Digital redesign of a continuous-time controller using the Padé and inverse-Padé approximation method (Q1916914)

Consider a continuous open loop system \(\dot x(t)= Ax(t)+ Bu(t)\) with state-feedback control law \(u(t)= -Kx(t)+ Er(t)\) where \(r\) is a reference input. A digital control law is obtained by sampling the \(u(t)\) and \(r(t)\) signals, but we still have a continuous-time state equation for the sampled-data system. Both the continuous and the sampled-data form can be discretized to give corresponding discrete-time models. The state-matching digital redesign problem is then to arrange that these two discrete models have matching states. In this paper, the Padé approximation of types \([2/2]\) and \([3/3]\) of the matrix exponential are used to obtain this result. Such a state-matching digital redesign has the effect that the states of the digitally controlled sampled-data system closely match those of the continuous-time controlled system for a longer sampling period. Of course the transformation from continuous to discretized form can also be obtained by a bilinear transform. The proposed method based on Padé approximation is compared with the bilinear transform method as well as with several other redesign methods.