Takayoshi Nakamizo

Synthesis of Nonlinear Control Systems with a Deterministic Input in the Presence of a Random Disturbance

A technique was established for improving the response of a saturating servo-system subjected to a deterministic input in the presence of random disturbance. To demonstrate this technique, attention is directed to establishing the analytical procedure of the response of nonlinear control systems by means of the statistical linearization technique. First, an analytical method of calculating the equivalent transfer characteristic of a nonlinear element with a deterministic input contaminated by a random disturbance is shown. Second, a graphical technique for evaluating the response of the closed system is developed. Two examples are presented, showing how the behaviors of nonlinear control systems may be analyzed. From these analytical considerations, it is possible to design the intentionally introduced nonlinear controller to optimize the control performance of a saturating servo-system for various inputmagnitudes. Detailed discussions for synthetic procedures are given. (auth)

A Study on the Statistical Synthesis of Optimum Nonlinear Control Systems Subjected to Non-Gaussian Random Inputs

In this paper, a practical synthesizing technique, in the statistical sense, of the optimum nonlinear control system subjected to non-Gaussian random inputs is presented. The technique described here is a method of circumventing difficulties of mathematical treatment. The description begins with the construction of the optimum nonlinear filter under the excitation of non-Gaussian time series. It is analytically shown that the optimum nonlinear filter consists of a nonlinear element of zero-memory type sandwitched between two linear filters. By applying these results to the synthesis of feedback control systems with a random signal in the presense of non-Gaussian random noise, the optimum control system containing a nonlinear element is derived. Detailed descriptions of these synthesizing procedures are illustrated by several examples.

A Study on Control Performance of Predictor-Relay Servo Systems Subjected to a Gaussian Random Input

The present problem is to construct the operation of controller generating the control signal which will switch the on-off relay in such a way that the mean square error becomes minimum. First, when the input to the system is a random with Gaussian amplitude probability distribution and the control signal is of some non-linear function of the error and its derivative, the general procedure of analysis for the evaluation of statistical behaviors of error signal is described. Second, the improvement of the control performance by introducing a predictor is proposed. Principal purpose of this paper is to evaluate how the optimum prediction time depends upon such important variables as (a) the value of system time constant and (b) the variance of random input signal. Finally, statistical evaluations of the response of such predictor-relay servo system are carried out and the improvement of the control performance is quantitatively shown.