Multiplexed model predictive control

Abstract

During the last two decades, Model Predictive Control (MPC) has established itself as an important form of advanced control due to its ability to deal with constraints. This results in demanding on-line optimization, hence computing resource can become an issue when applying MPC to complex systems with many inputs or with fast response times. In this thesis, a novel algorithm, called the Multiplexed MPC is proposed. The Multiplexed MPC scheme divides the MPC problem into a sequence of smaller optimizations, solves each subsystem sequentially and updates subsystem controls as soon as the solution is available, thus distributing the control moves over a complete update cycle while the total number of control moves in a given period remains the same as that of the original MPC problem. This results in reduced computational complexity and thus shorter computational time. This reduction in computational complexity allows Multiplexed MPC to be executed at higher sampling rate, which in turn reacts faster to disturbances and thus can lead to improved performance in some cases, despite finding sub-optimal solutions to the original problem. Stability of the Multiplexed MPC is established in this thesis. The stability proof can be easily extended to other Multiplexed MPC schemes. It is also shown that when the active constraints set is empty or known, Multiplexed MPC can be interpreted as a linear periodic state feedback law in an augmented state space. This provides a framework for systematic analysis and investigation of the properties of Multiplexed MPC. Finally, the proposed Multiplexed MPC scheme is successfully applied to a multi-zone heating process typically encountered in semiconductor manufacturing. The experimental results shows that Multiplexed MPC indeed is computationally more scalable than conventional MPC. This reduction in computational load has been gainfully used to increase the sampling rate of MMPC, leading to better disturbance rejection performance. This result is important for semiconductor wafter baking process as it could lead to increased throughput as well as reduction in wafer-to-wafer non-repeatability which will affect critical dimension of the wafer.