Computation of Control Law for State Transfer Problem in Efficient Way for a Single Input

This article proposes a modified way to compute open loop control for the state transfer problem (STP) for a linear time-invariant system. Solving STP analytically is a cumbersome task. This is mainly due to tedious computations of state-transition matrix and controllability Gramian matrix. The proposed modified method enables to find control law easily and with less computations. This approach is applicable even for a third-order or higher order system with single input case analytically and without use of computer. Moreover, the proposed approach minimizes the use of calculator and thereby reduces the computational rounding-off errors. Finally, it is shown that for some special case with knowledge of mode vector, the STP can be solved very quickly without even calculating the state-transition matrix and controllability Gramian matrix. Furthermore, theoretical as well as experimental evaluation of control law is provided. Experimental results are used to validate the proposed method.