JP2002318602A - Device and method for controlling discrete time sliding mode for process system having dead time - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a discrete time sliding mode control system whose robust stability and adaptive controllability is excellent for a process system having a dead time. SOLUTION: In this discrete time sliding mode controller designated for the model of a linear transmission function expressing an object 11 to be controlled, the model of the object 11 to be controlled includes a linear approximate formula obtained by Pad approximating the dead time elements of the object 11 to be controlled. A disturbance observer 12 estimates state variables x1 and x2 and disturbance d from an input u and an output y of the object 11 to be controlled. A supervisor 13 is provided with a function of optimizing a target value r in the process according to the history of a disturbance estimated value from the disturbance observer 12, and stabilizing an integrated value z of a deviation between a target value r and the output y of the object 11 to be controlled. Sliding mode arithmetic parts 14-23 calculates a control input u to the object 11 to be controlled based on the target value r and the output y of the object 11 to be controlled and the estimated values of the stage variables x1 and x2 from the disturbance observer 12.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to discrete-time sliding mode control for a process system having a dead time.

[0002]

2. Description of the Related Art PID control is widely used as a control method for a process system. Generally, a process system has a dead time element, but a moderately desirable control characteristic can be achieved by adjusting the gain of PID control or the like.

Here, as an example of a process system to which PID control has been conventionally applied, there is a cooling plate used for high-speed cooling of a wafer in a semiconductor manufacturing apparatus. FIG. 1 is a schematic sectional view of an example of the structure of such a cooling plate.

A cooling plate 1 shown in FIG. 1 has a disc-shaped water cooling plate 2 having a cooling water passage therein, and heat is transferred from one side to the other side by electric power using the Peltier effect, which is superposed thereon. A disk-shaped thermoelectric conversion module 3 to be moved;
And a disc-shaped surface plate 4 having good thermal conductivity superposed thereon. There are shims 6 having a very small height at several places on the upper surface of the front plate 4, and the semiconductor wafer 5 is placed on the shims 6. The shim 6 lifts and supports the semiconductor wafer 5 from the surface plate 5 by a very small height. A temperature sensor 7 is provided in the surface plate 5.
Is embedded.

The cooling plate 1 shown in FIG. 1 is controlled, for example, as follows. Cooling water continues to flow through the water cooling plate 2 at a constant flow rate. On this cooling plate 1, a hot semiconductor wafer 5 (for example, about 150 ° C.) is placed.
A control device (not shown) feeds back the temperature of the surface plate 4 from the temperature sensor 7 so that the semiconductor wafer 5 is cooled quickly and smoothly to a target temperature (for example, about 23 ° C.), and the thermoelectric conversion is performed according to the feedback value. Manipulate the input power (or current value) of the module 3 and thereby control the temperature of the face plate 4.

FIG. 2 is a graph showing the temperature of the wafer 5 (hereinafter, referred to as a wafer temperature), the temperature of the front plate 4 (hereinafter, referred to as a plate temperature), and the input power of the thermoelectric conversion module 3 (hereinafter, referred to as an operation amount). ) Is shown. In FIG. 2, a temperature value Tc is a target value of the plate temperature for maintaining the wafer temperature at the target value.

As shown in FIG. 2, when the wafer is placed, first, cooling is performed with the maximum operation amount -max, and the wafer temperature is rapidly lowered. When the plate temperature falls to a temperature Tc-Tm lower than the target value Tc by a predetermined value Tm, feedback PID control of the plate temperature is started. By the feedback PID control, the plate temperature increases toward the target value Tc, and accordingly, the wafer temperature decreases toward the target temperature. Then, the plate temperature and the wafer temperature ideally smoothly reach the respective target temperatures and settle as shown in the figure. In addition,
In the following description, in the locus of the plate temperature shown in FIG. 2, a point at which the temperature reaches Tc-Tm, that is, a point at which the temperature changes from falling to rising is referred to as a "turning point".

[0008]

The above-described conventional PID control of the cooling plate 1 has the following problems.

