Dead-beat control

In discrete-time control theory, the dead-beat control problem consists of finding what input signal must be applied to a system in order to bring the output to the steady state in the smallest number of time steps.

For an Nth-order linear system it can be shown that this minimum number of steps will be at most N (depending on the initial condition), provided that the system is null controllable (that it can be brought to state zero by some input). The solution is to apply feedback such that all poles of the closed-loop transfer function are at the origin of the z-plane. (For more information about transfer functions and the z-plane see z-transform). Therefore the linear case is easy to solve. By extension, a closed loop transfer function which has all poles of the transfer function at the origin is sometimes called a dead beat transfer function.