A special control law: deadbeat control

Most of the methods we have considered so far have their origins in linear control laws for systems described by linear constant coefficient differential equations, with sampled data control studied by adapting those theories. Even in the nominally linear control law realm, however, it is possible to develop a special and interesting performance property with discrete time control. In particular, it is possible in principle to achieve a zero error to an input after finite time with a linear control law; this contrasts with continuous time control, which can only asymptotically provide zero error, and follows from the fact that computer control commands are piecewise constant in nature. A response that quickly reaches zero error at the sampling instants and has little ripple between samples is called a deadbeat response. In this chapter we develop both transfer function oriented and state-space oriented approaches to design of the control laws, called deadbeat controllers, which yield such response.