Dynamic Quantizer Synthesis Based on Particle Swarm Optimization

Abstract

For the control of mechanical systems including discrete-valued devices such as discrete-level actuators and communication encoders, one of the promising approaches is to utilize dynamic quantizers. Here, the dynamic quantizer is a device which converts continuous-valued signals into discrete-valued ones depending on the past signal data. This paper focuses on a dynamic quantizer design problem which is to find a quantizer such that the output behavior of systems with quantizers is similar to that of ideal systems without quantizers. In this paper, we first formulate a design problem of fixed-order dynamic quantizers under several constraint conditions such as stability of quantizer, control input saturation, and pole assignment. Then, for getting a solution to the problem, we present an easy-to-use quantizer design method based on particle swarm optimization (PSO) which is a swarm intelligence technique and is one of the evolutionary computation algorithms. Finally, it is verified that the PSO based method gives satisfactory fixed-order dynamic quantizers through several numerical examples with a cart positioning system and an unstable mechanical system. Further we conclude that the proposed method could be an useful tool for the design of dynamic quantizers.