Merge pull request #88 from JuliaControl/doc_details

minor doc additions

Author: franckgaga

docs/src/manual/linmpc.md

@@ -90,10 +90,12 @@ automatically added to the model outputs by default if observability is preserve
     structure with `mpc = LinMPC(InternalModel(model), Hp=15, Hc=2, Mwt=[1, 1], Nwt=[0.1, 0.1])`.
     It was tested on the example of this page and it gave similar results.
 
-Before closing the loop, we call [`initstate!`](@ref) with the actual plant inputs and
-measurements to ensure a bumpless transfer. Since `model` simulates our plant here, its
-output will initialize the states. [`LinModel`](@ref) objects are callable for this purpose
-(an alias for [`evaloutput`](@ref)):
+Before closing the loop, the actual plant input ``\mathbf{u}`` and measurement ``\mathbf{y}``
+should initialize the estimates ``\mathbf{x̂}`` at the steady-state solution that leads to
+``\mathbf{ŷ}(0) = \mathbf{y}(0)``. This approach results in a bumpless transfer. The
+[`initstate!`](@ref) function finds this solution for [`LinModel`](@ref). Since `model`
+simulates our plant here, its output will initialize the states. [`LinModel`](@ref) objects
+are callable for this purpose (an alias for [`evaloutput`](@ref)):
 
 ```@example 1
 u, y = model.uop, model() # or equivalently : y = evaloutput(model)

docs/src/manual/nonlinmpc.md

@@ -373,9 +373,10 @@ nothing # hide
 ```
 
 The [`setmodel!`](@ref) method must be called after solving the optimization problem with
-[`moveinput!`](@ref), and before updating the state estimate with [`updatestate!`](@ref).
-The [`SimResult`](@ref) object is for plotting purposes only. The adaptive [`LinMPC`](@ref)
-performances are similar to the nonlinear MPC, both for the 180° setpoint:
+[`moveinput!`](@ref) and before updating the state estimate with [`updatestate!`](@ref),
+that is, when both ``\mathbf{u}(k)`` and ``\mathbf{x̂}_{k-1}(k)`` are available as the new
+operating point. The [`SimResult`](@ref) object is for plotting purposes only. The adaptive
+[`LinMPC`](@ref) performances are similar to the nonlinear MPC, both for the 180° setpoint:
 
 ```@example 1
 x_0 = [0, 0]; x̂_0 = [0, 0, 0]; ry = [180]

docs/src/public/plot_sim.md

@@ -24,6 +24,9 @@ SimResult
 
 ## Plotting Results
 
+The `plot` methods are based on [`Plots.jl`](https://github.com/JuliaPlots/Plots.jl) package.
+To install it run `using Pkg; Pkg.add("Plots")` in the Julia REPL.
+
 ```@docs
 ModelPredictiveControl.plot
 ```