PLC-based Implementation of Stochastic Optimization Method in the Form of Evolutionary Strategies for PID, LQR, and MPC Control

Programmable logic controllers (PLCs) are usually equipped with only basic direct control algorithms like proportional-integral-derivative (PID). Modules included in engineering software running on a personal computer (PC) are usually used to tune controllers. In this article, an alternative approach is considered, i.e. the development of a stochastic optimizer based on the (mu,lambda) evolution strategy (ES) in a PLC. For this purpose, a pseudorandom number generator (pRNG) was implemented, which is not normally available in most PLCs. The properties of popular random number generation methods were analyzed in terms of distribution uniformity and possibility of implementation in a PLC. The Wichmann-Hill (WH) algorithm was chosen for implementation. The developed generator with a uniform distribution was the basis for the implementation of a generator with a normal distribution. Both generators are the engines of the stochastic optimization algorithm in the form of the (mu, lambda) strategy. For verification purposes, a modular servomechanism laboratory set was used as a test object for PID and linear-quadratic regulator (LQR) control. Moreover, the possibility of using the developed optimizer was shown in an application of model predictive control (MPC). Comprehensive tests confirmed the correctness of the implementation and high functionality of the developed software. Calculation time issues are also investigated.