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## Q. 20.5

For Exercise 20.1, suppose that a constraint is placed on the manipulated variable, $u_{k+j} \leq 0.2$ for $j=1,2, \ldots$, $M-1$. Let $\Delta t=2$ and $N=40$. Select values of $M, P$, and $R$ so that these constraints are not violated after a unit step disturbance occurs.

## Verified Solution

There are many sets of values of $M, P$ and $R$ that satisfy the given constraint for a unit load change. One such set is $M=3, P=10, R=0.01$ as shown in Exercise 20.4(iii). Another set is $M=3, P=10, R=0.1$ as shown in Exercise 20.4(iv). A third set of values is $M=1, P=5, R=0$ as shown in Exercise 20.4(i).