Module 6 : Deadbeat Response Design

Lecture 2 : Deadbeat response design when some of the poles and zeros are on or outside the unit circle

 

Putting the expressions of M(z) and 1- M(z) in the controller equation



Thus




The output response is plotted in Figure 2.

 

\begin{figure} \centering \input{deadbt2.pstex_t} \end{figure}

Figure 2: Deadbeat Response of The System in Example 2

 


Note that although c(kT) tracks the unit step perfectly after 3 sampling periods, the maximum overshoot is 128 percent.

This is because of the fact that the digital plant is a type 2 system, hence a deadbeat response without overshoot cannot be obtained for a unit step input.

Thus one can conclude that it is not always possible to design dead beat response without any over shoot.