Dead-beat control

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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.

For nonlinear systems, dead beat control is an open research problem. (See Nesic reference below).

Dead beat controllers are often used in process control due to their good dynamic properties. They are a classical feedback controller where the control gains are set using a table based on the plant system order and normalized natural frequency.

The deadbeat response has the following characteristics:

  1. Zero steady-state error
  2. Minimum rise time
  3. Minimum settling time
  4. Less than 2% overshoot/undershoot
  5. Very high control signal output


  • Kailath, Thomas: Linear Systems, Prentice Hall, 1980, ISBN 9780135369616
  • [1] Nesic et al.:Output dead beat control for a class of planar polynomial systems
  • Warwick, Kevin: Adaptive dead beat control of stochastic systems, International Journal of Control, 44(3), 651-663, 1986.
  • Dorf, Richard C.; Bishop, Robert H. (2005). Modern Control Systems. Upper Saddle River, NJ 07458: Pearson Prentice Hall. pp. 617–619.