Method of control device and control device

Abstract

A method of designing a control device that controls a controlled variable of a plant to a set point, the control device including a feedback control system for outputting a manipulated variable of the plant based on an output of a feedback controller and a disturbance estimation value, including a step of selecting one of a first order transfer function, a second order transfer function, a third order transfer function, a first order and time delay transfer function, a second order and time delay transfer function, and a third order and time delay transfer function as a transfer function of the nominal plant in accordance with characteristics of the plant; and a step of determining a transfer function of the feedback controller based on a gain and time constant of the nominal plant.

Claims

1. A method of designing a control device that controls a controlled variable of a plant to a set point, the control device comprising a feedback control system, which includes: a feedback controller into which a difference between the set point and the controlled variable is input, and a disturbance feedback that outputs a disturbance estimation value wherein a difference between an output of a nominal plant into which an output of the feedback controller is input, and the controlled variable, is multiplied by a feedback gain, and which outputs a manipulated variable of the plant based on the output of the feedback controller and the disturbance estimation value, the method of designing a control device comprising: selecting one of a first order transfer function, a second order transfer function, a third order transfer function, a first order and time delay transfer function, a second order and time delay transfer function, and a third order and time delay transfer function as a transfer function of the nominal plant in accordance with characteristics of the plant; and determining a transfer function of the feedback controller based on a gain and time constant of the nominal plant, wherein when the first order transfer function in Equation (1) is selected as a transfer function P.sub.n of the nominal plant, a transfer function K of the feedback controller is determined in Equation (2) based on a gain K.sub.n and time constant T.sub.n of the nominal plant, when the second order transfer function in Equation (3) is selected as the transfer function P.sub.n of the nominal plant, the transfer function K of the feedback controller is determined as in Equation (4) based on the gain K.sub.n and time constants T.sub.1n and .sub.n of the nominal plant, and when the third order transfer function in Equation (5) is selected as the transfer function P.sub.n of the nominal plant, the transfer function K of the feedback controller is determined in Equation (6) based on the gain K.sub.n and time constants T.sub.1n, T.sub.2n, and .sub.n of the nominal plant, $\begin{array}{cc}{P}_n=\frac{K_n}{1+T_{n}s}& \left(1\right)\\ K=\frac{1}{2K_n{T}_{n}s}& \left(2\right)\\ P_n=\frac{K_n}{\left(1+T_{1n}s\right)\left(1+{}_{n}s\right)},{}_n<T_{1n}& \left(3\right)\\ K=\frac{T_{1n}}{2K_n{}_n}.Math.\frac{1+T_{1n}s}{T_{1n}s}& \left(4\right)\\ P_n=\frac{K_n}{\left(1+T_{1n}s\right)\left(1+T_{2n}s\right)\left(1+{}_{n}s\right)},{}_n<T_{2n}<T_{1n}& \left(5\right)\\ K=\frac{T_{1n}}{2K_n{}_n}.Math.\frac{\left(1+T_{1n}s\right)\left(1+T_{2n}s\right)}{T_{1n}s}.& \left(6\right)\end{array}$

2. The design method of control device according to claim 1, wherein when the first order and time delay transfer function, the second order and time delay transfer function, or the third order and time delay transfer function is selected as the transfer function of the nominal plant, a Smith compensator is appended to the transfer function of the feedback controller.

3. The design method of control device according to claim 1, wherein the feedback control system where the transfer function of the nominal plant is selected and the transfer function of the feedback controller is determined, is further equivalently converted to a two degrees of freedom control system.

4. A control device, designed by the design method of control device according to claim 1.

5. The control device according to claim 4, wherein the plant is any one of instruments including a compressor, a condenser, an expansion valve, and an evaporator forming a refrigerant cycle, or a system wherein the instruments are combined.

6. A method of designing a control device configured as a set point filter type two degrees of freedom PID control system, the control device comprising: a filter into which a set point of a controlled variable of a plant is input, and a first feedback controller into which a difference between an output of the filter and the controlled variable is input, and which outputs a manipulated variable of the plant, the control device controlling the controlled variable to the set point, the design method of the control device comprising: equivalently converting a feedback control system to the set point filter type two degree of freedom PID control system, the feedback control system including a second feedback controller into which a difference between the set point and the controlled variable is input, and a disturbance feedback that outputs a difference between an output of a nominal plant into which an output of the second feedback controller is input, and the controlled variable, with multiplying by a feedback gain; and in the equivalently converting the feedback control system, determining a transfer function F of the filter and a transfer function K of the first feedback controller based on the feedback gain L, a transfer function K of the second feedback controller, and a transfer function Pn of the nominal plant, according to following equations 7 and 8: $\begin{array}{cc}{K}^{}=L+K+{\mathrm{LP}}_{n}K& \left(7\right)\\ F=\frac{K+{\mathrm{LP}}_{n}K}{L+K+{\mathrm{LP}}_{n}K}.& \left(8\right)\end{array}$

7. The design method of control device according to claim 6, wherein a derivative time of the transfer function of the filter and the transfer function of the first feedback controller is 0, the transfer function of the nominal plant is a first order transfer function, and the transfer function of the second feedback controller is determined based on a gain and time constant of the nominal plant.

8. The design method of control device according to claim 7, wherein the first order transfer function is identified to obtain the gain and time constant of the nominal plant, and the transfer function of the filter and the transfer function of the first feedback controller are determined based on the gain and time constant of the nominal plant, with only the feedback gain as a tuning parameter.

9. A control device, designed by the design method of control device according to claim 6.

10. A control device that controls a controlled variable of a plant to a set point, comprising: a set point filter type two degrees of freedom PID control system including a filter into which the set point is input, and a first feedback controller into which a difference between an output of the filter and the controlled variable is input and which outputs a manipulated variable of the plant, wherein a feedback control system including a second feedback controller into which a difference between the set point and the controlled variable is input, and a disturbance feedback that outputs a difference between an output of a nominal plant into which an output of the second feedback controller is input, and the controlled variable, with multiplying by a feedback gain L, is equivalently converted to the set point filter type two degrees of freedom PID control system, a transfer function F of the filter and a transfer function K of the first feedback controller are configured to be determined by following equations 9 and 10 based on the feedback gain L, a transfer function K of the second feedback controller, and a transfer function Pn of the nominal plant, $\begin{array}{cc}{K}^{}=L+K+{\mathrm{LP}}_{n}K& \left(9\right)\\ F=\frac{K+{\mathrm{LP}}_{n}K}{L+K+{\mathrm{LP}}_{n}K}.& \left(10\right)\end{array}$

11. The control device according to claim 10, wherein a derivative time of the transfer function of the filter and the transfer function of the first feedback controller is 0, the transfer function of the nominal plant is a first order transfer function, and the transfer function of the second feedback controller is determined based on a gain and time constant of the nominal plant.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) FIG. 1 is a block diagram showing a configuration of a feedback control system including a disturbance feedback according to a design method of control device in a first embodiment of the invention.

