An algebraic expression of stable inversion for nonminimum phase systems and its applications ?

This paper proposes an algebraic expression of noncausal stable inversion based on the two-sided Laplace transform, which is a classic mathematical tool but has not been used very much in the field of control engineering. This expression brings an advantage that computing of stable inversion is reduced to simulation of the response of the plant and the reverse of time horizon without solving the boundary value problem of state-space equations as the conventional definition of stable inversion. An illustrative example demonstrates that this approach is useful to reduce the load of the programming for a search algorithm to determine the shape of a transition trajectory under the constraint of input saturation. As another application of the proposed expression, developed is a method of iterative learning control to obtain stable inversion for infinite dimensional systems. An experiment to apply the iterative learning control to tip control of a flexible arm is reported to demonstrate the effectiveness of the method.