Мultiobjective H2-control design for semi-active vehicle suspension with Magneto-Rheological damper – Part2: Linear quadratic Gaussian regulator synthesis

In the first part of the research were discussed the problems related to the synthesis of a combined linear quadratic regulator (LQR) having both state feedback and an excitation compensation, for control implementation in a semi-active car suspension. Arising of some numerical effects in the process of the state and excitation reconstruction, the noise in measurement, the changes in system parameters, and the semi-active damper’s nonlinearities, have a significant influence on the control quality. For reducing the influence of those effects and for the control quality improvement, a Luenberger’s observer is constructed. The combination of the proposed LQR and Luenberger’s observer forms a Linear Quadratic Gaussian (LQG) control, the synthesis of which is discussed in this publication. Obtaining of the observer’s gain matrix is considered in the context of the Kalman-Bucy filter for the case of the absence of correlation between the excitation and the measurement noise and in the case of coloured noise. Also is proposed by the authors a specific synthesizing approach from the condition for more robustness, more convenient for real-time applications. Numerical simulations are given, allowing for a comparison of the results, and confirming the effectiveness of the presented approach.