(2) FIG. 2 is a block diagram showing a configuration of a feedback control system including a disturbance feedback including a first order nominal plant according to the design method of control device in the first embodiment of the invention.

(3) FIG. 3 is a block diagram showing a configuration of a feedback control system including a disturbance feedback including a second order nominal plant according to the design method of control device in the first embodiment of the invention.

(4) FIG. 4 is a block diagram showing a configuration of a feedback control system including a disturbance feedback including a third order nominal plant according to the design method of control device in the first embodiment of the invention.

(5) FIG. 5 is a block diagram showing a configuration of a feedback control system including a disturbance feedback including a first order and time delay nominal plant according to the design method of control device in the first embodiment of the invention.

(6) FIG. 6 is a block diagram showing a configuration of a feedback control system including a disturbance feedback including a second order and time delay nominal plant according to the design method of control device in the first embodiment of the invention.

(7) FIG. 7 is a block diagram showing a configuration of a feedback control system including a disturbance feedback including a third order and time delay nominal plant according to the design method of control device in the first embodiment of the invention.

(8) FIG. 8 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 2 is equivalently converted to a feedforward type two degrees of freedom control system.

(9) FIG. 9 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 3 is equivalently converted to a feedforward type two degrees of freedom control system.

(10) FIG. 10 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 4 is equivalently converted to a feedforward type two degrees of freedom control system.

(11) FIG. 11 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 5 is equivalently converted to a feedforward type two degrees of freedom control system.

(12) FIG. 12 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 6 is equivalently converted to a feedforward type two degrees of freedom control system.

(13) FIG. 13 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 7 is equivalently converted to a feedforward type two degrees of freedom control system.

(14) FIG. 14 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 2 is equivalently converted to a feedback type two degrees of freedom control system.

(15) FIG. 15 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 3 is equivalently converted to a feedback type two degrees of freedom control system.

(16) FIG. 16 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 4 is equivalently converted to a feedback type two degrees of freedom control system.

(17) FIG. 17 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 5 is equivalently converted to a feedback type two degrees of freedom control system.

(18) FIG. 18 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 6 is equivalently converted to a feedback type two degrees of freedom control system.

(19) FIG. 19 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 7 is equivalently converted to a feedback type two degrees of freedom control system.

(20) FIG. 20 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 2 is equivalently converted to a filter type two degrees of freedom control system.

(21) FIG. 21 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 3 is equivalently converted to a filter type two degrees of freedom control system.

(22) FIG. 22 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 4 is equivalently converted to a filter type two degrees of freedom control system.

(23) FIG. 23 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 5 is equivalently converted to a filter type two degrees of freedom control system.

(24) FIG. 24 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 6 is equivalently converted to a filter type two degrees of freedom control system.

(25) FIG. 25 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 7 is equivalently converted to a filter type two degrees of freedom control system.

(26) FIG. 26 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 2 is equivalently converted to a loop type two degrees of freedom control system.

(27) FIG. 27 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 3 is equivalently converted to a loop type two degrees of freedom control system.

(28) FIG. 28 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 4 is equivalently converted to a loop type two degrees of freedom control system.

(29) FIG. 29 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 5 is equivalently converted to a loop type two degrees of freedom control system.

(30) FIG. 30 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 6 is equivalently converted to a loop type two degrees of freedom control system.

(31) FIG. 31 is a block diagram showing a configuration wherein the feedback control system including a disturbance feedback shown in FIG. 7 is equivalently converted to a loop type two degrees of freedom control system.

(32) FIG. 32 is a block diagram showing an example wherein the control device in the first and second embodiments of the invention is applied to a refrigeration cycle system.

(33) FIG. 33 is a block diagram showing the configuration of each control device in the refrigeration cycle system shown in FIG. 32 in the first embodiment of the invention.

(34) FIG. 34 is a diagram showing the relationship between manipulated variables and controlled variables in the refrigeration cycle system shown in FIG. 32.

(35) FIG. 35 is a block diagram showing a configuration of a feedback control system including a disturbance feedback according to a design method of control device in a second embodiment of the invention.

(36) FIG. 36 is a block diagram showing a configuration of a set point filter type two degrees of freedom PID control system according to the design method of control device in the second embodiment of the invention.

(37) FIG. 37 is a block diagram showing a configuration of a set point filter type two degrees of freedom PID control system wherein a feedback control system including a disturbance feedback has been equivalently converted.

(38) FIG. 38 is a block diagram showing the configuration of each control device in the refrigeration cycle system shown in FIG. 32 in the second embodiment of the invention.

(39) FIG. 39 is a block diagram showing a configuration of a general feedback control system control device.

(40) FIG. 40 is a diagram illustrating the effect of disturbance in the feedback control system shown in FIG. 39.

DESCRIPTION OF EMBODIMENTS

(41) From the details of the description and the attached figures, at least the following items are clear.

(42) (First Embodiment)

(43) Design Method of Control Device

(44) Hereafter, referring to FIG. 1 to FIG. 7, a description will be given of a design method of control device in a first embodiment.

(45) A control device of feedback control system 1 shown in FIG. 1 includes, in addition to a feedback controller 101 and adder 102, an adder 103 and disturbance feedback 110 in order to reduce the effect of disturbance d. Also, the disturbance feedback 110 includes a nominal plant 111, an adder 112, and a feedback gain 113.

(46) A control output (controlled variable y) from a plant 9 and a set point r are input into the adder 102, and the difference between the set point r and controlled variable y(ry) is input from the adder 102 into the feedback controller 101. Consequently, taking a transfer function of the feedback controller 101 to be K, an output u.sub.0 of the feedback controller 101 is [Equation. 1]
u.sub.0=K(ry)(1)

(47) The output u.sub.0 of the feedback controller 101 is input into the nominal plant 111 of the disturbance feedback 110. Consequently, taking a transfer function of the nominal plant 111 to be P.sub.n, an output y.sub.n of the nominal plant 111 is [Equation. 2]
y.sub.n=P.sub.nu.sub.0(2)
Also, the output y.sub.n of the nominal plant 111 and the controlled variable y are input into the adder 112, and a difference e between the output y.sub.n of the nominal plant 111 and the controlled variable y (=y.sub.ny) is input from the adder 112 into the feedback gain 113. Consequently, taking the value of the feedback gain 113 to be L (hereafter called the feedback gain L), a disturbance estimation value u.sub.d output from the feedback gain 113 is [Equation. 3]
u.sub.d=Le=L(y.sub.ny)(3)

(48) The output u.sub.0 of the feedback controller 101 and the disturbance estimation value u.sub.d are input into the adder 103, and the sum of the output u.sub.0 of the feedback controller 101 and the disturbance estimation value u.sub.d is output from the adder 102 as a control input (manipulated variable u) with respect to the plant 9. Consequently, the manipulated variable u is

(49) $\begin{array}{cc}\left[\mathrm{Equation}.4\right]& \\ \begin{array}{c}u=u_0+u_d\\ =K\left(r-y\right)+L\left[P_{n}K\left(r-y\right)-y\right]\\ =\left(K+{\mathrm{LP}}_{n}K\right)r-\left(L+K+{\mathrm{LP}}_{n}K\right)y\end{array}& \left(4\right)\end{array}$
Herein, the disturbance estimation value u.sub.d, being estimated so as to attenuate the disturbance d, is negative when the disturbance d is positive, and positive when the disturbance d is negative. Further, by the disturbance estimation value u.sub.d added to the output u.sub.0 of the feedback controller 101 in the adder 103, the disturbance d added to the manipulated variable u in an adder 8 is compensated.

