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Additional info for Ashrae Standarts. Methods of testing to determine the termal performance Solar Collectors
1 shows the relation between the dimension of x and the allowed grid size used for the table of function values. F o r p greater than about 3, the number of values which can be taken for each coordinate is very small. I n addition, increasing the memory size from 212 to 216 only allows M to be increased by 21/p, which for p = 4 is an increase of only about 20%. Thus the storage problem limits the number of dimensions possible for x rather severely. This limit, encountered in the solution of (4.
This corresponds to a closed-loop structure analogous to that in Fig. 5. , when its stability can be investigated. This concept has been discussed by Boudarel rt al. [ I , Vol. I ] as summarized in the following. A free stationary system is said to be asymptotically stable if, for any initial state x o , the corresponding trajectory converges toward a point A , called a fixed point, such that, if the system equation is x , , + ~=@(x,,), the point A satisfies A = @ ( A ) . If in addition the trajectories are continuous with respect to the initial point, the system is said to be uniformly asymptotically stable.
Rn ~ x = f ( x , u,n ) n=n+l Change c=) satisf led output Do . . DN-1 FIG. 7. Flow chart for calculation of the optimal control law for a process with an additive-type constraint. complete calculation of the functions R(x, n, A) and g(x, n, A). If these latter functions were calculated in full, the problem would again be of dimension p 1 as in the first method. With this iterative procedure, a direct solution, leading to a closed-loop controller g’(x, n), is no longer possible. , a closed-loop controller.