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ClosedLoop

UI.ClosedLoop History

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November 01, 2013, at 06:45 PM by mk -
Changed line 34 from:
Now we want to verify how the controller performs if connected to a different system, say @@x^+ = A x + B u@@ with @@A = [1 1; 0.2 1]@@, @@B = [1; 0.8]@@:
to:
Now we want to verify how the controller performs if connected to a different system, say {$ x^+ = A x + B u $} with {$ A = \begin{bmatrix} 1 & 1 \\ 0.2 & 1 \end{bmatrix} $}, {$ B = \begin{bmatrix} 1 \\ 0.8 \end{bmatrix} $}:
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November 01, 2013, at 06:44 PM by mk -
Changed lines 16-18 from:
* @@A = [1 1; 0 1]@@, @@B = [1; 0.5]@@
* state constraints @@[-5; -5] <= x <= [5; 5]@@
* input constraints @@-1 <= u <= 1@@
to:
* {$ A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix} $}, {$ B = \begin{bmatrix} 1 \\ 0.5 \end{bmatrix} $}
* state constraints {$ \begin{bmatrix} -5 \\ -5 \end{bmatrix} \le x \le \begin{bmatrix} 5 \\ 5 \end{bmatrix} $}
* input constraints {$ -1 \le u \le 1 $}
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November 01, 2013, at 06:42 PM by mk -
Changed line 15 from:
As an example, consider MPC for a linear system @@x^+ = A x + B u@@ with following properties:
to:
As an example, consider MPC for a linear system {$ x^+ = A x + B u$} with following properties:
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November 01, 2013, at 06:41 PM by mk -
Changed line 52 from:
*NOTE:* if you change the controller and/or the system in your MATLAB workspace, the change(s) will be *automatically* propagate to the closed-loop object without the need to re-create it. In other words, in the example above we can as well do:
to:
'''NOTE:''' if you change the controller and/or the system in your MATLAB workspace, the change(s) will '''automatically''' propagate to the closed-loop object without the need to re-create it. In other words, in the example above we can as well do:
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August 29, 2013, at 07:24 AM by Michal Kvasnica -
Changed line 18 from:
* input constraints @@-1 <= x <= 1@@
to:
* input constraints @@-1 <= u <= 1@@
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July 26, 2013, at 07:51 PM by Michal Kvasnica -
Changed lines 28-29 from:
prediction_model.x.penalty = Penalty([1 0; 0 1], 2);
prediction_model.u.penalty = Penalty(1, 2);
to:
prediction_model.x.penalty = QuadFunction([1 0; 0 1]);
prediction_model.u.penalty = QuadFunction(1);
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May 23, 2013, at 08:20 PM by Michal Kvasnica -
Added lines 1-57:
! Closed-loop simulations

MPT3 introduces a special object to represent closed-loop systems, consisting of a [[UI.Systems|dynamical system]] and an [[UI.Control|MPC controller]]:
(:source lang=MATLAB -getcode:) [@
loop = ClosedLoop(mpc, sys)
@]
where @@mpc@@ represents an MPC controller (either on-line or explicit MPC), and @@sys@@ describes the dynamical system.

After a closed-loop object is constructed, you can simulate it by
(:source lang=MATLAB -getcode:) [@
data = loop.simulate(x0, Nsim)
@]
where @@x0@@ is the initial state for the simulation, and @@Nsim@@ is the number of simulation steps.

As an example, consider MPC for a linear system @@x^+ = A x + B u@@ with following properties:
* @@A = [1 1; 0 1]@@, @@B = [1; 0.5]@@
* state constraints @@[-5; -5] <= x <= [5; 5]@@
* input constraints @@-1 <= x <= 1@@
* prediction horizon 4
* quadratic cost function with unity weighting matrices

(:source lang=MATLAB -getcode:) [@
prediction_model = LTISystem('A', [1 1; 0 1], 'B', [1; 0.5]);
prediction_model.x.min = [-5; -5];
prediction_model.x.max = [5; 5];
prediction_model.u.min = -1;
prediction_model.u.max = 1;
prediction_model.x.penalty = Penalty([1 0; 0 1], 2);
prediction_model.u.penalty = Penalty(1, 2);
N = 4;
mpc = MPCController(prediction_model, N);
@]

Now we want to verify how the controller performs if connected to a different system, say @@x^+ = A x + B u@@ with @@A = [1 1; 0.2 1]@@, @@B = [1; 0.8]@@:
(:source lang=MATLAB -getcode:) [@
simulation_model = LTISystem('A', [1 1; 0.2 1], 'B', [1; 0.8]);
loop = ClosedLoop(mpc, simulation_model);
x0 = [4; 0];
Nsim = 20;
data = loop.simulate(x0, Nsim)

data =

      X: [2x21 double]
      U: [1x20 double]
      Y: []
    cost: [1x20 double]

plot(data.X')
@]

*NOTE:* if you change the controller and/or the system in your MATLAB workspace, the change(s) will be *automatically* propagate to the closed-loop object without the need to re-create it. In other words, in the example above we can as well do:
(:source lang=MATLAB -getcode:) [@
mpc.N = 10;
data = loop.simulate(x0, Nsim)
@]
and the simulation will automatically use the new controller with prediction horizon @@10@@.
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