(50) The sign of the disturbance estimation value u.sub.d may be changed appropriately in accordance with the treatment of the disturbance estimation value u.sub.d in the adder 103 or the treatment of the disturbance d in the adder 8. For example, in FIG. 1, when the adder 103 is changed such that the disturbance estimation value u.sub.d is subtracted from the output u.sub.0 of the feedback controller 101, the disturbance d can be attenuated by the disturbance estimation value u.sub.d estimated such that the reference sign corresponds with the disturbance d. Also, for example, in FIG. 1, when the adder 8 is changed such that the disturbance d is subtracted from the manipulated variable u, it is sufficient that the disturbance estimation value u.sub.d is estimated such that the reference sign corresponds with the disturbance d.

(51) The transfer function P.sub.n of the nominal plant 111 is selected from six types, which are first order plant, second order plant, third order plant, first order and time delay plant, second order and time delay plant, and third order and time delay plant, depending on the characteristics of the plant 9. Specifically, firstly, the first order, second order, third order, first order and time delay, second order and time delay, and third order and time delay transfer functions of the nominal plant 111 are each identified from experiment or simulation data in accordance with a least squares method, a prediction error method, or the like. Also, with a conformity rate FIT shown in the following Equation (5) as an indicator, the conformity of each of the identified transfer functions with the experiment or simulation data is determined.

(52) $\begin{array}{cc}\left[\mathrm{Equation}.5\right]& \\ \mathrm{FIT}=\left(1-\frac{\sqrt{\underset{k=1}{\overset{N}{.Math.}}{\left[\hat{y}\left(k\right)-y\left(k\right)\right]}^2}}{\sqrt{\underset{k=1}{\overset{N}{.Math.}}{\left[y\left(k\right)-\stackrel{\_}{y}\right]}^2}}\right)100& \left(5\right)\end{array}$
Herein, N is the total number of data point (N points), and k (=1, . . . , N) indicates the k-th points of data. Further, the transfer function with the highest conformity rate FIT at equation (5) is selected as the transfer function P.sub.n of the nominal plant 111.

(53) The transfer function K of the feedback controller 101 is uniquely determined depending on the type of nominal plant 111 selected. In this embodiment, a Betrag method is used as an example of a method of determining the control parameters of the feedback controller 101 (for example, refer to PTL 2 and pages 198 and 199, Modulus and Symmetrical Optimum of NPL 1).

(54) FIG. 2 shows the configuration of the feedback control system when the nominal plant 111 is a first order plant. The transfer function P.sub.n of the nominal plant 111 in this case is described by the following Equation (6).

(55) $\begin{array}{cc}\left[\mathrm{Equation}.6\right]& \\ P_n=\frac{K_n}{1+T_{n}s}& \left(6\right)\end{array}$
Herein, K.sub.n and T.sub.n are a gain and time constant respectively of the nominal plant 111. Further, using the gain K.sub.n and time constant T.sub.n of the nominal plant 111, the transfer function K of the feedback controller 101 is determined as in

(56) $\begin{array}{cc}\left[\mathrm{Equation}.7\right]& \\ K=\frac{1}{2K_n{T}_{n}s}& \left(7\right)\end{array}$

(57) FIG. 3 shows the configuration of the feedback control system when the nominal plant 111 is a second order plant. The transfer function P.sub.n of the nominal plant 111 in this case is described by the following Equation (8).

(58) $\begin{array}{cc}\left[\mathrm{Equation}.8\right]& \\ P_n=\frac{K_n}{\left(1+T_{1n}s\right)\left(1+{}_{n}s\right)}& \left(8\right)\end{array}$
Herein, K.sub.n and T.sub.1n, .sub.n are the gain and time constants respectively of the nominal plant 111. As .sub.n<T.sub.1n at this time, the characteristics of the nominal plant 111 (transfer function P.sub.n) in this case are provided such that the longer time constant T.sub.1n is dominant. Therefore, the transfer function K of the feedback controller 101 is designed so as to attenuate the characteristics of the time constant T.sub.1n. Further, using the gain K.sub.n and time constants T.sub.1n, .sub.n of the nominal plant 111, the transfer function K of the feedback controller 101 is determined as in

(59) $\begin{array}{cc}\left[\mathrm{Equation}.9\right]& \\ K=\frac{T_{1n}}{2K_n{}_n}.Math.\frac{1+T_{1n}s}{T_{1n}s}& \left(9\right)\end{array}$

(60) FIG. 4 shows the configuration of the feedback control system when the nominal plant 111 is a third order plant. The transfer function P.sub.n of the nominal plant 111 in this case is described by the following Equation (10).

(61) $\begin{array}{cc}\left[\mathrm{Equation}.10\right]& \\ P_n=\frac{K_n}{\left(1+T_{1n}s\right)\left(1+T_{2n}s\right)\left(1+{}_{n}s\right)}& \left(10\right)\end{array}$
Herein, K.sub.n and T.sub.1n, T.sub.2n, .sub.n are the gain and time constants respectively of the nominal plant 111. As .sub.n<T.sub.2n<T.sub.1n at this time, the characteristics of the nominal plant 111 (transfer function P.sub.n) in this case are provided such that the longer time constants T.sub.1n and T.sub.2n are dominant. Therefore, the transfer function K of the feedback controller 101 is designed so as to attenuate the characteristics of the time constants T.sub.1n and T.sub.2n. Further, using the gain K.sub.n and time constants T.sub.1n, T.sub.2n, .sub.n of the nominal plant 111, the transfer function K of the feedback controller 101 is determined as in

(62) $\begin{array}{cc}\left[\mathrm{Equation}.11\right]& \\ K=\frac{T_{1n}}{2K_n{}_n}.Math.\frac{\left(1+T_{1n}s\right)\left(1+T_{2n}s\right)}{T_{1n}s}& \left(11\right)\end{array}$

(63) FIG. 5 shows the configuration of the feedback control system when the nominal plant 111 is a first order and time delay. The transfer function P.sub.n of the nominal plant 111 in this case is described by the following Equation (12).

(64) $\begin{array}{cc}\left[\mathrm{Equation}.12\right]& \\ P_n=\frac{K_n}{1+T_{n}s}{e}^{-L_{\mathrm{dn}}s}& \left(12\right)\end{array}$
Herein, K.sub.n, T.sub.n, and L.sub.dn are the gain, time constant, and time delay respectively of the nominal plant 111. Also, a Smith compensator 104 into which the output u.sub.0 of the feedback controller 101 is input, is appended to the feedback controller 101, and the difference between the output of the adder 102 and the Smith compensator 104 is input via an adder 105. At this time, a transfer function S of the Smith compensator 104 is expressed from the transfer function P.sub.n of the nominal plant 111 as in the following Equation (13).

