Optimum Control of Linear Systems With Transportation Lag

A necessary condition for the optimum control of a linear system with input delay or transportation lag is derived in terms of the system weighting function. For a general quadratic integrand in an integral-type index of performance and a linear time invariant system with input delay, an expression for the optimum controller is given in the Laplace domain in terms of the system transfer function. This expression simplifies the calculation of the optimum controller. The results are applicable to systems with or without input delay. An example is given to illustrate the procedure.