In this project, the modeling and design of an L1 state feedback adaptive control system applied for vibration control of a smart piezoelectric Euler–Bernoulli cantilever beam is presented. For a Single-Input Single-Output (SISO) case by considering the first two dominant vibratory modes, the dynamics of the system are presented. Three Piezoelectric patches, two as actuators and the other as a sensor are bonded to the structure at the support of the beam and along the length of the beam. L1 adaptive control law, with time-varying parameters and in the presence of disturbance, is employed to suppress the vibration of the beam. The beam structure is modeled in the state space form using the concept of piezoelectric theory, the Euler–Bernoulli beam theory, and the Finite Element technique. The proposed controller is also compared with PID and LQR control systems.