(65) 0$\begin{array}{cc}\left[\mathrm{Equation}.13\right]& \\ S=\frac{K_n}{1+T_{n}s}\left(1-e^{-L_{\mathrm{dn}}s}\right)& \left(13\right)\end{array}$
Meanwhile, the transfer function K of the feedback controller 101, in the same way as in the case of FIG. 2, is determined as in Equation (7) above, by using the gain K.sub.n and time constant T.sub.n of the nominal plant 111.

(66) FIG. 6 shows the configuration of the feedback control system when the nominal plant 111 is a second order and time delay. The transfer function P.sub.n of the nominal plant 111 in this case is described by the following Equation (14).

(67) $\begin{array}{cc}\left[\mathrm{Equation}.14\right]& \\ P_n=\frac{K_n}{\left(1+T_{1n}s\right)\left(1+{}_{n}s\right)}{e}^{-L_{\mathrm{dn}}s}& \left(14\right)\end{array}$
Herein, K.sub.n, T.sub.1n, .sub.n, and L.sub.dn are the gain, time constants, and time delay respectively of the nominal plant 111. Also, the Smith compensator 104 into which the output u.sub.0 of the feedback controller 101 is input, is appended to the feedback controller 101, and the difference between the output of the adder 102 and the Smith compensator 104 is input via the adder 105. At this time, the transfer function S of the Smith compensator 104 is expressed from the transfer function P.sub.n of the nominal plant 111 as in the following Equation (15).

(68) $\begin{array}{cc}\left[\mathrm{Equation}.15\right]& \\ S=\frac{K_n}{\left(1+T_{1n}s\right)\left(1+{}_{n}s\right)}\left(1-e^{-L_{\mathrm{dn}}s}\right)& \left(15\right)\end{array}$
Meanwhile, the transfer function K of the feedback controller 101, in the same way as in the case of FIG. 3, is determined as in Equation (9) above, by using the gain K.sub.n and time constants T.sub.1n, .sub.n of the nominal plant 111.

(69) FIG. 7 shows the configuration of the feedback control system when the nominal plant 111 is a third order and time delay. The transfer function P.sub.n of the nominal plant 111 in this case is described by the following Equation (16).

(70) $\begin{array}{cc}\left[\mathrm{Equation}.16\right]& \\ P_n=\frac{K_n}{\left(1+T_{1n}s\right)\left(1+T_{2n}s\right)\left(1+{}_{n}s\right)}{e}^{-L_{\mathrm{dn}}s}& \left(16\right)\end{array}$
Herein, K.sub.n, T.sub.1n, T.sub.2n, .sub.n, and L.sub.dn are the gain, time constants, and time delay respectively of the nominal plant 111. Also, the Smith compensator 104 into which the output u.sub.0 of the feedback controller 101 is input, is appended to the feedback controller 101, and the difference between the output of the adder 102 and the Smith compensator 104 is input via the adder 105. At this time, the transfer function S of the Smith compensator 104 is expressed from the transfer function P.sub.n of the nominal plant 111 as in the following Equation (17).

(71) $\begin{array}{cc}\left[\mathrm{Equation}.17\right]& \\ S=\frac{K_n}{\left(1+T_{1n}s\right)\left(1+T_{2n}s\right)\left(1+{}_{n}s\right)}\left(1-e^{-L_{\mathrm{dn}}s}\right)& \left(17\right)\end{array}$
Meanwhile, the transfer function K of the feedback controller 101, in the same way as in the case of FIG. 4, is determined as in Equation (11) above, by using the gain K.sub.n and time constants T.sub.1n, T.sub.2n, .sub.n of the nominal plant 111.

(72) In this way, the transfer function P.sub.n of the nominal plant 111 and the transfer function K of the feedback controller 101 are determined. Because of this, from Equation (4), it is possible to design the control device of feedback control system 1 with only the feedback gain L as a tuning parameter.

(73) As heretofore described, in the design method of control device of this embodiment, the engineer, firstly, selects the transfer function with the highest conformity rate FIT (whose characteristics are the most similar), from the first order, second order, third order, first order and time delay, second order and time delay, and third order and time delay transfer functions, as the transfer function P.sub.n of the nominal plant 111 in the feedback control system including the disturbance feedback 110 shown in FIG. 1. Also, the engineer determines the transfer function K of the feedback controller 101 based on the parameters (gain and time constants) of the nominal plant 111.

(74) At this time, it is possible to identify the transfer function P.sub.n of the nominal plant 111 from experiment or simulation data, by depending on a least squares method, a prediction error method, or the like, and possible to determine the transfer function K of the feedback controller 101 from the parameters of the transfer function P.sub.n. Consequently, the engineer can design the control device of feedback control system 1 with only the feedback gain L as a tuning parameter.

(75) Equivalent Conversion to Two Degrees of Freedom Control System

(76) It is possible to change equivalently from the feedback control system including disturbance feedback shown in FIG. 2 to FIG. 7 to various types of two degrees of freedom control system, such as a feedforward type or loop type (for example, refer to NPL 2).

(77) FIG. 8 to FIG. 13 show configurations wherein the feedback control systems shown in FIG. 2 to FIG. 7 respectively are equivalently converted to a feedforward type two degrees of freedom control system.

(78) In FIG. 8 to FIG. 10, the feedback controller 101, adders 102, 103, and 123, the feedback gain 113, and compensating elements 120 to 122 enclosed by broken lines correspond to a configuration such that an output that a proportional device (the compensating element 122) is added to the product of an integrator (the compensating element 120) and a first order transfer function (the compensating element 121) and then multiplied by L, is added to the output of a general (one-degree-of freedom) PID control system (the output u.sub.o of the feedback controller 101). Furthermore, a feedforward path formed of a (feedforward) compensating element 124 and adder 125, entering directly from the set point r to the manipulated variable u, is added to the configuration of the feedforward type two degree of freedom control system. Also, in FIG. 11 to FIG. 13, the Smith compensator 104 and adder 105 are added to the configurations of FIG. 8 to FIG. 10 respectively, and a first order and time delay transfer function (compensating element 130) is used in place of the first order transfer function (compensating element 121).

(79) Herein, the product of the compensating element 120 and compensating element 121 (130) in FIG. 8 to FIG. 13 is equivalent to the product of the transfer function P.sub.n of the nominal plant 111 and transfer function K of the feedback controller 101 in FIG. 2 to FIG. 7 respectively. Consequently, taking the output of the feedback gain 113 to be u.sub.c, the manipulated variable u in the feedforward type two degrees of freedom control systems is

(80) $\begin{array}{cc}\left[\mathrm{Equation}.18\right]& \\ \begin{array}{c}u=u_0+u_e+\left(-\mathrm{Lr}\right)\\ =K\left(r-y\right)+L\left(1+P_{n}K\right)\left(r-y\right)-\mathrm{Lr}\\ =\left(L+K+{\mathrm{LP}}_{n}K\right)\left(r-y\right)-\mathrm{Lr}\\ =\left(K+{\mathrm{LP}}_{n}K\right)r-\left(L+K+{\mathrm{LP}}_{n}K\right)y\end{array}& \left(18\right)\end{array}$
corresponding to the manipulated variable u in the feedback control system including disturbance feedback shown in Equation (4).

