Speaker
Description
Increasing energy efficiency and saving raw materials promote the lightweight design of mechanical structures, like beams and strings. Such systems are typically underactuated and require an accurate inverse model, which is essential in the two-degree-of-freedom control structure for robust trajectory tracking. The dynamic inversion of underactuated mechanical systems can be formulated in the servo-constraint framework using a set of differential-algebraic equations (DAEs). In case of a high differentiation index, the inversion-based feedforward control design poses significant challenges. For instance, standard time-integration methods solving the inverse problem sequentially over time with a sufficiently small time step size can show numerical instabilities. Although index reduction techniques might be a common approach to addressing these issues, their practical applicability is limited. In this contribution, we present a simultaneous inversion method for flat and minimum phase systems to overcome the shortcomings of sequential methods due to a high differentiation index. The key idea is to discretize the equations of motion on the entire time grid, which yields the continuity conditions for all trajectories. By combining these conditions with servo-constraints at all time points, a global system of equations with a large number of unknowns is obtained. Despite its high dimensionality, an efficient solution of the inverse dynamics is made possible by exploiting the sparse Jacobian matrix. The performance of the simultaneous approach is demonstrated with a numerical experiment, in which we generate a feedforward trajectory controller for a large-scale finite-segment model of a nonlinear string.
