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.
Chapter 20
Q. 20.5
Step-by-Step
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).