Functions: Simulations and Plots

sim!(plant::SimModel, N::Int, u=plant.uop.+1, d=plant.dop; x_0=plant.xop) -> res

Open-loop simulation of plant for N time steps, default to unit bump test on all inputs.

The manipulated inputs $\mathbf{u}$ and measured disturbances $\mathbf{d}$ are held constant at u and d values, respectively. The plant initial state $\mathbf{x}(0)$ is specified by x_0 keyword arguments. The function returns SimResult instances that can be visualized by calling plot on them. Note that the method mutates plant internal states.

Examples

julia> plant = NonLinModel((x,u,d,_)->0.1x+u+d, (x,_,_)->2x, 5, 1, 1, 1, 1, solver=nothing);

julia> res = sim!(plant, 15, [0], [0], x_0=[1])
Simulation results of NonLinModel with 15 time steps.

sim!(
    estim::StateEstimator,
    N::Int,
    u = estim.model.uop .+ 1,
    d = estim.model.dop;
    <keyword arguments>
) -> res

Closed-loop simulation of estim estimator for N steps, default to input bumps.

See Arguments for the available options. The noises are provided as standard deviations σ vectors. The simulated sensor and process noises of plant are specified by y_noise and x_noise arguments, respectively.

Arguments

• estim::StateEstimator : state estimator to simulate
• N::Int : simulation length in time steps
• u = estim.model.uop .+ 1 : manipulated input $\mathbf{u}$ value
• d = estim.model.dop : plant measured disturbance $\mathbf{d}$ value
• plant::SimModel = estim.model : simulated plant model
• u_step = zeros(plant.nu) : step load disturbance on plant inputs $\mathbf{u}$
• u_noise = zeros(plant.nu) : gaussian load disturbance on plant inputs $\mathbf{u}$
• y_step = zeros(plant.ny) : step disturbance on plant outputs $\mathbf{y}$
• y_noise = zeros(plant.ny) : additive gaussian noise on plant outputs $\mathbf{y}$
• d_step = zeros(plant.nd) : step on measured disturbances $\mathbf{d}$
• d_noise = zeros(plant.nd) : additive gaussian noise on measured dist. $\mathbf{d}$
• x_noise = zeros(plant.nx) : additive gaussian noise on plant states $\mathbf{x}$
• x_0 = plant.xop : plant initial state $\mathbf{x}(0)$
• x̂_0 = nothing or xhat_0 : initial estimate $\mathbf{x̂}(0)$, initstate! is used if nothing
• lastu = plant.uop : last plant input $\mathbf{u}$ for $\mathbf{x̂}$ initialization

Examples

julia> model = LinModel(tf(3, [30, 1]), 0.5);

julia> estim = KalmanFilter(model, σR=[0.5], σQ=[0.25], σQint_ym=[0.01], σPint_ym_0=[0.1]);

julia> res = sim!(estim, 50, [0], y_noise=[0.5], x_noise=[0.25], x_0=[-10], x̂_0=[0, 0])
Simulation results of KalmanFilter with 50 time steps.

sim!(
    mpc::PredictiveController, 
    N::Int,
    ry = mpc.estim.model.yop .+ 1, 
    d  = mpc.estim.model.dop,
    ru = mpc.estim.model.uop;
    <keyword arguments>
) -> res

Closed-loop simulation of mpc controller for N steps, default to output setpoint bumps.

The output and manipulated input setpoints are held constant at ry and ru, respectively. The keyword arguments are identical to sim!(::StateEstimator, ::Int).

Examples

julia> model = LinModel([tf(3, [30, 1]); tf(2, [5, 1])], 4);

julia> mpc = setconstraint!(LinMPC(model, Mwt=[0, 1], Nwt=[0.01], Hp=30), ymin=[0, -Inf]);

julia> res = sim!(mpc, 25, [0, 0], y_noise=[0.1], y_step=[-10, 0])
Simulation results of LinMPC with 25 time steps.

SimResult(obj::SimModel,             U_data, Y_data, D_data=[]; <keyword arguments>)
SimResult(obj::StateEstimator,       U_data, Y_data, D_data=[]; <keyword arguments>)
SimResult(obj::PredictiveController, U_data, Y_data, D_data=[]; <keyword arguments>)

Manually construct a SimResult to quickly plot obj simulations.

