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:
- Zero steady-state error.
- Minimum rise time.
- Minimum settling time.
- Less than 2% overshoot/undershoot.
- Very high control signal output.
Famous quotes containing the words dead, beat and/or control:
“So vulnerable.
She is already trampled, that one,
having traveled so far from the heart.
She weighs so little.
She is so light and vulnerable.
She is the dead bee called love.”
—Anne Sexton (1928–1974)
“The barge she sat in, like a burnished throne
Burned on the water. The poop was beaten gold;
Purple the sails, and so perfumed that
The winds were love-sick with them. The oars were silver,
Which to the tune of flutes kept stroke, and made
The water which they beat to follow faster,
As amorous of their strokes.”
—William Shakespeare (1564–1616)
“If someone does something we disapprove of, we regard him as bad if we believe we can deter him from persisting in his conduct, but we regard him as mad if we believe we cannot. In either case, the crucial issue is our control of the other: the more we lose control over him, and the more he assumes control over himself, the more, in case of conflict, we are likely to consider him mad rather than just bad.”
—Thomas Szasz (b. 1920)