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, provided that the system is null controllable. The solution is to apply feedback such that all poles of the closed-loop transfer function are at the origin of the z-plane. . 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. .
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
