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 is 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 non-linear 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.

Famous quotes containing the words dead, beat and/or control:

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    Gilbert Keith Chesterton (1874–1936)

    They shall beat their swords into plowshares, and their spears into pruninghooks: nation shall not lift up sword against nation, neither shall they learn war any more.
    Bible: Hebrew Isaiah, 2:4.

    The words reappear in Micah 4:3, and the reverse injunction is made in Joel 3:10 (”Beat your plowshares into swords ...”)

    I have not ceased being fearful, but I have ceased to let fear control me. I have accepted fear as a part of life, specifically the fear of change, the fear of the unknown, and I have gone ahead despite the pounding in the heart that says: turn back, turn back, you’ll die if you venture too far.
    Erica Jong, U.S. author. In an essay in The Writer on Her Work, ch. 13 (1980)