An application of Newton-like algorithm for H∞ proportional–integral–derivative controller synthesis of seesaw-cart system

This paper is concerned with the synthesis of proportional–integral–derivative (PID) controller according to the [Formula: see text] optimality criterion for seesaw-cart system. The equations of dynamics are obtained through modelling a seesaw-cart system actuated by direct-current motor via rack and pinion mechanism using the Euler–Lagrange approach. The obtained model is linearised and synthesis of the PID controller for linear model is performed. An algorithm based on the sub-gradient method, the Newton method, the self-adapting backpropagation algorithm and the Adams method is proposed to calculate the PID controller gains. The proposed control strategy is tested and compared with standard linear matrix inequality (LMI)-based method on computer simulations and experimentally on a laboratory model.

Supervisory controller synthesis and implementation for safety PLCs

The development of supervisory controllers for cyber-physical systems is a laborious and error-prone process. Supervisor synthesis enables control designers to automatically synthesize a correct-by-construction supervisor from a model of the plant combined with a model of the control requirements. From the supervisor model, controller code can be generated which is suitable for the implementation on a programmable logic controller (PLC). Supervisors for industrial systems that operate in close proximity to humans have to adhere to strict safety standards. To achieve these standards, safety PLCs (SPLCs) are used. For SPLC implementation, the supervisor has to be split into a regular part and a safety part. In previous work, a method is proposed to automatically split a supervisor model for this purpose. The method assumes that the provided plant model is a collection of finite automata. In this paper, the extension to extended finite automata is described. Additionally, guidelines are provided for modeling the plant and the requirements to achieve a favorable splitting. A case study on a rotating bridge is elaborated which has been used to validate the method. The case study spans all development steps, including the implementation of the resulting supervisor to control the real bridge.