The magnetorheological elastomer membrane is an interesting kind of smart material that is gaining new innovative applications. This work is focused on the design of the control system for magnetorheological elastomer actuators. In general, the plant is characterized by fast oscillations and slow drift. Therefore, controllers utilize the described features to obtain the solution aimed at, which makes them unique. We analyze two approaches based on output feedback with state estimation. The control algorithms have different observers to estimate the state. The first is a Linear Extended State Observer, which is applied to reject the disturbances in a case with a simple model. The second is a Linear State Observer, which is used to estimate a state based on the plant model. Furthermore, in both cases, we have the same proportional-derivative controller after decoupling the dynamics. The main goal of the paper is to examine both controllers for the magnetorheological actuator. Therefore, the designed control systems are verified in a series of experiments.