of the disturbances may be greatly reduced, by choosing the : of good of the reference variable is obtained, since 3y(z )/3r(z) I in this if no feedback control = 0), then one incurs the cost that I, but

doi:10.4324/9780203814628-129

Chapter

of the disturbances may be greatly reduced, by choosing the

ABSTRACT

Now let us suppose that all the variables r, U, y and m are scalars, in order to keep the mathematics simple. Suppose that we have made an error in modelling the economy, so that the true relation of U to y is

and hence

3T(z) = 3G(z)

3T(z)/T(z) 3G(z)/G(z)

p(z) (59) [1 + G(z)p(z)P

In other words, the proportional error in the closed-loop behaviour is the proportional error in the open-loop behaviour, reduced by the same sensitivity function as defined in equation (56). We see here another benefit of feedback, but again obtained at the same cost as the benefits derived earlier. A similar, but more complicated, relationship can be derived if the variables are vectors.