pid.jl
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Authored by
QUENTIN Guilloteau
Edited
pid.jl 36.33 KiB
### A Pluto.jl notebook ###
# v0.19.12
using Markdown
using InteractiveUtils
# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
quote
local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
local el = $(esc(element))
global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
el
end
end
# ╔═╡ e8f6d188-e3cf-11eb-2617-63b03b15571a
using Plots
# ╔═╡ 74693b5d-ab28-43ac-8790-7ccb7690c20e
# ╔═╡ fd99a3e4-e3cd-11eb-2c58-6d5034511cad
md"# Playing with PI Controllers"
# ╔═╡ 8f221d50-e3ce-11eb-0d6c-019fe54043ed
md"""
The plant is described as:
$$y(k + 1) = a y(k) + b u(k - d)$$
where:
- ``y(k)`` is the system output at time ``k``
- ``u(k)`` is the system input at time ``k``
- ``a`` and ``b`` are the coefficients of the model
- ``d`` is the delay of the plant
"""
# ╔═╡ 11a5edf2-e3ce-11eb-005c-f178d0d62be3
begin
slider_a = @bind a html"<input type=range min=0 max=1.5 step=0.1 value = 0.8>"
slider_b = @bind b html"<input type=range min=0 max=1.5 step=0.1, value = 0.5>"
slider_plant_delay = @bind plant_delay html"<input type=range min=0 max=5 value = 0>"
md"""
a: $(slider_a)
b: $(slider_b)
plant delay: $(slider_plant_delay)
"""
end
# ╔═╡ 475378a6-e3d2-11eb-0c5a-25462b0139d7
md"## Open Loop Plant"
# ╔═╡ 2bedf474-e3cf-11eb-2fa4-9b14566a4479
begin
slider_max_duration = @bind max_duration html"<input type=range min=0 max=100>"
slider_step = @bind step html"<input type=range min=0 max=10, value =2>"
slider_start_step = @bind start_step html"<input type=range min=0 max=100>"
md"""
Duration: $(slider_max_duration)
Step Amplitude: $(slider_step)
Step Start: $(slider_start_step)
"""
end
# ╔═╡ 89c45c18-e3d0-11eb-1ee8-2d5391a1e2db
md"""
a = $(a), b = $(b), d = $(plant_delay)
duration = $(max_duration), step = $(step), start step = $(start_step)
"""
# ╔═╡ d50716b8-e3ce-11eb-2e58-c1353e1e487b
begin
input = [(n >= start_step) ? step : 0 for n in 1:max_duration]
output = zeros(max_duration)
time = [n for n in 1:max_duration]
ctrl_input = zeros(max_duration)
ctrl_output = zeros(max_duration)
errors = zeros(max_duration)
end
# ╔═╡ bb083f6c-e3ce-11eb-0755-ed0fec5dfac3
begin
for i in 1:max_duration
if i > 1
if i > plant_delay
output[i] = a * output[i - 1] + b * input[i - plant_delay]
else
output[i] = a * output[i - 1]
end
end
end
plot_output = plot(time, output, ylabel = "Output", label = "Output")
plot_input = plot(time, input, ylabel = "Input", label = "Input")
plot(plot_output, plot_input, layout = (2, 1), xlabel = "Time")
end
# ╔═╡ 54d3b772-e3d2-11eb-2cac-cbe399ab5927
md"## PI Controller"
# ╔═╡ 3c04af12-7ef1-4fbc-a637-21749cd56f7b
md"""
In **discrete** time:
$$u(k) = K_p e(k) + K_i \sum_{i=0}^k e(i)$$
where:
- ``u(k)`` is the next input
- ``e(k)`` is the control error (``e(k) = r(k) - y(k)``)
- ``K_p`` is the Porportional Gain
- ``K_i`` is the Integral Gain
"""
# ╔═╡ 5fe88e8a-e3d2-11eb-10c4-350b9c45a561
begin
slider_kp = @bind kp html"<input type=range min=0 max=2 step=0.05>"
slider_ki = @bind ki html"<input type=range min=0 max=2 step=0.05>"
slider_ref = @bind ref html"<input type=range min=0 max=10>"
md"""
kp: $(slider_kp)
ki: $(slider_ki)
Reference: $(slider_ref)
"""
end
# ╔═╡ 5bdf3144-e3d3-11eb-23e5-e5ccae630c37
md"""
kp: $(kp)
ki: $(ki)
"""
# ╔═╡ b92f3444-e3d2-11eb-0326-1903115f292d
begin
for i in 1:max_duration
if i > 1
errors[i] = ref - ctrl_output[i - 1]
ctrl_input[i] = ctrl_input[i - 1] + (ki + kp) * errors[i] - kp * errors[i - 1]
else
ctrl_input[i] = 0
end
if i > 1
if i > plant_delay
ctrl_output[i] = a * ctrl_output[i - 1] + b * ctrl_input[i - plant_delay]
else
ctrl_output[i] = a * ctrl_output[i - 1]
end
else
ctrl_output[i] = b * ctrl_input[i]
end
if i > start_step
ctrl_output[i] = ctrl_output[i] + step
end
end
plot_load = plot(time, ctrl_output, ylabel = "Output", label = "Output")
plot!(time, ref * ones(max_duration), label = "Ref")
plot_ctrl_input = plot(time, ctrl_input, ylabel = "Input", label = "Input")
plot(plot_load, plot_ctrl_input, layout = (2, 1), xlabel = "Time")
end
# ╔═╡ 00000000-0000-0000-0000-000000000001
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deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"
[[deps.Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"
[[deps.Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"
[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"
[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"
[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"
[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"
[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"
[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"
[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"
[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"
[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"
[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"
[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"
[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"
[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.12+3"
[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e45044cd873ded54b6a5bac0eb5c971392cf1927"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.2+0"
[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "868e669ccb12ba16eaf50cb2957ee2ff61261c56"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.29.0+0"
[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.4.0+0"
[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"
[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.1.1+0"
[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"
[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"
[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"
[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.48.0+0"
[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+0"
[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"
[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"
[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "9ebfc140cc56e8c2156a15ceac2f0302e327ac0a"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+0"
"""
# ╔═╡ Cell order:
# ╟─fd99a3e4-e3cd-11eb-2c58-6d5034511cad
# ╟─e8f6d188-e3cf-11eb-2617-63b03b15571a
# ╟─8f221d50-e3ce-11eb-0d6c-019fe54043ed
# ╟─11a5edf2-e3ce-11eb-005c-f178d0d62be3
# ╟─89c45c18-e3d0-11eb-1ee8-2d5391a1e2db
# ╟─475378a6-e3d2-11eb-0c5a-25462b0139d7
# ╟─2bedf474-e3cf-11eb-2fa4-9b14566a4479
# ╟─d50716b8-e3ce-11eb-2e58-c1353e1e487b
# ╟─bb083f6c-e3ce-11eb-0755-ed0fec5dfac3
# ╟─54d3b772-e3d2-11eb-2cac-cbe399ab5927
# ╟─3c04af12-7ef1-4fbc-a637-21749cd56f7b
# ╟─5fe88e8a-e3d2-11eb-10c4-350b9c45a561
# ╟─5bdf3144-e3d3-11eb-23e5-e5ccae630c37
# ╟─b92f3444-e3d2-11eb-0326-1903115f292d
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002
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