(1) There is a demand for shortening the wafer cooling settling time (= the time from when the wafer is placed until the wafer temperature is settled to the target temperature as shown in FIG. 2). For example, conventionally, it takes about 30 seconds for the wafer cooling settling time, but there is a demand to reduce this to less than 20 seconds. As can be seen from the trajectory of the operation amount in FIG. 2, the feedback PID control is effective only in the last part of the wafer cooling settling time. Set the wafer cooling settling time to, for example, 1
If it is shortened to about 8 seconds, feedback PI
The period during which D control can be used is only the last few seconds. Therefore, a control ability for surely stabilizing the control amount to the target value in the short time of several seconds is required. To do so, it is necessary to design a control system that takes into account the dead time of the process system. However, in the design of the conventional PID control system, dead time is treated vaguely.
Therefore, it is difficult to satisfy the above requirements.

(2) Cooling plate 1 shown in FIG.
The temperature of the cooling water flowing through the chamber fluctuates, for example, in the range of about 15 ° C. to 30 ° C. Due to the fluctuation of the cooling water temperature, system parameters of the cooling plate 1 largely fluctuate. If the system parameters change, the control characteristics of PID control deteriorate unless the control parameters are adjusted. For example, when the cooling water temperature increases, an overshoot appears on the plate temperature trajectory, and when the cooling water temperature decreases, an undershoot appears. Therefore, there is a demand for a control system that is more excellent in robust stability, which can cope with fluctuations in system parameters without adjusting control parameters, and in adaptive controllability, which can always be properly constrained to a desired control trajectory. . Conventionally, sliding mode control is known as one of the control methods excellent in robust stability and adaptive controllability. However, even in the sliding mode control, there has not been known a control in which dead time is dealt with from the front as described in (1) above.

(3) The initial temperature of the wafer is, for example, 70 ° C.
It fluctuates in the range of about 150 ° C. That is, there are initial disturbances having different magnitudes. In the conventional control described with reference to FIG. 2, feedback PID control is started when the plate temperature reaches a turning point (point of temperature Tc-Tm). That is, no consideration is given to the influence of the initial temperature of the wafer before that. Therefore, if the initial temperature of the wafer is different, the time required for the plate temperature to reach the turning point changes, and accordingly, the wafer cooling settling time changes. As described above, the conventional control also has a problem in adaptive controllability with respect to the initial disturbance.

(4) The cooling plate 1 illustrated in FIG. 1 is a one-input one-output system. However, the surface area of the plate is divided into a plurality of zones, and the dynamic characteristics and the magnitude of external thermal disturbance are different for each zone, so that it is necessary to apply a different control system to each zone. And a cooling plate of a multi-input multi-output system. In such control of a multi-input multi-output system, a control system capable of uniformly controlling all outputs without adjusting control parameters is also desired.

Accordingly, it is an object of the present invention to provide a discrete time sliding mode control system which is excellent in robust stability and adaptive controllability for a process system having a dead time.

It is another object of the present invention to provide a control system for a multi-input multi-output process system which can control all outputs as evenly as possible without adjusting control parameters.

[0015]

A control device according to a first aspect of the present invention is a discrete-time sliding mode control device designed for a model of a linear transfer function representing a control object, the control device comprising: Includes a linear approximation formula that linearly approximates a dead time element of the control target. The discrete-time sliding mode controller includes a disturbance observer for estimating a state variable and a disturbance of the model from an input and an output of the control object, a given target value, an output of the control object, and a state variable from the disturbance observer. And a sliding mode calculation unit that calculates a control input to the control target based on the estimated value of the control mode. This control device can perform control excellent in robust stability and adaptive controllability on a process system having a dead time.

In the calculation of the control input, an integrated value obtained by integrating the deviation between the target value and the output of the controlled object is used. In a preferred embodiment, a high-speed control is achieved by calculating a stable value for the integrated value based on the output of the controlled object and setting the integrated value to the stable value at a predetermined point in the process. Can be

Also, a preferred embodiment is that during the process
Based on the history of disturbance estimates from the disturbance observer,
The system further includes an online optimization mechanism for optimizing the target value. Thereby, adaptive controllability against disturbance is improved.

