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2.1 Double integrator | Contents | 2.3 Harvest system |
x(k+1=a·x(k)+b·u(k),
k=1,2,...,N.
f(x,u)=q·x(N+1)^2+sum(s·x(k)^2+r·u(k)^2),
k=1:N.
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1 | 45 | 100 | 1 | 1 | 1 | 1 | 1 | 16180.3399 |
2 | 45 | 100 | 10 | 1 | 1 | 1 | 1 | 109160.7978 |
3 | 45 | 100 | 1000 | 1 | 1 | 1 | 1 | 10009990.0200 |
4 | 45 | 100 | 1 | 10 | 1 | 1 | 1 | 37015.6212 |
5 | 45 | 100 | 1 | 1000 | 1 | 1 | 1 | 287569.3725 |
6 | 45 | 100 | 1 | 1 | 0 | 1 | 1 | 16180.3399 |
7 | 45 | 100 | 1 | 1 | 1000 | 1 | 1 | 16180.3399 |
8 | 45 | 100 | 1 | 1 | 1 | 0.01 | 1 | 10000.5000 |
9 | 45 | 100 | 1 | 1 | 1 | 1 | 0.01 | 431004.0987 |
10 | 45 | 100 | 1 | 1 | 1 | 1 | 100 | 10000.9999 |
The linear-quadratic system is identical to a single integrator with positive feedback. A continuous version of this problem using a Simulink model, an s-function and Control System Toolbox routines is implemented in objlinq2. The model used by the objective function is chosen through the first parameter of the function, the default is the Simulink model.
The Simulink method uses the model in figure 2 (simlinq1).
dx1/dt=x1+u;
y=x1.
G(s)=1/(s-1)
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GEATbx: | Main page Tutorial Algorithms M-functions Parameter/Options Example functions www.geatbx.com |