(81) FIG. 14 to FIG. 19 show configurations wherein the feedback control systems shown in FIG. 2 to FIG. 7 respectively are equivalently converted to a feedback type two degrees of freedom control system. In FIG. 14 to FIG. 16, the feedback controller 101, adders 102 and 103, feedback gain 113, and compensating elements 120 and 121 enclosed by broken lines correspond to a configuration such that an output that is the product of an integrator (the compensating element 120) and a first order transfer function (the compensating element 121) multiplied by L, is added to the output of a general (one-degree-of freedom) PID control system (the output u.sub.o of the feedback controller 101). Furthermore, a feedback path formed of a (feedback) compensating element 126 and adder 127, entering directly from the controlled variable y to the manipulated variable u, is added to the configuration of the feedback type two degrees of freedom control system. Also, in FIG. 17 to FIG. 19, the Smith compensator 104 and adder 105 are added to the configurations of FIG. 14 to FIG. 16 respectively, and a first order and time delay transfer function (the compensating element 130) is used in place of the first order transfer function (compensating element 121).

(82) Herein, the product of the compensating element 120 and compensating element 121 (130) in FIG. 14 to FIG. 19 is equivalent to the product of the transfer function P.sub.n of the nominal plant 111 and transfer function K of the feedback controller 101 in FIG. 2 to FIG. 7 respectively. Consequently, taking the output of the feedback gain 113 to be u.sub.f, the manipulated variable u in the feedback type two degrees of freedom control systems is

(83) $\begin{array}{cc}\left[\mathrm{Equation}.19\right]& \\ \begin{array}{c}u=u_0+u_f-\mathrm{Ly}\\ =K\left(r-y\right)+{\mathrm{LP}}_{n}K\left(r-y\right)-\mathrm{Ly}\\ =\left(K+{\mathrm{LP}}_{n}K\right)\left(r-y\right)-\mathrm{Ly}\\ =\left(K+{\mathrm{LP}}_{n}K\right)r-\left(L+K+{\mathrm{LP}}_{n}K\right)y\end{array}& \left(19\right)\end{array}$
corresponding to the manipulated variable u in the feedback control system including disturbance feedback shown in Equation (4).

(84) FIG. 20 to FIG. 25 show configurations wherein the feedback control systems shown in FIG. 2 to FIG. 7 respectively are equivalently converted to a filter type two degrees of freedom control system. In FIG. 20 to FIG. 22, the feedback controller 101, adders 102, 103, and 123, feedback gain 113, and compensating elements 120 to 122 enclosed by broken lines correspond to a configuration such that an output that is a proportional device (the compensating element 122) added to the product of an integrator (the compensating element 120) and a first order transfer function (the compensating element 121) and then multiplied by L, is added to the output of a general (one-degree-of freedom) PID control system (the output u.sub.o) of the feedback controller 101). Furthermore, in the configuration of the filter type two degrees of freedom control system, a (filter) compensating element 128 is added before the input of the set point r into the adder 102. Also, in FIG. 23 to FIG. 25, the Smith compensator 104 and adder 105 are added to the configurations of FIG. 20 to FIG. 22 respectively, and a first order and time delay transfer function (the compensating element 130) is used in place of the first order transfer function (compensating element 121).

(85) Herein, the product of the compensating element 120 and compensating element 121 (130) in FIG. 20 to FIG. 25 is equivalent to the product of the transfer function P.sub.n of the nominal plant 111 and transfer function K of the feedback controller 101 in FIG. 2 to FIG. 7 respectively. Also, a transfer function F of the compensating element 128 is described by the following Equation (20) in each case.

(86) $\begin{array}{cc}\left[\mathrm{Equation}.20\right]& \\ F=\frac{K+{\mathrm{LP}}_{n}K}{L+K+{\mathrm{LP}}_{n}K}& \left(20\right)\end{array}$
Consequently, taking the output of the feedback gain 113 to be u.sub.g, the manipulated variable u in the filter type two degrees of freedom control systems is

(87) $\begin{array}{cc}\left[\mathrm{Equation}.21\right]& \\ \begin{array}{c}u=u_0+u_g\\ =K\left(\mathrm{Fr}-y\right)+L\left(1+P_{n}K\right)\left(\mathrm{Fr}-y\right)\\ =\left(L+K+{\mathrm{LP}}_{n}K\right)\left(\frac{K+{\mathrm{LP}}_{n}K}{L+K+{\mathrm{LP}}_{n}K}r-y\right)\\ =\left(K+{\mathrm{LP}}_{n}K\right)r-\left(L+K+{\mathrm{LP}}_{n}K\right)y\end{array}& \left(21\right)\end{array}$
corresponding to the manipulated variable u in the feedback control system including disturbance feedback shown in Equation (4).

(88) FIG. 26 to FIG. 31 show configurations wherein the feedback control systems shown in FIG. 2 to FIG. 7 respectively are equivalently converted to a loop type two degrees of freedom control system. In FIG. 26 to FIG. 28, the feedback controller 101, adders 102 and 103, feedback gain 113, and compensating elements 120 and 121 enclosed by broken lines correspond to a configuration such that an output that the product of an integrator (the compensating element 120) and a first order transfer function (the compensating element 121) is multiplied by L, is added to the output of a general (one-degree-of freedom) PID control system (the output u.sub.o of the feedback controller 101). Furthermore, in the configuration of the loop type two degrees of freedom control system, a (loop) compensating element 129 is added before the input of the manipulated variable y into the adder 102. Also, in FIG. 29 to FIG. 31, the Smith compensator 104 and adder 105 are added to the configurations of FIG. 26 to FIG. 28 respectively, and a first order and time delay transfer function (the compensating element 130) is used in place of the first order transfer function (compensating element 121).

(89) Herein, the product of the compensating element 120 and compensating element 121 (130) in FIG. 26 to FIG. 31 is equivalent to the product of the transfer function P.sub.n of the nominal plant 111 and transfer function K of the feedback controller 101 in FIG. 2 to FIG. 7 respectively. Also, a transfer function C of the compensating element 129 is described by the following Equation (22) in each case.

