Minimum-energy ripple-free dead-beat control of type-I second-order plants

The design of digital controllers for minimum-energy ripple-free dead-beat control of type-I second-order plants is considered. Two recently introduced necessary and sufficient conditions for ripple-free dead-beat response are utilized for the solution of the optimization problem posed, thus leading to analytical expressions for the digital controller pulse transfer function. It is readily seen that a linear increment in the overall system order results in a proportional increase in the settling-time and an exponential decrease not only in the energy of the control signal needed to attain the desirable response, but the maximum control signal, as well.