This dissertation presents a self-tuning regulator (STR) design method developed based upon a state-space linear quadratic Gaussian (LQG) control strategy for rejecting a disturbance in a flexible structure in the face of model uncertainty. The parameters to be tuned are treated as additional state variables and are estimated recursively together with the system state that is needed for feedback. Also, the feedback gains are designed in the LQ framework based upon the estimated model parameters. Two problems concerning the uncertainty of model parameters are recognized. First, we consider the uncertainty in the system matrix of the state space model. The self-tuning regulator is implemented by computer and the control law is obtained based upon a discrete-time model; however, only selected continuous-time parameters with physical meanings to which the controller is highly sensitive are tuned. It is formulated as a nonlinear filtering problem such that both the estimated state and the unknown parameters can be obtained by an extended Kahman filter. The capability of this design method is experimentally demonstrated by applying it to the rejection of a disturbance in a simply supported plate. The other problem considered is that the location where the disturbance enters the system is unknown. This corresponds to an unknown disturbance influence matrix. Under the assumption that the system matrix is known and the disturbance can be measured, it is formulated as a linear filtering problem with an approximate discrete-time design model. Similarly, the estimated state for feedback and the unknown parameters are identified simultaneously and recursively. Also, the feedback gains are calculated approximately by recursively solving the discrete-time control Riccati equation. The effectiveness of the controller is shown by applying it to a simply-supported plate, when the location of the disturbance is assumed unknown. Since implementing LQG self-tuning controllers for vibration control systems requires significant real-time computation, methods that can reduce the computing load are examined. In addition, the possibility of extending the self tuning to disturbance model parameters is explored. / Ph. D.