(90) $\begin{array}{cc}\left[\mathrm{Equation}.22\right]& \\ C=\frac{L+K+{\mathrm{LP}}_{n}K}{K+{\mathrm{LP}}_{n}K}\left(=\frac{1}{F}\right)& \left(22\right)\end{array}$
Consequently, taking the output of the feedback gain 113 to be u.sub.h, the manipulated variable u in the loop type two degrees of freedom control systems is

(91) 0$\begin{array}{cc}\left[\mathrm{Equation}.23\right]& \\ \begin{array}{c}u=u_0+u_h\\ =K\left(r-\mathrm{Cy}\right)+{\mathrm{LP}}_{n}K\left(r-\mathrm{Cy}\right)\\ =\left(K+{\mathrm{LP}}_{n}K\right)\left(r-\frac{L+K+{\mathrm{LP}}_{n}K}{K+{\mathrm{LP}}_{n}K}y\right)\\ =\left(K+{\mathrm{LP}}_{n}K\right)r-\left(L+K+{\mathrm{LP}}_{n}K\right)y\end{array}& \left(23\right)\end{array}$
corresponding to the manipulated variable u in the feedback control system including disturbance feedback shown in Equation (4).

(92) Application Example of Control Device

(93) Hereafter, referring to FIG. 32 to FIG. 34, a description will be given of an example wherein the control device of this embodiment is applied to a refrigeration cycle system. FIG. 32 shows the configuration of the whole refrigeration cycle system, FIG. 33 shows the configuration of each control device in the refrigeration cycle system, and FIG. 34 shows the relationship between manipulated variables (control device outputs) and controlled variables (plant outputs) in the refrigeration cycle system.

(94) The refrigeration cycle system shown in FIG. 32 includes control devices 11 to 14, a refrigerant pipe 90, a compressor 91, a condenser 92, an expansion valve 93, an evaporator 94, and sensors S1, S2, S3a, S3b, and S4. The compressor 91, condenser 92, expansion valve 93, and evaporator 94 are connected to each other via the refrigerant pipe 90, and a refrigerant circulates inside the refrigerant pipe 90. Also, the condenser 92 and evaporator 94 include fans F2 and F4 respectively.

(95) A control device 1m (m=1, 2, 3, 4) shown in FIG. 33 has a configuration same as that of the control device 1 shown in FIG. 1, a controlled variable ym of the plant 9 and a set point rm are input, and a manipulated variable um of the plant 9 is output. The combinations (pairings) of manipulated variables and controlled variables shown in FIG. 34 are an example, and are not limited.

(96) In the application example of FIG. 32, the sensor S1 measures evaporation pressure (low pressure) y1, and the control device 11 outputs the rotation speed u1 of the compressor 91 as a manipulated variable based on the evaporation pressure y1 as a controlled variable and a set point r1 (not shown). Also, the sensor S2 measures condensation pressure (high pressure) y2, and the control device 12 outputs rotation speed u2 of the fan F2 as a manipulated variable based on the condensation pressure y2 as a controlled variable and a set point r2 (not shown). Also, the sensors S3a and S3b measure inlet temperature Ti and outlet temperature To respectively of the evaporator 94, and the control device 13 outputs an open degree u3 of the expansion valve 93 as a manipulated variable based on a degree of overheat y3 (=ToTi) as a controlled variable and a set point r3 (not shown). Also, the sensor S4 measures a supply temperature y4, and the control device 14 outputs rotation speed u4 of the fan F4 as a manipulated variable based on the supply temperature y4 as a controlled variable and a set point r4 (not shown).

(97) In this way, according to the control device of this embodiment, it is possible to control each controlled variable of the refrigeration cycle system (plant) to the set point. As the instruments forming the refrigerant cycle are connected to each other via the refrigerant pipe 90, it may happen that controls by the control devices interfere with each other, and affect other controls as disturbance. Because of this, by the control device of this embodiment applied to a refrigerant cycle system, it is possible to control the controlled variables to the set point while reducing the effect of interference and disturbance. The control device of this embodiment is also applicable to any one instrument of the compressor 91, condenser 92, expansion valve 93, and evaporator 94 forming the refrigerant cycle, or to a system wherein these instruments are combined.

(98) As previously described, in the design method of the control device of feedback control system 1 including the feedback controller 101 and disturbance feedback 110, by the transfer function most similar to the characteristics of the plant 9 among the six kinds of transfer functions, which are the first order, second order, third order, first order and time delay, second order and time delay, and third order and time delay, being selected as the transfer function P.sub.n of the nominal plant 111, and the transfer function K of the feedback controller 101 determined based on the parameters (gain and time constants) of the nominal plant 111, it is possible to easily design a feedback control system control device that, with only the feedback gain L as an tuning parameter and without using state-space representation, balances set point response controlling the controlled variable y to the set point r and disturbance response reducing the effect of the disturbance d. Furthermore, this kind of feedback control system including a disturbance feedback may be equivalently converted to a two degrees of freedom control system.

(99) Also, by the control device 1 (11 to 14) designed in this way applied to a refrigerant cycle system, it is possible to control the controlled variables to the set points while reducing the effect of interference and disturbance, even when controls by the control devices interfere with each other and affect other controls as disturbance.

(100) (Second Embodiment)

(101) Design Method of Control Device

(102) Hereafter, referring to FIG. 35 to FIG. 37, a description will be given of a design method of control device in a second embodiment.

(103) In this embodiment, firstly, a feedback control system shown in FIG. 35 is equivalently converted to a two degrees of freedom PID control system shown in FIG. 36.

(104) A feedback control system control device 3 shown in FIG. 35 includes, in addition to a feedback controller 301 and adder 302, an adder 303 and disturbance feedback 310 in order to reduce the effect of the disturbance d. Also, the disturbance feedback 310 includes a nominal plant 311, an adder 312, and a feedback gain 313.

(105) A control output (controlled variable y) from the plant 9 and the set point r are input into the adder 302, and the difference between the set point r and controlled variable y (ry) is input from the adder 302 into the feedback controller 301 (second feedback controller). Consequently, taking a transfer function of the feedback controller 301 to be K, the output u.sub.0 of the feedback controller 301 is as in Equation (1) above.

(106) The output u.sub.0 of the feedback controller 301 is inputs into the nominal plant 311 of the disturbance feedback 310. Consequently, taking a transfer function of the nominal plant 311 to be P.sub.n, the output y.sub.n of the nominal plant 311 is as in Equation (2) above. Also, the output y.sub.n of the nominal plant 311 and the controlled variable y are input into the adder 312, and the difference e between the output y.sub.n of the nominal plant 311 and the controlled variable y (=y.sub.ny) is input from the adder 312 into the feedback gain 313. Consequently, taking the value of the feedback gain 313 to be L (hereafter called the feedback gain L), the disturbance estimation value u.sub.d outputs from the feedback gain 313 is as in Equation (3) above.

(107) The output u.sub.0 of the feedback controller 301 and the disturbance estimation value u.sub.d are input into the adder 303, and the sum of the output u.sub.0 of the feedback controller 301 and the disturbance estimation value u.sub.d is output from the adder 303 as a control input (manipulated variable u) with respect to the plant 9. Consequently, the manipulated variable u is [Equation. 24]
u=u.sub.0+u.sub.d(24)
Herein, the disturbance estimation value u.sub.d, being estimated so as to attenuate the disturbance d, is negative when the disturbance d is positive, and positive when the disturbance d is negative. Further, by the disturbance estimation value u.sub.d added to the output u.sub.0 of the feedback controller 301 in the adder 303, the disturbance d added to the manipulated variable u in the adder 8 is compensated.

