This research proposes some new data-driven control methods to control a nonlinear dynamic model. The nonlinear dynamic model linearizes by using the Koopman theory. The Koopman operator is the most important part of designing the Koopman theory. The data mode decomposition (DMD) is used to obtain the Koopman operator. The proposed data-driven control method applies to different nonlinear systems such as microelectromechanical systems (MEMS), Worm robots, and 2 degrees of freedom (2 DoF) robot manipulators to verify the performance of the proposed method. For the MEMS gyroscope, three control methods are applied to the linearized dynamic model by the Koopman theory: linear quadratic regulator (LQR), compound fractional PID sliding mode control, and fractional order PID controller tuned with bat algorithm. For the Worm robot, an LQR controller is proposed to control the linearized dynamic model by the Koopman theory. A new fractional sliding mode control is proposed to control the 2 DoF arm robot. All the proposed controllers applied to the linearized dynamic model by the Kooman theory are compared with some conventional proposed controllers such as PID, sliding mode control, and conventional fractional sliding mode control to verify the performance of the proposed controllers. Simulation results validate their performance in high tracking performance, low tracking error, low frequency, and low maximum overshoot.