regexp = "/k_start=.*\\.csv$") %>% # get file paths
vroom::vroom(id = "file") %>% # read files
dplyr::mutate( # add extra columns
file = file %>% fs::path_ext_remove() %>% fs::path_file(), # get file name
# get parameters
k_start = file %>% get_param("k_start=([.0-9]+)"),
k_p = file %>% get_param("kp=([.0-9]+)"),
k_i = file %>% get_param("Ki=([.0-9]+)"),
k_tgt = file %>% get_param("k_tgt=([.0-9]+)"),
k_windup = file %>% get_param("k_windup=([.0-9]+)"),
# reconstruct the missing nodes
i1 = k_tgt - z,
i2 = i1 - dz,
i3 = e * k_p,
i9 = lag(ei, n = 1, default = 0),
i4 = e + i9,
i5 = i4 %>% clip(-k_windup, k_windup),
i6 = ei * k_i,
i7 = i3 + i6,
i8 = i7 %>% clip(0, 1)
) %>%
# add time variable per file
dplyr::group_by(file) %>%
dplyr::mutate(t = 1:n()) %>%
dplyr::ungroup()Rows: 1500 Columns: 6── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
dbl (5): z, dz, e, ei, u
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.dplyr::glimpse(d_wide)Rows: 1,500
Columns: 21
$ file <chr> "k_start=10.00_k_tgt=5.00_kp=0.20_Ki=3.00_k_windup=0.20", "k_…
$ z <dbl> 10.000, 9.999, 9.998, 9.995, 9.992, 9.987, 9.982, 9.975, 9.96…
$ dz <dbl> -0.058, -0.156, -0.254, -0.352, -0.450, -0.548, -0.646, -0.74…
$ e <dbl> -4.942, -4.843, -4.744, -4.643, -4.542, -4.439, -4.335, -4.23…
$ ei <dbl> -0.2, -0.2, -0.2, -0.2, -0.2, -0.2, -0.2, -0.2, -0.2, -0.2, -…
$ u <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ k_start <dbl> 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 1…
$ k_p <dbl> 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0…
$ k_i <dbl> 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3…
$ k_tgt <dbl> 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5…
$ k_windup <dbl> 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0…
$ i1 <dbl> -5.000, -4.999, -4.998, -4.995, -4.992, -4.987, -4.982, -4.97…
$ i2 <dbl> -4.942, -4.843, -4.744, -4.643, -4.542, -4.439, -4.336, -4.23…
$ i3 <dbl> -0.9884, -0.9686, -0.9488, -0.9286, -0.9084, -0.8878, -0.8670…
$ i9 <dbl> 0.0, -0.2, -0.2, -0.2, -0.2, -0.2, -0.2, -0.2, -0.2, -0.2, -0…
$ i4 <dbl> -4.942, -5.043, -4.944, -4.843, -4.742, -4.639, -4.535, -4.43…
$ i5 <dbl> -0.2, -0.2, -0.2, -0.2, -0.2, -0.2, -0.2, -0.2, -0.2, -0.2, -…
$ i6 <dbl> -0.6, -0.6, -0.6, -0.6, -0.6, -0.6, -0.6, -0.6, -0.6, -0.6, -…
$ i7 <dbl> -1.5884, -1.5686, -1.5488, -1.5286, -1.5084, -1.4878, -1.4670…
$ i8 <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ t <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18…Where possible compare the calculated values with the values recorded from the simulator.
Nodes with a single input edge can be checked against the output of the predecessor node.
The nodes which can be checked are: e, ei, u
Min. 1st Qu. Median Mean 3rd Qu. Max.
-1.000e-03 0.000e+00 0.000e+00 1.733e-05 0.000e+00 1.000e-03 Min. 1st Qu. Median Mean 3rd Qu. Max.
-1e-03 0e+00 0e+00 -1e-05 0e+00 1e-03 Min. 1st Qu. Median Mean 3rd Qu. Max.
-2.000e-03 -8.000e-04 0.000e+00 3.627e-05 1.000e-03 2.000e-03 Display a quick summary of the values of all the nodes.
Note that these summaries are over all the input files pooled.
