Optimization of sensor parameters in programmable logic controller via mixed integer programming

Programmable logic controller (PLC) has been widely used in the industrial control as the controller for the manufacturing system, process control, and so on. This class of control system, in comparison with the standard continuous valued control system, is characterized by its use of low-resolution (typically ON/OFF) actuators and sensors. Although several languages for the PLC have been developed, the sequential function chart (SFC) is one of the most promising languages thanks to its graphical representation. The SFC can visually represent the precedence relationship among actions. 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. The proposed model unifies the discrete logical behavior of the SFC and the continuous behavior of the plant harmoniously. 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.