(108) The reference sign of the disturbance estimation value u.sub.d may be changed appropriately in accordance with the treatment of the disturbance estimation value u.sub.d in the adder 303 or the treatment of the disturbance d in the adder 8. For example, in FIG. 35, when the adder 303 is changed such that the disturbance estimation value u.sub.d is subtracted from the output u.sub.0 of the feedback controller 301, the disturbance d can be attenuated by the disturbance estimation value u.sub.d estimated such that the reference sign corresponds with the disturbance d. Also, for example, in FIG. 35, when the adder 8 is changed such that the disturbance d is subtracted from the manipulated variable u, it is sufficient that the disturbance estimation value u.sub.d is estimated such that the reference sign corresponds with the disturbance d.

(109) A two degrees of freedom PID control system control device 4 shown in FIG. 36 includes, in addition to a feedback controller 401 and adder 402, a filter 403. The two degrees of freedom PID control system, being formed such that the set point r is input into the PID control system via the filter 403, is called a set point filter type (for example, refer to NPL 3).

(110) The set point r is input into the filter 403, and the output of the filter 403 and the controlled variable y are input into the adder 402. Also the difference between the output of the filter 403 and the controlled variable y is input from the adder 402 into the feedback controller 401 (first feedback controller), and the manipulated variable u is output from the feedback controller 401. Consequently, taking the transfer functions of the feedback controller 401 and filter 403 to be K and F respectively, the manipulated variable u is [Equation. 25]
u=K(Fry)(25)

(111) In the set point filter type two degrees of freedom PID control system, the transfer function K of the feedback controller 401 and the transfer function F of the filter 403 are expressed as in the following Equation (26) and Equation (27) respectively

(112) $\begin{array}{cc}\left[\mathrm{Equation}.26\right]& \\ K^{}\left(s\right)K_P\left\{1+\frac{1}{T_{I}s}+T_{D}D\left(s\right)\right\}& \left(26\right)\\ F\left(s\right)=\frac{1+\left(1-\right)T_{I}s+\left(1-\right)T_I{T}_D\mathrm{sD}\left(s\right)}{1+T_{I}s+T_I{T}_D\mathrm{sD}\left(s\right)}& \left(27\right)\end{array}$
Herein, K.sub.P is proportional gain, T.sub.I is integral time, T.sub.D is derivative time, and and are two degrees of freedom parameters. Also, D (s) is an approximate derivative, taken to be

(113) $\begin{array}{cc}\left[\mathrm{Equation}.27\right]& \\ D\left(s\right)=\frac{s}{1+s}& \left(28\right)\end{array}$
Herein is a time constant.

(114) When Equation (2) and Equation (1) are substituted into Equation (3), the following Equation (29) is obtained. [Equation. 28]
u.sub.d=LP.sub.nK(ry)Ly(29)
Furthermore, when Equation (1) and Equation (29) are substituted into Equation (24), the following Equation (30) is obtained. [Equation. 29]
u=K(ry)+LP.sub.nK(ry)Ly(30)
Further, when Equation (30) is rearranged in terms of the set point r and controlled variable y, the following Equation (31) is obtained.

(115) $\begin{array}{cc}\left[\mathrm{Equation}.30\right]& \\ u=\left(L+K+{\mathrm{LP}}_{n}K\right)\left(\frac{K+{\mathrm{LP}}_{n}K}{L+K+{\mathrm{LP}}_{n}K}r-y\right)& \left(31\right)\end{array}$
Consequently, when comparing Equation (25) and Equation (31),

(116) $\begin{array}{cc}\left[\mathrm{Equation}.31\right]& \\ K^{}=L+K+{\mathrm{LP}}_{n}K& \left(32\right)\\ F=\frac{K+{\mathrm{LP}}_{n}K}{L+K+{\mathrm{LP}}_{n}K}& \left(33\right)\end{array}$

(117) In this way, a feedback control system including a disturbance feedback can be equivalently converted to a set point filter type two degrees of freedom PID control system, as shown in FIG. 37. Further, from Equation (32) and Equation (33), the transfer function K of the feedback controller 401 and the transfer function F of the filter 403 are both determined based on the feedback gain L, transfer function K of the feedback controller 301, and transfer function P.sub.n of the nominal plant 311.

(118) Next, the transfer function K of the feedback controller 301 and transfer function P.sub.n of the nominal plant 311 are defined such that the transfer function K of the feedback controller 401 and transfer function F of the filter 403 conform to the forms of Equation (26) and Equation (27) respectively.

(119) In this embodiment, the transfer function P.sub.n of the nominal plant 311 is defined as a first order transfer function shown in the following Equation (34).

(120) $\begin{array}{cc}\left[\mathrm{Equation}.32\right]& \\ P_n\left(s\right)=\frac{K_{\mathrm{pn}}}{1+T_{\mathrm{pn}}s}& \left(34\right)\end{array}$
Herein, K.sub.pn and T.sub.pn are a gain and time constant respectively of the nominal plant 311. Also, using the gain K.sub.pn and time constant T.sub.pn of the nominal plant 311, the transfer function K of the feedback controller 301 is defined as

(121) $\begin{array}{cc}\left[\mathrm{Equation}.35\right]& \\ K\left(s\right)=\frac{1+T_{\mathrm{pn}}s}{K_{\mathrm{pn}}s}\left(=\frac{1}{P_n}.Math.\frac{1}{s}\right)& \left(35\right)\end{array}$

(122) When substituting Equation (34) and Equation (35) into Equation (32), and rearranging in terms of 1/s, the following Equation (36) is obtained.

(123) $\begin{array}{cc}\left[\mathrm{Equation}.34\right]& \\ \begin{array}{c}{K}^{}\left(s\right)=L+\frac{1+T_{\mathrm{pn}}s}{K_{\mathrm{pn}}s}+L\frac{1}{s}\\ =\left(\frac{K_{\mathrm{pn}}L+T_{\mathrm{pn}}}{K_{\mathrm{pn}}}\right)\left(1+\frac{K_{\mathrm{pn}}L+1}{K_{\mathrm{pn}}L+T_{\mathrm{pn}}}.Math.\frac{1}{s}\right)\end{array}& \left(36\right)\end{array}$
Consequently, when comparing Equation (26) and Equation (36),

(124) $\begin{array}{cc}\left[\mathrm{Equation}.35\right]& \\ K_P=\frac{K_{\mathrm{pn}}L+T_{\mathrm{pn}}}{K_{\mathrm{pn}}}& \left(37\right)\\ T_I=\frac{K_{\mathrm{pn}}L+T_{\mathrm{pn}}}{K_{\mathrm{pn}}L+1}& \left(38\right)\\ T_D=0& \left(39\right)\end{array}$

(125) Also, when substituting Equation (34) and Equation (35) into Equation (33), and rearranging in terms of s, the following Equation (40) is obtained.