In a preferred embodiment, the disturbance observer has an approximation error system for calculating an approximation difference obtained by linearly approximating the dead time, and a state variable is calculated based on the approximation error and the output of the controlled object. And the disturbance is estimated. Thereby, chattering or the like due to the approximation error is suppressed, and robust stability is improved.

In a preferred embodiment, the disturbance observer is
It has a gain determined by a predetermined optimal pole assignment algorithm.

The control device of the present invention has a very simple control structure with one degree of freedom, and has a significantly improved target value response characteristic as compared with the conventional method despite a small calculation load. Can be.

The control device according to the second aspect of the present invention is for a multi-input multi-output process system, and one of the plurality of single input / output systems constituting the multi-input multi-output system. A discrete-time sliding mode controller designed for a model representing a reference system and a discrete-time sliding mode controller designed for a model representing each system other than the reference system are provided. And the discrete-time sliding mode controller for each of the other systems is:
It is configured as a model reference type control device using the model of the reference system as a reference model.

An observer design method according to a third aspect of the present invention is a model of a linear transfer function model representing a controlled object, the model including a linear approximation formula obtained by linearly approximating a dead time element of the controlled object. Calculating a state variable and a disturbance by using a predetermined optimum pole arrangement algorithm to calculate a pole (for example, an optimum pole described later) of the disturbance observer for estimating the state variable and the disturbance from the input and output of the control object; Determining a gain.

A computer program according to a fourth aspect of the present invention is a computer program, comprising: a model of a linear transfer function representing a control target, the model including a linear approximation formula that linearly approximates a dead time element of the control target. A computer program for causing a computer to execute a calculation step of calculating a pole (for example, an optimum pole described later) of a disturbance observer that estimates a variable and a disturbance from inputs and outputs of a control target.

In a preferred embodiment, the calculation step calculates the pole based on a condition created from the viewpoint of limiting the estimated speed of the disturbance observer.

In a preferred embodiment, the computer program causes the computer to further execute a step of determining a gain of the disturbance observer using the calculated pole.

The control device according to the present invention comprises dedicated hardware,
It can be realized by any of a programmed computer or a combination thereof.

[0027]

DESCRIPTION OF THE PREFERRED EMBODIMENTS A. First Embodiment An embodiment of the present invention applied to temperature control of a cooling plate 1 having the structure shown in FIG. 1 will be described.

A.0 Design Specifications of Control System The design specifications aimed at by the present embodiment are as follows as an example.

1) The wafer is cooled from 150 to 23 [° C], the wafer cooling settling time is within 18 [s] under the conditions of temperature distribution in the wafer surface ± 0.2 [° C] and cooling water temperature = 25 [° C]. And By the way,
In conventional PID control products, the wafer cooling settling time under the same conditions is nearly 30 seconds.

2) Adaptability and robustness to water temperature fluctuation range of 15 to 30 ° C. (time-varying system; static characteristics and dynamic characteristics greatly fluctuate) are established, and the above 1 is adjusted without adjusting control parameters. The same cooling performance as that of (1) is realized. Incidentally, in a conventional PID control product, the wafer cooling settling time greatly varies in the range of about 25 to 35 [s] (including product variation).

3) Variation range of initial temperature of wafer 70 to 150 [° C]
Adaptability to (disturbances having different magnitudes) is established, and a cooling settling time similar to the above 1) is realized without adjusting the control parameters.

A.1 Modeling of Controlled System The dynamic characteristics of the thermoelectric conversion module 3 having the structure shown in FIG. 1 have large nonlinearity, and it is difficult to create a physical model. Therefore, here, considering the application to general-purpose control equipment for other process systems, the system is approximated by “first-order delay + dead time” as shown in the following equation (1), and the system parameters are closed-loop Estimate by the square method.

A.1.1 Parameter successive estimation

(Equation 1)

Firstly, consider the following equation (2) obtained by discretizing the sampling interval T _s of formula (1).

(Equation 2) Here, k represents a dead time in a discrete time system, and represents a maximum integer satisfying L> kT _s .

Further, consider the following equation (3) corresponding to equation (2).

