Endpoint vibrations of flexible manipulators (FM) are suppressed using active or passive control techniques. Suppressing vibrations increases the dynamic performance of the FM in engineering applications. In this study, a model extraction approach is proposed for vibration suppression of single-link flexible smart and composite manipulators. Active and passive control (APC) of residual vibrations is studied theoretically and experimentally. The smart manipulator consists of patching a piezoelectric (PZT) actuator to an aluminum and composite link. The finite element (FE) model of smart manipulators, including revolute joint and PZT actuator, is created in ANSYS. The motion profile and actuator voltage are the inputs, the tip displacement is the output. Then, the state-space (SS) mathematical models of the smart manipulators are extracted from the FE models by using the inputs and outputs. The open-loop and closed-loop simulations are performed using the extracted mathematical models in MATLAB. Passive control is achieved by the motion profiles, while active control is achieved by the PZT actuators. The PD controller with the displacement feedback is used to create the actuation voltages. For the optimized APC, the PD gains are optimized with a genetic algorithm by using the integral of the squared error and integral of absolute magnitude of the error fitness functions. Residual vibrations of smart manipulators are successfully reduced by the optimized APC. To verify the simulation results, open-loop and closed-loop experiments are carried out. The SS mathematical model successfully predicts the dynamic performance of FSM for various motion profiles, according to experimental results.