Programmable Logic Controller (PLC) has been widely used in the industrial control. Inherently, the PLC-based system is a class of Hybrid Dynamical System (HDS) in which continuous state of the plant is controlled by the discrete logic-based controller. This paper firstly presents the formal algebraic model of the PLC-based control systems which enable the designer to formulate the various kinds of optimization problem. Secondly, the optimization problem of the 'sensor parameters,' such as the location of the limit switch in the material handling system, the threshold temperature of the thermostat in the temperature control system, is addressed. Finally, we formulate this problem as Mixed Logical Dynamical Systems (MLDS) form which enables us to optimize the sensor parameters by applying the Mixed Integer Programming.

The PLC (Programmable Logic Controller) has been widely used in the industrial world as a controller for manufacturing systems, as a process controller and so on. The conventional PLC has been designed and verified as a pure Discrete Event System (DES) by using an abstract model of a controlled plant. In verifying the PLC, however, it is also important to take into account the physical behavior (e.g. dynamics, shape of objects) of the controlled plant in order to guarantee such important factors as safety. This paper presents a new verification technique for the PLC-based control system, which takes into account these physical behaviors, based on a Hybrid Dynamical System (HDS) framework. The other key idea described in the paper is the introduction of the concept of signed distance which not only measures the distance between two objects but also checks whether two objects interfere with each other. The developed idea is applied to illustrative material handling problems, and its usefulness is demonstrated.