Quantized-state Control: a Method for Discrete Event Control of Continuous Systems

This paper introduces a new method for the digital implementation of controllers 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 convergence in finite time of system trajectories to arbitrarily small regions around the equilibrium 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. Further, a design algorithm for the digital controller 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. Keywords— Digital Control, Discrete Event Systems, Quantized Systems, Nonlinear Systems.