The block diagram of TDCC is shown in Fig.1 in the usage of the two-degrees-of-freedom control.        Besides the usual comparison between a desired value and a controlled variable , the time difference comparison between the reference value (which is obtained as the desired value is delayed by a delay element as shown in Fig.1) and the controlled valuable is newly equipped.        The each deviation error obtained by the usual comparison and the time difference comparison are multiplied by the ratios and respectively.        Then, these two multiplied ones are added into a renewal deviation error which will be inputted to next stage of controller or compensator, for example, PID or PI controller in a feedback loop.
   If we take the equivalent conversion of the block diagram given in Fig.1, we obtain the block diagram of the desired-value's filter of TDC compensator as shown in Fig.2.        The transfer function of this filter is expressed as .        Although may be arbitrarily selected, it is investigated by us that, in the most cases, the most simple transfer function such as the first order delay element is sufficient to be used in the two-degrees-of-freedom control.        If we adjust two parameters of the first order delay time and the ratio properly in , we obtain a sufficient characteristics of the improvement in the desired-value's response.        In this case, the transfer function of the desired-value's filter is written as .        Thus, the design of the two-degrees-of-freedom control with the use of this method becomes easier, and furthermore, the characteristics of desired-value's response or the compliance of the feedback system can be realized better than the ordinary one.

   We introduce the feedback control system constructed as shown in Fig.3.        In Fig.3, , and indicate the transfer functions of a desired-value's filter constructed with TDCC, a PID controller and a controlled object respectively.        In precise, please see the reference (1) described below. [If you click this column, the thesis in PDF files will appear.].

       PID controller is described as
           ,                       (1)
where , and indicate proportional gain coefficient, integral time and differential time respectively.
       The desired-value's filter of TDCC is described as
           ,                       (2)
where and indicate the partition ratio of the direct comparison and the first order delay time of the TDCC.
       As expressed in Eq.(2), the desired-value's filter is composed of both of the phase-lead and the phase-lag elements and .        Therefore, the phase-lead time which is defined in the following equation may be used as a parameter instead of the parameter .

           .                       (3)

       As a reference, it is noticed that as in the considerable usage.        This fact is opposite to the magnitude correlation between the phase-lead and the phase-lag times of the fundamental phase-lead and lag compensator which may be situated in the feedback loop.

       Thus, the set of the tuning parameters of this Two-Degrees-of-Freedom Control is       or       when the desired-value's filter is composed with the use of the first order delay element in as shown in Fig.1.

       Design method is as follows.
Step 1 :       We design the PID controller as the robustness becomes to be maximized, or the influence of a disturbance to the controlled output comes to be minimized under some appointed gain margin.
Step 2 :       We design the desired-value's filter constructed with the TDCC as the response to the desired value becomes into an optimal condition.

       As mentioned above, big feature in this two-degrees-of-freedom control is that there are three big advantages, which are not difficult only by PID controller, as described in the followings.
(Advantage 1)      Arbitrarily desired gain margin is able to be settled.
(Advantage 2)       It is possible that the robustness becomes to be maximized, or the influence of a disturbance to the controlled output comes to be minimized.
(Advantage 3)       The compliance to the desired value can be designed arbitrarily by TDCC.

    The design guaidance mentioned of this two-degrees-of-freedom control mentioned above is gathered in Table 1.

       As an instance, we treat a servo system including a dead time .
   In the case of , the indicial response by the TDCC method) is shown as the curve a in Fig.4.       The other curves from b to e indicate the indicial responses by the usual two-degrees-of-freedom controls.        The curve f indicates the indicial responses when the TDCC is removed.        In this case, we use TDCC parameters and which are decided by the design rules described in the reference (1) with the use of the most simple style of the delay element .
    This TDCC method indicated by curve a is the most excellent as same as the usual two-degrees-of-freedom control method indicated by curve b.        However, the construction of this TDCC method is more simple than its usual one, and therefore, this TDCC method can be designed more simply than that.        Furthermore, its usual method must be taken in account that it includes a differential element whereas the TDCC method does not.
    Comparison of the indicial response of the TDCC method a with that of its usual method b is shown in Fig 5 in the case of .        The response in the TDCC method a indicates to be faster than that in its usual one b.        As a erference, curve c indicates the indicial response when the desired-value's filter is removed.

    When this two-degrees-of-freedom control is applied to the real servo-system in which the control object possesses mechanism of nonlinear friction with hysteresis, it has to be taken into account that there may be difficulty in design of this two-degrees-of-freedom control likely as in the ordinary control method.

(1) Nobuo YAMAMOTO and Hitoshi OOUCHI: Two-Degrees-of-Freedom PID Control with the Use of Desired-Value's Filter Composed of Time-Difference Comparison, IEEJ Trans. D, Vol.123, No.3, pp.247-256 (2003) (in Japanese).

(2) Nobuo YAMAMOTO: Time-Difference Comparison Compensation Method of Control Systems, The 30th united meetings of automatic controls in Japan, pp.185-186 (1987) (in Japanese).

(3) Nobuo YAMAMOTO and Etsushi UENO: Digital Design of Feedback Control with the Use of Time Difference Comparison Compensation (TDCC) Method, Research Reports of Ibaraki National College of Technology, No.40, pp.59-64 (2005) (in Japanese).

(4) Nobuo YAMAMOTO: "Versatile Time Difference Comparison Compensation Method of Control System and its Equipment", Japan Patent, No.2716437 (1998) (in Japanese).

(5) Nobuo YAMAMOTO: "Versatile Time Difference Comparison Compensation Method of Control System", United States Patent , No.4953076 (1990).

(6) Nobuo YAMAMOTO: "Method and apparatus of two-degrees-of-freedom time difference comparison compensator", United States Patent , No.5182703 (1993).

(7) Nobuo YAMAMOTO: Feed-forward Compensation Cooperating with Internal Model and Time- Differential Comparison Compensation of Feedback Control: Reprint of the Signals Systems Control Symposium, JAACE, pp.25-28 (1988) (in Japanese).

(8) Nobuo YAMAMOTO: Two-Degrees-of-Freedom PID Control with the Use of 2nd-Order Time Difference Comparison Compensation (TDCC) Method, Research Reports of Ibaraki National College of Technology, No.40, pp. 43-50, (2005) (in Japanese).