Quantized-State Control. A Method for Discrete Event Control of Continuous Systems

Abstract — This paper introduces a new method for the digital implementation of con-trollers designed in continuous time. Through the quantization of its state and input variables the original continuous controller is mapped into a discrete event model within the DEVS formalism framework that can be implemented in a digital device. Under certain conditions on the original continuous control system (CCS), this implementation guarantees regional con-vergence in finite time of system trajectories to arbitrarily small regions around the equilib-rium points even in the presence of A/D and D/A quantization effects. The convergence of the new scheme to the CCS is demonstrated when the quantization width goes to zero. Fur-ther, a design algorithm for the digital con-troller is given, which fulfills specifications of admissible final error and convergence speed. Also discussed is the computational efficiency of the scheme, along practical implementation issues. Two numerical examples are provided illustrating some benefits of the new method