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The simplest controller is the proportional controller. With this term proportional, the feedback control signal is computed in proportion to the feedback error with the formula,

(1.1)

where is the proportional gain and the feedback error is the difference between the reference signal and the output signal (). The block diagram for the closed-loop feedback control configuration is shown in Figure 1.1 where , , , and are the Laplace transforms of the reference signal, feedback error, control signal, and output signal, respectively. represents the Laplace transfer function of the plant.

Figure 1.1 Proportional feedback control system.

Because of its simplicity, the proportional controller is often used in the cases when little information about the system is available and the required control performance in steady-state operation is not demanding. As the controller only involves one parameter to be determined, it is possible to choose without detailed information about the plant.

One of the limitations of a simple proportional controller is that the steady-state error of the closed-loop control system will not be completely eliminated. We illustrate this point with the following example.