| Name | d_wide |
| Number of rows | 1500 |
| Number of columns | 21 |
| _______________________ | |
| Column type frequency: | |
| character | 1 |
| numeric | 20 |
| ________________________ | |
| Group variables | None |
Variable type: character
| skim_variable | n_missing | complete_rate | min | max | empty | n_unique | whitespace |
|---|---|---|---|---|---|---|---|
| file | 0 | 1 | 53 | 54 | 0 | 3 | 0 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| z | 0 | 1 | 5.41 | 1.32 | 2.00 | 4.92 | 5.11 | 5.70 | 10.00 | ▁▇▅▁▁ |
| dz | 0 | 1 | -0.33 | 1.10 | -4.37 | -0.66 | -0.11 | 0.07 | 2.70 | ▁▂▆▇▁ |
| e | 0 | 1 | -0.08 | 0.57 | -4.94 | 0.00 | 0.00 | 0.00 | 3.27 | ▁▁▁▇▁ |
| ei | 0 | 1 | 0.16 | 0.08 | -0.20 | 0.17 | 0.17 | 0.18 | 0.20 | ▁▁▁▁▇ |
| u | 0 | 1 | 0.51 | 0.12 | 0.00 | 0.52 | 0.53 | 0.54 | 1.00 | ▁▁▇▁▁ |
| k_start | 0 | 1 | 6.67 | 3.40 | 2.00 | 2.00 | 8.00 | 10.00 | 10.00 | ▇▁▁▇▇ |
| k_p | 0 | 1 | 0.20 | 0.00 | 0.20 | 0.20 | 0.20 | 0.20 | 0.20 | ▁▁▇▁▁ |
| k_i | 0 | 1 | 3.00 | 0.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | ▁▁▇▁▁ |
| k_tgt | 0 | 1 | 5.00 | 0.00 | 5.00 | 5.00 | 5.00 | 5.00 | 5.00 | ▁▁▇▁▁ |
| k_windup | 0 | 1 | 0.20 | 0.00 | 0.20 | 0.20 | 0.20 | 0.20 | 0.20 | ▁▁▇▁▁ |
| i1 | 0 | 1 | -0.41 | 1.32 | -5.00 | -0.70 | -0.11 | 0.08 | 3.00 | ▁▁▅▇▁ |
| i2 | 0 | 1 | -0.08 | 0.57 | -4.94 | 0.00 | 0.00 | 0.00 | 3.27 | ▁▁▁▇▁ |
| i3 | 0 | 1 | -0.02 | 0.11 | -0.99 | 0.00 | 0.00 | 0.00 | 0.65 | ▁▁▁▇▁ |
| i9 | 0 | 1 | 0.16 | 0.08 | -0.20 | 0.17 | 0.17 | 0.18 | 0.20 | ▁▁▁▁▇ |
| i4 | 0 | 1 | 0.08 | 0.64 | -5.04 | 0.17 | 0.17 | 0.18 | 3.44 | ▁▁▁▇▁ |
| i5 | 0 | 1 | 0.16 | 0.08 | -0.20 | 0.17 | 0.17 | 0.18 | 0.20 | ▁▁▁▁▇ |
| i6 | 0 | 1 | 0.48 | 0.24 | -0.60 | 0.52 | 0.52 | 0.54 | 0.60 | ▁▁▁▁▇ |
| i7 | 0 | 1 | 0.46 | 0.34 | -1.59 | 0.52 | 0.52 | 0.54 | 1.25 | ▁▁▁▇▁ |
| i8 | 0 | 1 | 0.51 | 0.12 | 0.00 | 0.52 | 0.52 | 0.54 | 1.00 | ▁▁▇▁▁ |
| t | 0 | 1 | 250.50 | 144.39 | 1.00 | 125.75 | 250.50 | 375.25 | 500.00 | ▇▇▇▇▇ |
R version 4.1.0 (2021-05-18)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 21.04
Matrix products: default
BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0
locale:
[1] LC_CTYPE=en_AU.UTF-8 LC_NUMERIC=C
[3] LC_TIME=en_AU.UTF-8 LC_COLLATE=en_AU.UTF-8
[5] LC_MONETARY=en_AU.UTF-8 LC_MESSAGES=en_AU.UTF-8
[7] LC_PAPER=en_AU.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_AU.UTF-8 LC_IDENTIFICATION=C
attached base packages:
[1] stats graphics grDevices datasets utils methods base
other attached packages:
[1] skimr_2.1.3 stringr_1.4.0 dplyr_1.0.7 vroom_1.5.1 here_1.0.1
[6] fs_1.5.0
loaded via a namespace (and not attached):
[1] Rcpp_1.0.6 highr_0.9 pillar_1.6.1 compiler_4.1.0
[5] later_1.2.0 git2r_0.28.0 workflowr_1.6.2 base64enc_0.1-3
[9] tools_4.1.0 digest_0.6.27 bit_4.0.4 jsonlite_1.7.2
[13] evaluate_0.14 lifecycle_1.0.0 tibble_3.1.2 pkgconfig_2.0.3
[17] rlang_0.4.11 rstudioapi_0.13 cli_2.5.0 parallel_4.1.0
[21] yaml_2.2.1 xfun_0.24 repr_1.1.3 knitr_1.33
[25] generics_0.1.0 vctrs_0.3.8 rprojroot_2.0.2 bit64_4.0.5
[29] tidyselect_1.1.1 glue_1.4.2 R6_2.5.0 fansi_0.5.0
[33] rmarkdown_2.9 bookdown_0.22 tidyr_1.1.3 purrr_0.3.4
[37] tzdb_0.1.1 magrittr_2.0.1 whisker_0.4 promises_1.2.0.1
[41] ellipsis_0.3.2 htmltools_0.5.1.1 renv_0.13.2 httpuv_1.6.1
[45] utf8_1.2.1 stringi_1.6.2 crayon_1.4.1