Abstract
The paper describes how to synthesize a servomechanism with a controlled process whose transfer function is 1/s(s+1), in order to obtain good response. Desired input signal to the system is assumed Gaussian stationary random with the power spectrum density P/(Ts2ω2+1). Saturation of manipulated variable is taken into consideration using Booton's linearization.
Under these conditions, following results are found.
(1) When the transfer function of the controller is simple gain K, it is shown that the larger value of K makes the smaller mean square error, if Ts>1.
(2) Transfer function of the optimum linear controller that minimizes mean square error is determined by means of the linearization.
(3) Neglecting small parameters contained above transfer function, the optimum transfer function of the controller is found as (s+1)/(αs+1). The system with this optimum controller shows good response.
