Motion planning and open loop control design for linear distributed parameter systems with lumped controls

Abstract

Motion planning and open loop boundary control schemes for linear spatially one dimensional distributed parameter systems with lumped control are discussed. Using Mikusiński's operational calculus the models are formulated as ordinary (operational) boundary value problems. Their solutions are parameterized by introducing a so-called basic variable as an appropriate free parameter. Particular classes of models considered lead to series representations involving derivatives of the basic variable of arbitrary order or to convolution operators which can be interpreted as distributed delays and advances. Examples of bending motions on a ring-shaped plate and a heat exchanger illustrate the results.