Feedforward trajectory design for output transitions in discrete-time systems: disk-drive example

The article proposes a direct approach to solve the optimal (minimal input energy) output-transition problem for linear discrete-time systems. The goal is to transfer and maintain the output from an initial value (y(k) = y_ for all k ≤ k_i) to a final value (y(k) = y~ for all k ≥ k^f) within a prescribed number of time steps (k_f-k_i). Previous methods solve this output-transition problem by transforming it into a state-transition problem, i.e., the initial and final states(κ(k_i) and κ(k_f), respectively) are chosen and a minimum-energy state-to-state transition problem is solved. However, the choice of the initial and final states can be ad hoc and the resulting output-transition cost (input energy) may not be minimal. In contrast, the contribution of this article is the solution of the optimal output-transition problem for linear discrete-time systems. Example discrete-time model of a disk-drive servo system is studied to illustrate the proposed method. Simulation results show substantial reduction of transition costs with the use of the proposed method when compared to the use of approaches that are based on minimum-energy state transitions.