Advanced Control With PLC—Code Generator for aMPC Controller Implementation and Cooperation With External Computational Server for Dealing With Multidimensionality, Constraints and LMI Based Robustness

The manufacturers of Programmable Logic Controllers (PLC) usually equip their products with extremely simple control algorithms, such as PID and on-off regulators. However, modern PLCs have much more efficient processors and extensive memory, which enables implementing more sophisticated controllers. The paper discusses issues related to the implementation of matrix operations, time limitations for code execution within one PLC cycle, and memory requirements. The adaptive Model Predictive Controller (aMPC) algorithm is selected for predictive control with on-line adaptation of model parameters. The combination of predictive and adaptive properties in the regulator enables control of many industrial objects for which PID control is ineffective, e.g. nonstationary plants with time-varying delays. The presented generic approach consists in developing a C++ application for desktop PC that generates, based on user provided parameters - such as MPC horizons, the code in Structured Text (ST) language compliant with the IEC-61131 standard for PLCs. Despite the enhanced capabilities of programmable controllers, there are limitations to this platform that cannot be overcome. The implementation of optimization-based control algorithms requires cooperation with an external computing server. In the article, the PLC/external computer cooperation is used to implement the control with constraints taken into account. The robust control using the Linear Matrix Inequalities (LMI) for a multivariable plant is also presented. A number of tests were carried out to verify the correctness of implementation of this control in software-in-the-loop and hardware-in-the-loop structures.