diff --git a/class07/background_materials/Example_Unscented_vs_Robust b/class07/background_materials/Example_Unscented_vs_Robust new file mode 100644 index 0000000..c414d5d --- /dev/null +++ b/class07/background_materials/Example_Unscented_vs_Robust @@ -0,0 +1,1297 @@ +### A Pluto.jl notebook ### +# v0.20.19 + +using Markdown +using InteractiveUtils + +# ╔═╡ 624a9e60-9ed7-11f0-2d92-5f53e7aefee8 +using Random, Plots, Statistics + +# ╔═╡ 62c1d144-1e66-46ee-8e58-d3905609e25a +begin + Random.seed!(42) +end + +# ╔═╡ 176ce1f2-aab0-4896-8ba1-484fdb6bfe7a +# --------------------------- +# System parameters +# --------------------------- +begin + V = 1.0 + F1, F2 = 0.5, 0.3 + T1_nom, T2_nom = 350.0, 200.0 + T_env = 298.0 + + dt = 0.02 + T_total = 50.0 + N = Int(T_total / dt) +end + +# ╔═╡ acb1e09d-bf4a-433b-bf22-f6ee01435742 +# --------------------------- +# Setpoint definition +# --------------------------- +begin + T_set = zeros(N) + T_set[1:Int(N*0.25)] .= 330.0 + T_set[Int(N*0.25)+1:Int(N*0.5)] .= 210.0 + T_set[Int(N*0.5)+1:Int(N*0.75)] .= 340.0 + T_set[Int(N*0.75)+1:end] .= 320.0 +end + + +# ╔═╡ 0de7fd3a-c00e-49a2-96f4-64c3b4b1256c +md""" +# Question 1: + +Why do we choose these setpoint steps? + +""" + + +# ╔═╡ a767ed8c-ce75-45f4-8112-49a58a06f84a +# --------------------------- +# Reaction & disturbance parameters +# --------------------------- +begin + reaction_coeff = 5e-5 + feed_noise_std = 0.1 +end + +# ╔═╡ 89d5e261-95db-48a9-a57d-89d90a1de712 +# --------------------------- +# Robust baseline controller parameters +# --------------------------- +begin + K_robust = 9.0 + robust_limits = (-2.5, 2.5) +end + + +# ╔═╡ eed0ea34-670b-4b3e-9228-eda8d08d53dd +# --------------------------- +# Unscented-like controller parameters +# --------------------------- +begin + K_uoc = 45.0 + alpha = 6.0 + sigma_std = 1.0 + uoc_limits = (-120.0, 120.0) +end + + +# ╔═╡ cb000516-425a-4ab1-83e3-4a32a509de6d +# --------------------------- +# Reaction rate function +# --------------------------- +begin + reaction_rate(T) = reaction_coeff * (T - T_env)^2 +end + + +# ╔═╡ 9864ce09-1a94-4eb2-9fb3-0ad1443d9995 +# --------------------------- +# R² metric function +# --------------------------- +begin + function r2_manual(y_true, y_pred) + ss_res = sum((y_true .- y_pred).^2) + ss_tot = sum((y_true .- mean(y_true)).^2) + ss_tot == 0 ? NaN : 1 - ss_res / ss_tot + end +end + + +# ╔═╡ dcbbbdd2-5d96-45b3-9d68-e803c727f3bd +# --------------------------- +# Simulation loop +# --------------------------- +begin +T_robust = zeros(N) +T_uoc = zeros(N) +T_uoc_std = zeros(N) +robust_saturated = zeros(N) + +T_robust[1] = 300.0 +T_uoc[1] = 300.0 +T_uoc_std[1] = sigma_std + +for k in 1:N-1 + T1 = T1_nom + randn() * feed_noise_std + T2 = T2_nom + randn() * feed_noise_std + + # ---- Robust P controller ---- + u_robust = K_robust * (T_set[k] - T_robust[k]) + u_robust = clamp(u_robust, robust_limits[1], robust_limits[2]) + robust_saturated[k] = u_robust in (robust_limits[1], robust_limits[2]) ? 1 : 0 + dT_robust = (F1*(T1 - T_robust[k]) + F2*(T2 - T_robust[k]) + + u_robust + reaction_rate(T_robust[k])) / V + T_robust[k+1] = T_robust[k] + dt * dT_robust + + # ---- Unscented-like controller ---- + sigma_points(T) = [T, T + sigma_std, T - sigma_std, T + 2*sigma_std, T - 2*sigma_std] + propagate_sigma(T_sigma, u, T1, T2) = [T + dt * (F1*(T1 - T) + F2*(T2 - T) + u + reaction_rate(T)) for T in T_sigma] + + u_candidate = K_uoc * (T_set[k] - T_uoc[k]) + T_sigma = sigma_points(T_uoc[k]) + T_sigma_next = propagate_sigma(T_sigma, u_candidate, T1, T2) + error_mean = mean(T_sigma_next) - T_set[k] + u_final = clamp(u_candidate - alpha * error_mean, uoc_limits[1], uoc_limits[2]) + std_next = std(T_sigma_next) + + dT_uoc = (F1*(T1 - T_uoc[k]) + F2*(T2 - T_uoc[k]) + + u_final + reaction_rate(T_uoc[k])) / V + T_uoc[k+1] = T_uoc[k] + dt * dT_uoc + T_uoc_std[k+1] = std_next +end +end + + + +# ╔═╡ 88cdfd9f-1365-4a64-8a6e-82ea581a5820 +md""" +# Question 2: +What is the role of T_{uoc}_{std}? + +It tracks the predicted standard deviation of the Unscented-like controller, +""" + + +# ╔═╡ d833e119-53f6-40fa-9104-667dd9b676bf +# --------------------------- +# Compute performance metrics +# --------------------------- +begin + r2_robust = r2_manual(T_set, T_robust) + r2_uoc = r2_manual(T_set, T_uoc) + rmse_robust = sqrt(mean((T_set .