Neural network based LQ control of a semiactive quarter-car model

The paper presents an application of LQ control dedicated to a semiactive quarter-car model (2 degrees of freedom) which includes nonlinear model of a magnetorheological (MR) damper. Optimal control gains are derived based on known quarter car model parameters and limitations imposed on absolute vertical velocities of sprung and unsprung masses as well as on desired force generated by MR damper. Solutions of the algebraic Riccati equation obtained for LQ continous time infinite horizon problem using system output and control weights matrices are approximated using neural network. The static feedforward neural network model was identified using Levenberg-Marquardt backpropagation method in order to map nonlinear relations between system variables limitations and control gains. The algorithm was adapted to the semiactive system using a linearized inverse MR damper model. Simulation based analysis of vibration mitigation was carried out in frequency domain for different experiments conditions; the analysis justifies application of neural networks in LQ based control of semiactive suspension.