debug manual nonlinmpc

Author: franckgaga

docs/src/manual/nonlinmpc.md

@@ -27,14 +27,14 @@ friction coefficient at the pivot point, and ``m``, the mass attached at the end
 pendulum. Here, the explicit Euler method discretizes the system to construct a
 [`NonLinModel`](@ref):
 
-```@example 2
+```@example 1
 using ModelPredictiveControl
 function pendulum(par, x, u)
     g, L, K, m = par        # [m/s], [m], [kg/s], [kg]
     θ, ω = x[1], x[2]       # [rad], [rad/s]
     τ  = u[1]               # [N m]
     dθ = ω
-    dω = -g/L*sin(θ) - k/m*ω + τ/m/L^2
+    dω = -g/L*sin(θ) - K/m*ω + τ/m/L^2
     return [dθ, dω]
 end
 Ts  = 0.1                   # [s]
@@ -48,42 +48,42 @@ model = NonLinModel(f, h, Ts, nu, nx, ny)
 The output function ``\mathbf{h}`` converts the angular position ``θ`` to degrees. It
 is good practice to first simulate `model` using [`sim!`](@ref) as a quick sanity check:
 
-```@example 2
+```@example 1
 using Plots
 u = [0.5] # τ = 0.5 N m
 plot(sim!(model, 60, u), plotu=false)
 ```
 
 An [`UnscentedKalmanFilter`](@ref) estimates the plant state :
 
-```@example 2
+```@example 1
 estim = UnscentedKalmanFilter(model, σQ=[0.5, 2.5], σQ_int=[0.5])
 ```
 
 The standard deviation of the angular velocity ``ω`` is higher here (`σQ` second value)
 since ``\dot{ω}(t)`` equation includes an uncertain parameter: the friction coefficient
 ``K``. The estimator tuning is tested on a plant simulated with a different ``K``:
 
-```@example 2
+```@example 1
 par_plant = (par[1], par[2], par[3] + 0.25, par[4])
 f_plant(x, u, _) = x + Ts*pendulum(par_plant, x, u)
 plant = NonLinModel(f_plant, h, Ts, nu, nx, ny)
 res = sim!(estim, 30, [0.5], plant=plant, y_noise=[0.5]) # τ = 0.5 N m
-p2 = plot(res, plotu=false, plotx=true, plotx̂=true)
+plot(res, plotu=false, plotx=true, plotx̂=true)
 ```
 
 The Kalman filter performance seems sufficient for control. As the motor torque is limited
 to -1.5 to 1.5 N m, we incorporate the input constraints in a [`NonLinMPC`](@ref):
 
-```@example 2
+```@example 1
 mpc = NonLinMPC(estim, Hp=20, Hc=2, Mwt=[0.1], Nwt=[1.0], Cwt=Inf)
 mpc = setconstraint!(mpc, umin=[-1.5], umax=[+1.5])
 ```
 
 We test `mpc` performance on `plant` by imposing an angular setpoint of 180° (inverted
 position):
 
-```@example 2
+```@example 1
 res = sim!(mpc, 30, [180.0], x̂0=zeros(mpc.estim.nx̂), plant=plant, x0=zeros(plant.nx))
 plot(res, plotŷ=true)
 ```