Feedback Gain Sensitivities of Closed-Loop Modal Parameters of Controlled Structures

Computer algebra (MACSYMA) has been used to derive the characteristic polynomials that determine the closed-loop frequencies and damping coefficients of output-feedba ck controlled structures. These expressions show explicitly how the locations of the actuator/sensor pairs and the displacement and velocity feedback gains influence the frequencies and damping parameters of the closed-loop system modes. For lightly coupled modes, simple relations are obtained between the modal parameters and the coordinates of the sensor/actuator pairs as well as the displacement and velocity feedback gains. Using the example of a cantilevered uniform beam controlled by a single sensor/actuator pair, numerical results are used to illustrate the sensitivity of the closedloop modal parameters to the placement of the sensor/actuator pair as well as the feedback gains. Such results help answer questions about optimal placement of sensor/actuat or pairs for the active control of a flexible structure.