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

Abstract

This paper is concerned with the synthesis of proportional–integral–derivative (PID) controller according to the ${\mathcal{H}}_{\infty }$ 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.