On Finite-Horizon Optimal Control of First-Order Plus Time Delay Systems

In this work, a finite-horizon optimal control problem for first-order plus time delay (FOPTD) processes is investigated. We show that if the control horizon is greater than three and the prediction horizon is great than the control horizon plus the time delay in discrete time, the optimal controller is not affected by either of the two parameters. Also, under these conditions, the controller parameters are explicitly calculated, the closed-loop system is shown to be stable, and the controller is dead-beat. The problem considered is related to the results on linear quadratic regulation of linear systems with time delays; however, the detailed parameterization of the state-space model introduced by the FOPTD process provides an additional opportunity to investigate the exact controller structure and properties (e.g., the locations of the closed-loop poles), which are also the major difficulties encountered and overcome in this work. This problem is motivated from phenomena experienced in designing industrial model predictive control (MPC) tuning algorithms, and extensive numerical examples indicate that the proposed results speed up the MPC autotuning algorithms by 70%.