Recently the adaptive control system, which keeps the control system always optimal by adjusting the control parameters automatically according to the variations of the plant parameters, have become very important in the field of control engineering. The adaptive control systems are usally composed of the plant identification, the decision of the optimal control parameters, and the adjustment of the control parameters. This paper deals with a method of the adaptive control system when PI or PID controller is used in the feed back control system. Its controlled object (the plant) is assumed to be described by the transfer function of $frac{ke^{-LS}}{1+TS}$ where k, T and L are steady state gain, time constant and pure dead time respectively, and their values are variable in accordance with the change of environmental circumstance. It has been known that a pseudo-random binary signal is quite effective for the measurement of an impulse response of a plant. In adaptive control systems, however, the impulse response itself is not appropriate to determine the control parameters. In this paper, the authors propose a method to estimate directly the parameters of the plant k, T and L by means of the correlation technique using 3 level M-sequence signal as a test signal. The authors also propose a method to determine the optimal parameters of the PI or PID controller in the sense of minimizing the square integral of the control error in the feed back control system, and the values of the optimal parameters are computed numerically for various values of T and L, and the results are examined and compared with those of the conventional methods. Finally the above-mentioned two methods are combined and an algorithm to struct an adaptive control system is suggested. The experiments for the indicial responses by means of both the model of the temperature control system using SCR actuater and the analog simulations have shown good results as expected, and the effectiveness of the proposed method is verified. The M-sequence generator and the time delay circuit, which are manufactured for the experiments, are operated in quite a good condition.