Improvement of steady-state performance for discrete-valued input control with an integrator utilizing feedback control of integrated value of input

In this study, we considered the regulator problem for discrete-valued input control with an integrator. In some cases, the state does not converge to the origin in the discrete-valued input control when the plant possesses an integrator. Therefore, a method that adds minor feedback control to the integrated value of the input was proposed. However, the effect of the feedback control of the integrated value of the input was not theoretically interpreted, and the feedback gain for the state of the integrated value of the input was designed with trial and error. Herein, we clarify the effect of feedback control on the integrated value of the input. Furthermore, we reveal that the trade-off between the steady-state and transient performances is controlled by one parameter, that is, the feedback gain for the integrated value of the input.