A Generalized One-Bit Control System Using a $\Delta\Sigma$ -Quantizer

This paper presents the use of a delta-sigma quantizer for generalized one-bit control processing. An equivalent control strategy based on sliding-mode control is employed to derive the necessary condition for the convergence of the proposed one-bit control system in both the continuous-time and discrete-time domains. Under the convergence condition, the binary signals generated by delta-sigma quantizers in the one-bit control system effectively replace their counterpart signals in conventional control systems. This enables a significant reduction in the number of multipliers and overall hardware cost for computing the control laws in one-bit control systems. Our result is applied to design a multiplier-less one-bit generalized proportional and integral controller for the position control of an experimental prototype of a DC motor. An implementation of the one-bit control system is carried out using an FPGA platform to demonstrate the behavior of one-bit generalized proportional and integral controller and compare the results with the standard in terms of implementation efficiency. The results of the simulation and experiment show that the one-bit generalized proportional and integral controller effectively controls the system and achieves the desired specifications. At the same time, the proposed one-bit control system consumes significantly fewer hardware resources than the standard control syst.