(126) $\begin{array}{cc}\left[\mathrm{Equation}.36\right]& \\ F\left(s\right)=\frac{\frac{1+T_{\mathrm{pn}}s}{K_{\mathrm{pn}}s}+L\frac{1}{s}}{L+\frac{1+T_{\mathrm{pn}}s}{K_{\mathrm{pn}}s}+L\frac{1}{s}}=\frac{\frac{1+T_{\mathrm{pn}}}{K_{\mathrm{pn}}L+1}s}{1+\frac{K_{\mathrm{pn}}L+T_{\mathrm{pn}}}{K_{\mathrm{pn}}L+1}s}& \left(40\right)\end{array}$
Consequently, when comparing Equation (27) and Equation (40),

(127) 0$\begin{array}{cc}\left[\mathrm{Equation}.37\right]& \\ T_I=\frac{K_{\mathrm{pn}}L+T_{\mathrm{pn}}}{K_{\mathrm{pn}}L+1}& \left(41\right)\\ \left(1-\right)=\frac{T_{\mathrm{pn}}}{K_{\mathrm{pn}}L+1}\frac{1}{T_I}=\frac{T_{\mathrm{pn}}}{K_{\mathrm{pn}}L+T_{\mathrm{pn}}}& \left(42\right)\\ T_D=0& \left(43\right)\end{array}$
Equation (41) and Equation (43) correspond to Equation (38) and Equation (39) respectively.

(128) In this way, from Equation (36) and Equation (40), the transfer function K of the feedback controller 401 and transfer function F of the filter 403 in the set point filter type two degrees of freedom PID control system after equivalent conversion are determined based on the gain K.sub.pn and time constant T.sub.pn of the nominal plant 311 and on the feedback gain L. Also, because of this, the proportional gain K.sub.P is given by Equation (37), the integral time T.sub.1 is given by Equation (38) and Equation (41), and the two degrees of freedom parameter is given by Equation (42). Furthermore, from Equation (39) and Equation (43), the derivative time T.sub.D is 0, and setting of the two degrees of freedom parameter is unnecessary.

(129) As heretofore described, in this embodiment, the engineer, firstly, carries out equivalent conversion of the feedback control system including a disturbance feedback of FIG. 35 to the set point filter type two degrees of freedom PID control system of FIG. 36. Next, in the set point filter type two degrees of freedom PID control system after equivalent conversion, the derivative time T.sub.D of the transfer function K of the feedback controller 401 and transfer function F of the filter 403 is set to 0. Also, in the feedback control system before equivalent conversion, a first order transfer function applied to the transfer function P.sub.n of the nominal plant 311, and furthermore, the transfer function K of the feedback controller 301 is determined based on the gain K.sub.pn and time constant T.sub.pn of the nominal plant 311.

(130) Because of this, the transfer function K of the feedback controller 401 and transfer function F of the filter 403 are determined based on the gain K.sub.pn and time constant T.sub.pn of the nominal plant 311, and on the feedback gain L. Therefore, the engineer, by identifying the first order transfer function of the nominal plant 311 from experiment or simulation data in accordance with a least squares method, a prediction error method, or the like, thus obtaining the gain K.sub.pn and time constant T.sub.pn, can determine the transfer function K of the feedback controller 401 and transfer function F of the filter 403, with only the feedback gain L as an tuning parameter. Further, as the control device 4 designed in this way outputs the same manipulated variable u as the control device 3 including disturbance feedback, it is possible to balance set point response controlling the controlled variable y to the set point r and disturbance response reducing the effect of the disturbance d.

(131) Also, the control device 4 of this embodiment is applicable to the kind of refrigerant cycle system shown in FIG. 32, in the same way as the control device 1 of the first embodiment. The control device 1m (m=1, 2, 3, 4) shown in FIG. 38 is a configuration the same as that of the control device 4 shown in FIG. 36; and the controlled variable ym of the plant 9 and the set point rm thereof are input, and the manipulated variable um of the plant 9 is output.

(132) As previously described, in the design method of control device whereby the controlled variable y of the plant 9 is controlled to the set point r, by the transfer function K of the feedback controller 401 (first feedback controller) and the transfer function F of the filter 403 in the set point filter type two degrees of freedom PID control system of FIG. 36, both being determined based on the feedback gain L, transfer function K of the feedback controller 301 (second feedback controller), and transfer function P.sub.n of the nominal plant 311 in the feedback control system including disturbance feedback of FIG. 35, it is possible to easily design a control device such that a feedback control system including a disturbance feedback is equivalently converted to a set point filter type two degrees of freedom PID control system, without using an state-space representation. Further, as the control device 4 designed in this way outputs the same manipulated variable u as the control device 3 including disturbance feedback, it is possible to balance set point response controlling the controlled variable y to the set point r and disturbance response reducing the effect of the disturbance d.

(133) Also, by the derivative time T.sub.D of the transfer function K of the feedback controller 401 and transfer function F of the filter 403 set to 0 in the set point filter type two degrees of freedom PID control system after equivalent conversion, a first order transfer function adopted as the transfer function P.sub.n of the nominal plant 311 in the feedback control system before equivalent conversion, and furthermore, the transfer function K of the feedback controller 301 determined based on the gain K.sub.pn and time constant T.sub.pn of the nominal plant 311, the transfer function K of the feedback controller 401 and transfer function F of the filter 403 can be determined based on the gain K.sub.pn and time constant T.sub.pn of the nominal plant 311, and on the feedback gain L.

(134) Also, by identifying the first order transfer function of the nominal plant 311, thus obtaining the gain K.sub.pn and time constant T.sub.pn, it is possible to determine the transfer function K of the feedback controller 401 and transfer function F of the filter 403, with only the feedback gain L as a tuning parameter. That is, while normally needing to tune five parameters (the proportional gain K.sub.P, integral time T.sub.I, derivative time T.sub.D, and two degrees of freedom parameters and ) when designing a two degrees of freedom PID control system, as shown in Equation (26) and Equation (27), in the design method of control device of the heretofore described embodiment, it is possible to design with only the one tuning parameter (L).

(135) Also, by the control device 4 (11 to 14) designed in this way applied to a refrigerant cycle system, it is possible to control the controlled variables to the set points while reducing the effect of interference and disturbance, even when controls by the control devices interfere with each other and affect other controls as disturbance.

(136) The heretofore described embodiments are for facilitating understanding of the invention, and interpretation of the invention is not limited to this. The invention may be changed or improved without departing from the scope thereof, and equivalents thereof are also included in the invention.

REFERENCE SIGNS LIST

(137) 1 to 4 Control device 8 Adder 9 Plant 1m (11 to 14) Control device 90 Refrigerant pipe 91 Compressor 92 Condenser 93 Expansion valve 94 Evaporator 101, 201 Feedback controller 102, 103, 105, 112, 123, 125, 127, 202 Adder 104 Smith compensator 110 Disturbance feedback 111 Nominal plant 113 Feedback gain 120 to 122, 124, 126, 128 to 130 Compensating element 301, 401 Feedback controller 302, 303, 312, 402 Adder 310 Disturbance feedback 311 Nominal plant 313 Feedback gain 403 Filter F2, F4 Fan S1, S2, S3a, S1b, S4 Sensor