A new binary arithmetic for finite-word-length linear controllers: MEMS applications

This paper addresses the problem of optimal hardware-realization of finite-word-length (FWL) linear controllers dedicated to MEMS applications. The biggest challenge is to ensure satisfactory control performances with a minimal hardware. To come up, two distinct but complementary optimizations can be undertaken: in control theory and in binary arithmetic. Only the latter is involved in this work. Because MEMS applications are targeted, the binary arithmetic must be fast enough to cope with the rapid dynamic of MEMS; power-efficient for an embedded control; highly scalable for an easy adjustment of the control performances; and easily predictable to provide a precise idea on the required logic resources before the implementation. The exploration of a number of binary arithmetics showed that radix-2r is the best candidate that fits the aforementioned requirements. It has been fully exploited to designing efficient multiplier cores, which are the real engine of the linear systems. The radix-2r arithmetic was applied to the hardware integration of two FWL structures: a linear time variant PID controller and a linear time invariant LQG controller with Kaiman filtering. Both controllers showed a clear superiority over their existing counterparts, or in comparison to their initial non-optimized forms.