(Equation 3) Here, it indicates a minimum estimate of the time it k _m ham, m and k
_m is set so as to satisfy the _{k m <k <k m +} m. Next, (3)
Parameters in expressions

(Equation 4) Is estimated by the following successive least squares method.

[0036]

(Equation 5) Here, ω is a forgetting factor, given as 0 <ω <1. ε
(t) indicates the prediction error signal. Also,

(Equation 6) Is an estimated value of the unknown parameter θ. ψ (t−1) is a data vector, which is given by the following equation.

(Equation 7)

At this time, using the estimated value of the system parameter shown in the above equation (4), the process gain

(Equation 8) , Time constant

(Equation 9) And dead time

(Equation 10) Can be calculated by the following equation.

[0038]

[Equation 11]

A.1.2 Design Model For a specific cooling plate having the structure shown in FIG. 1, a step response (target temperature is set near the operating point (23 ° C./equilibrium point; 25 ° C.)) is set. Step rise from 22 ° C to 28 ° C,
Based on the experimental results of performing proportional control (P = 13.0 [% / ° C.]) on the step drop from 28 ° C. to 22 ° C.), the above-described successive parameter estimation was actually performed. As a result, it was found that there were large fluctuations in the process gain, the time constant, and the dead time.The average of the values from the step change of the target temperature until the plate temperature settled for this parameter estimation result was as follows. It became like.

[0040]

(Equation 12)

Accordingly, the controlled object near the operating point on average is represented by the following equation (10).

[0042]

(Equation 13)

Further, consider the following equation (11) in which a first-order Paddy approximation is applied to the dead time element of equation (10) as a design model.

[0044]

[Equation 14]

Next, when the equation (11) is rewritten into a pair of a state equation and an output equation, the following equation (12) is obtained.

[0046]

(Equation 15)

[0047] (12) is by the coordinate transformation x _a = Tx to canonical systems as follows in equation (13).

[0048]

(Equation 16)

Since the equation (13) is a continuous time system, if it is converted to a discrete time system at a sampling interval h = 0.05 [s], the following (1)
4) It becomes like the formula. However, it includes the system uncertainty d (k). Here, k is a value that satisfies the time t = Kh (not the dead time in the continuous time system shown in the above equation (2)).

[Equation 17]

Further, with respect to the above plate temperature y≡T _p ,
The dynamic characteristic of the wafer temperature is expressed by the following equation (15).

(Equation 18) Where C _w is the heat capacity of the wafer, α _w is the equivalent heat transfer coefficient between the plate and wafer, _Sw is the equivalent heat transfer area between the plate and wafer, α _∞ is the heat transfer coefficient to the atmosphere, and T _∞ is the atmosphere Temperature. Λ is a coefficient for converting disturbance into the same unit as the input u, α _c is a heat transfer coefficient to the water cooling plate, S _c is a heat transfer area to the water cooling plate, and T _c is a cooling water temperature.

[0051] In (15), the thermal disturbance d _w and the heat endothermic d _c of the time to varying water cooling plate from the wafer, the following definitions (16), the matching condition is satisfied.

[Equation 19] Here, _Hmax is a predetermined upper limit value.

A.2 Control System Design For a system having non-linearity, parameter fluctuation, time-variation, and unknown disturbance, a control system using sliding mode control and a disturbance estimation observer is constructed as follows.

A.2.1 Discrete Time Sliding Mode Control of Servo System First, in equation (14), it is necessary to design a type 1 servo system. In this case, an expansion system is used in which the integral value z of the difference between the target value r and the output y is added to the state variable of the equation (14). For the state variables that cannot be observed, the values estimated by the disturbance estimation observer are used.

(Equation 20) Here, σ (k) is a switching function.

A.2.1.1 Design of Equivalent Control System In the sliding mode of the discrete time system, σ (k) =
From σ (k + 1) = σ (k + 1) =…, if the equivalent control input u _eq (k) does not consider disturbance,

(Equation 21) And the equivalent control system is expressed by the following equation.

