  Model inversion is a fundamental technique in feedforward control. Unstable
inverse models present a challenge in that useful feedforward control
trajectories cannot be generated by directly propagating them. Stable inversion
is a process for generating useful trajectories from unstable inverses by
handling their stable and unstable modes separately. Piecewise affine (PWA)
systems are a popular framework for modeling complicated dynamics. The primary
contributions of this article are closed-form inverse formulas for a general
class of PWA models, and stable inversion methods for these models. Both
contributions leverage closed-form model representations to prove sufficient
conditions for solution existence and uniqueness, and to develop solution
computation methods. The result is implementable feedforward control synthesis
from PWA models with either stable or unstable inverses. In practice,
feedforward control alone may yield substantial tracking errors due to mismatch
between the known system model and the unknowable complete system physics.
Iterative learning control (ILC) is a technique for achieving robustness to
model error in feedforward control. To demonstrate the primary contributions'
validity and utility, this article also integrates PWA stable inversion with
ILC in simulations based on a physical printhead positioning system.