Except for obj, all the arguments should be matrices of N columns, where N is the number of time steps. SimResult objects allow to quickly plot simulation results. Simply call plot on them.

Arguments

• obj : simulated SimModel/StateEstimator/PredictiveController
• U_data : manipulated inputs
• Y_data : plant outputs
• D_data=[] : measured disturbances
• X_data=nothing : plant states
• X̂_data=nothing or Xhat_data : estimated states
• Ŷ_data=nothing or Yhat_data : estimated outputs
• Ry_data=nothing : plant output setpoints
• Ru_data=nothing : manipulated input setpoints
• plant=get_model(obj) : simulated plant model, default to obj internal plant model

Examples

julia> model = LinModel(tf(1, [1, 1]), 1.0);

julia> N = 5; U_data = fill(1.0, 1, N); Y_data = zeros(1, N);

julia> for i=1:N; updatestate!(model, U_data[:, i]); Y_data[:, i] = model(); end; Y_data
1×5 Matrix{Float64}:
 0.632121  0.864665  0.950213  0.981684  0.993262

julia> res = SimResult(model, U_data, Y_data)
Simulation results of LinModel with 5 time steps.

plot(res::SimResult{<:Real, <:SimModel}; <keyword arguments>)

Plot the simulation results of a SimModel.

Arguments

• res::SimResult{<:Real, <:SimModel} : simulation results to plot
• ploty=true : plot plant outputs $\mathbf{y}$
• plotu=true : plot manipulated inputs $\mathbf{u}$
• plotd=true : plot measured disturbances $\mathbf{d}$ if applicable
• plotx=false : plot plant states $\mathbf{x}$

Examples

julia> res = sim!(LinModel(tf(2, [10, 1]), 2.0), 25);

julia> using Plots; plot(res, plotu=false)

plot(res::SimResult{<:Real, <:StateEstimator}; <keyword arguments>)

Plot the simulation results of a StateEstimator.

Arguments

• res::SimResult{<:Real, <:StateEstimator} : simulation results to plot
• plotŷ=true or plotyhat : plot estimated outputs $\mathbf{ŷ}$
• plotx̂=false or plotxhat : plot estimated states $\mathbf{x̂}$
• plotxwithx̂=false or plotxwithxhat : plot plant states $\mathbf{x}$ and estimated states $\mathbf{x̂}$ together
• plotx̂min=true or plotxhatmin : plot estimated state lower bounds $\mathbf{x̂_{min}}$ if applicable
• plotx̂max=true or plotxhatmax : plot estimated state upper bounds $\mathbf{x̂_{max}}$ if applicable
• <keyword arguments> of plot(::SimResult{<:Real, <:SimModel})

Examples

julia> res = sim!(KalmanFilter(LinModel(tf(3, [2.0, 1]), 1.0)), 25, [0], y_step=[1]);

julia> using Plots; plot(res, plotu=false, plotŷ=true, plotxwithx̂=true)

plot(res::SimResult{<:Real, <:PredictiveController}; <keyword arguments>)

Plot the simulation results of a PredictiveController.

Arguments

• res::SimResult{<:Real, <:PredictiveController} : simulation results to plot
• plotry=true : plot plant output setpoints $\mathbf{r_y}$ if applicable
• plotymin=true : plot predicted output lower bounds $\mathbf{y_{min}}$ if applicable
• plotymax=true : plot predicted output upper bounds $\mathbf{y_{max}}$ if applicable
• plotru=true : plot manipulated input setpoints $\mathbf{r_u}$ if applicable
• plotumin=true : plot manipulated input lower bounds $\mathbf{u_{min}}$ if applicable
• plotumax=true : plot manipulated input upper bounds $\mathbf{u_{max}}$ if applicable
• <keyword arguments> of plot(::SimResult{<:Real, <:SimModel})
• <keyword arguments> of plot(::SimResult{<:Real, <:StateEstimator})

Examples

julia> model = LinModel(tf(2, [5.0, 1]), 1.0);

julia> res = sim!(setconstraint!(LinMPC(model), umax=[1.0]), 25, [0], u_step=[-1]);

julia> using Plots; plot(res, plotŷ=true, plotry=true, plotumax=true, plotx̂=[2])