State-space modelling and decoupling control of electromagnetic actuators for car vibration excitation

Unstable electromagnetic actuators are employed for car vibration excitation to perform Squeak and Rattle analyses. Couplings in the dual-shaker system demand for multiple input multiple output (MIMO) control. Unlike most approaches in literature that depend on cumbersome measurements and MIMO system identifications, control design in the present contribution is based on an analytical model. A state-space description of the entire plant with actuators and car is composed, whereof six states refer to the car body and are estimated by a reduced observer. A comparison with measurements verifies the modelling assumptions. Then a multivariable feedback controller is deduced. One main control design goal is an input-output-decoupling of the closed-loop system. To additionally rise bandwidth and adapt the state-space controller for reference tracking purposes, it is enhanced by a tracking error estimator. Fundamental controller criteria are robust stabilization of the unstable actuators and bandwidth and tracking attributes that match the road profiles to be reproduced. The MIMO controller shows convincing performance in all these aspects. The controlled system remains stable even for signals with high energy content and strong car movements due to the incorporated car body states. With the aid of the analytical plant model, controller and observer calculations for prospective use of four shakers on different car types can be carried out easily and without additional measurements.