Non-minimal state variable feedback decoupling control for multivariable continuous-time systems

Abstract

Most research into non-minimal state variable feedback control, in which the state vector is implemented directly from the measured input and output signals of the controlled process, has considered discrete-time systems represented using either the backward shift or delta operator. However, mechanistic models with physically meaningful parameters are often expressed in terms of differential equations, represented using the Laplace transform or s-operator, and this article is concerned with multivariable design for such models. The controllability conditions are developed and it is shown how the introduction of a diagonal polynomial matrix for filtering yields a control system that is immediately realisable in practice. Worked examples include optimal control with multi-objective optimisation and pole assignment design with analytical multivariable decoupling, with the latter illustrated by its application to a nonlinear wind turbine simulation.

Keywords:

• multivariable continuous-time systems
• non-minimal state space
• linear quadratic optimal
• pole assignment
• multi-objective optimisation