- T_robust).^2)) + rmse_uoc = sqrt(mean((T_set .- T_uoc).^2)) + + println("R² Robust control: ", round(r2_robust, digits=4)) + println("R² Unscented control: ", round(r2_uoc, digits=4)) + println("RMSE Robust: ", round(rmse_robust, digits=3), " K, RMSE UOC: ", round(rmse_uoc, digits=3), " K") + println("Robust actuator saturation fraction: ", round(mean(robust_saturated), digits=3)) + println("Max |T_robust|: ", maximum(abs.(T_robust))) + println("Max |T_uoc|: ", maximum(abs.(T_uoc))) +end + + +# ╔═╡ fccfd8cd-0a5a-4638-a74f-1137446ff478 +# --------------------------- +# Plot results +# --------------------------- +begin + plot(1:N, T_set, linestyle=:dash, label="Setpoint") + plot!(1:N, T_robust, label="Robust") + plot!(1:N, T_uoc, label="UOC") + plot!(1:N, T_uoc .- T_uoc_std, alpha=0.25, label="") + plot!(1:N, T_uoc .+ T_uoc_std, alpha=0.25, label="UOC sigma") +end + + +# ╔═╡ 50733baf-1683-46fc-9490-0c46c5cee1e9 +md""" +# Question 3: + +Why is the Unscented controller better here than the Robust one? +""" + + +# ╔═╡ 00000000-0000-0000-0000-000000000001 +PLUTO_PROJECT_TOML_CONTENTS = """ +[deps] +Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" +Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" + +[compat] +Plots = "~1.41.1" +""" + +# ╔═╡ 00000000-0000-0000-0000-000000000002 +PLUTO_MANIFEST_TOML_CONTENTS = """ +# This file is machine-generated - editing it directly is not advised + +julia_version = "1.11.6" +manifest_format = "2.0" +project_hash = "a8820582a5d4c7473ae0c0f61c21d6f06ce0cdd6" + +[[deps.AliasTables]] +deps = ["PtrArrays", "Random"] +git-tree-sha1 = "9876e1e164b144ca45e9e3198d0b689cadfed9ff" +uuid = "66dad0bd-aa9a-41b7-9441-69ab47430ed8" +version = "1.1.3" + +[[deps.ArgTools]] +uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" +version = "1.1.2" + +[[deps.Artifacts]] +uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" +version = "1.11.0" + +[[deps.Base64]] +uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f" +version = 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"8e850ede-7688-5339-a07c-302acd2aaf8d" +version = "1.59.0+0" + +[[deps.p7zip_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" +version = "17.4.0+2" + +[[deps.x264_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "14cc7083fc6dff3cc44f2bc435ee96d06ed79aa7" +uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a" +version = "10164.0.1+0" + +[[deps.x265_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl"] +git-tree-sha1 = "e7b67590c14d487e734dcb925924c5dc43ec85f3" +uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" +version = "4.1.0+0" + +[[deps.xkbcommon_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"] +git-tree-sha1 = "fbf139bce07a534df0e699dbb5f5cc9346f95cc1" +uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd" +version = "1.9.2+0" +""" + +# ╔═╡ Cell order: +# ╠═624a9e60-9ed7-11f0-2d92-5f53e7aefee8 +# ╠═62c1d144-1e66-46ee-8e58-d3905609e25a +# ╠═176ce1f2-aab0-4896-8ba1-484fdb6bfe7a +# ╠═acb1e09d-bf4a-433b-bf22-f6ee01435742 +# ╠═0de7fd3a-c00e-49a2-96f4-64c3b4b1256c +# ╠═a767ed8c-ce75-45f4-8112-49a58a06f84a +# ╠═89d5e261-95db-48a9-a57d-89d90a1de712 +# ╠═eed0ea34-670b-4b3e-9228-eda8d08d53dd +# ╠═cb000516-425a-4ab1-83e3-4a32a509de6d +# ╠═9864ce09-1a94-4eb2-9fb3-0ad1443d9995 +# ╠═dcbbbdd2-5d96-45b3-9d68-e803c727f3bd +# ╠═88cdfd9f-1365-4a64-8a6e-82ea581a5820 +# ╠═d833e119-53f6-40fa-9104-667dd9b676bf +# ╠═fccfd8cd-0a5a-4638-a74f-1137446ff478 +# ╠═50733baf-1683-46fc-9490-0c46c5cee1e9 +# ╟─00000000-0000-0000-0000-000000000001 +# ╟─00000000-0000-0000-0000-000000000002