Effect of structural resonances on LQR controlled mechanical systems

The design of a MIMO controller for a mechanical system using the LQR method provides a controller with satisfactory performance in many cases. The design is performed by minimizing a cost criterion which weights the response and the actuator forces. As the system is described by a set of first order differential equations, the controlled system should be intrinsically stable. However, mechanical systems appear often to be unstable, due to additional resonances in the mechanical system, which are not taken into account in the system of first order differential e quations. Therefore, the performance of the controlled system should be evaluated on the set of first order differential equations of the resonant system. To demonstrate this, a 2DOF pick and place unit is used. First, the first o rder e quations o f m otion a re d etermined u sing t he Hamilton method. These non-linear equations are linearised and a controller is designed using the LQR-method. Next, the non-linear set is expanded by additional DOF’s which represent additional resonances of the pick and place unit. The controller is evaluated using this non-linear expanded set. The effect of additional resonances is a significant reduction of the control performance. Future research aims to incorporate stability criteria in the LQR cost function.status: publishe