Pole-placement Predictive Functional Control for under-damped systems with real numbers algebra

摘要

This paper presents the new algorithm of PP-PFC (Pole-placement Predictive\udFunctional Control) for stable, linear under-damped higher-order processes. It\udis shown that while conventional PFC aims to get first-order exponential behavior,\udthis is not always straightforward with significant under-damped modes and\udhence a pole-placement PFC algorithm is proposed which can be tuned more\udprecisely to achieve the desired dynamics, but exploits complex number algebra\udand linear combinations in order to deliver guarantees of stability and performance.\udNevertheless, practical implementation is easier by avoiding complex\udnumber algebra and hence a modified formulation of the PP-PFC algorithm\udis also presented which utilises just real numbers while retaining the key attributes\udof simple algebra, coding and tuning. The potential advantages are\uddemonstrated with numerical examples and real-time control of a laboratory\udplant.