Sensor And Actuator Location In Motion Control Of Flexible Structures

In this paper, a methodology is proposed for determination of actuator and sensor locations in motion control of flexible structures which can be used before a control strategy is developed. The proposed approach relies on certain quantitative measures of degree of controllability and observability based on the controllability and observability gramians. These criteria are arrived at by considering the energies of the input and the output under conditions of transient as well as persistent disturbances. Proposed optimality criteria for the sensor and actuator locations provide a balance between the importance of the lower order and the higher order modes. Since for flexible structures closed form solutions for the gramians can be found, the method is not computationally intensive, requiring only determination of eigenvalues of corresponding gramians at each step of optimization. These eigenvalues can be obtained in closed form when the structural damping is small and natural frequencies are distinct and well spaced. In that case force actuators and velocity sensors are found to be collocated. The method is illustrated for a simply supported beam and a rectangular plate.