(Equation 22)

A.2.1.2 Design of Hyperplane In order to determine the switching matrix S, a design method that specifies a stability margin (the real part of the eigenvalue of the equivalent control system is −ε or less) is applied. That is, the switching matrix S of the hyperplane is determined using the solution P of the following discrete system algebraic Riccati equation.

(Equation 23)

Here, it is assumed that Q = I and ε = 0.075, and the eigenvalue of the designed equivalent control system using S is as follows.

(Equation 24)

A.2.1.3 Design of Sliding Mode Controller As shown in the following equation (22), the control input u is composed of a linear control input u _l and a non-linear control input u _nl .

(Equation 25) Here, the linear control input u _l is the equivalent control input u _eq described above. β (k) is a disturbance suppression term in the nonlinear control input.

Here, the influence of disturbance will be considered. It is assumed that a disturbance that satisfies the matching condition for the servo system of Expression (17) is as follows.

(Equation 26)

At this time, if β (k) ≡0, the deviation of the state from the switching plane is expressed by the following equation (24).

[Equation 27] Have a relationship. (24)

[Equation 28] Is almost constant, if 0 <η <2,

(Equation 29) Becomes Therefore, if η is increased within a stable range, the steady-state deviation decreases. In general, when the sampling period is made sufficiently small, the element of Γ becomes relatively small, so that the steady-state deviation also becomes small, and it becomes robust against disturbance.

A.2.2 Configuration of Discrete-Time Disturbance Estimation Observer In equation (14), a disturbance estimation observer is configured. The purpose of the disturbance estimation observer is to estimate the thermal disturbance from the wafer and the fluctuation of the cooling water temperature as a disturbance superimposed on the input, and to estimate and feed back the state in consideration of the thermal history of the disturbance.

[Equation 30]

The observer gain G is pole-arranged by trial and error in a simulation.

(Equation 31)

A.2.3 Block Diagram FIG. 3 shows a block diagram of the final discrete-time sliding mode controller designed as described above.

In FIG. 3, a block 11 indicates a system to be controlled (in this embodiment, the cooling plate 1 shown in FIG. 1). The disturbance observer 12 is the control target 1
The output y of 1 (the plate temperature detected by the sensor 7 in FIG. 1) is input, and the state of the system (state variables x ₁ , x ₂ and disturbance d) is estimated according to the above equation (26). Estimate

(Equation 32) Is output. As will be described later, the supervisor 13 has a mechanism for supplying a stable value of the servo system integrated value z (k) and a mechanism for optimizing the plate temperature trajectory online, and the output (plate temperature) y of the control target system. And the disturbance (d) estimated value from the disturbance observer 2, and outputs a stable value of z (k) and a target value r of the optimized plate temperature.

Blocks 14 to 23 are sliding mode controllers based on the above equation (22) and the like. The block 15 is an integrator, which inputs the deviation between the plate temperature target value r and the plate temperature y from the differencer 14 and outputs the integrated value z (k). A block 16 is a vectorizer that integrates the integral value z (k) from the integrator 15 and the disturbance observer 1.
Vectorized with the estimated values of the state variables x ₁ , x _{2 from} (2) (ie, generate a vector x _s (k) for calculating the switching function σ (k) in the above-mentioned equation (17)) Output. Block 17 is a multiplier with the switching matrix S shown in the above equation (21), and as shown in the equation (17), the switching matrix S
Is multiplied by the vector x _s (k) from the vectorizer 16 to determine the value of the switching function σ (k). Block 18 is a smoothing function, and || σ (k) || · s of the nonlinear control term shown in the equation (22).
Calculate a value substantially corresponding to gn [σ (k)]. The block 19 receives the calculated value of the smoothing function 8 and calculates the nonlinear control term u _nl (k) shown in the equation (22). Here, the disturbance suppression term β (k) in the nonlinear control term u _nl (k) in equation (22) is β (k) ≡0
And Blocks 20 to 22 calculate the linear control term u _l (k) in equation (22). At block 23, (22) a control input _{u (k) = u l (} k) + u nl (k) is obtained.

A.2.4 Mechanism for Stabilizing Servo System Integral Value z (k) for High-Speed Cooling Control In the control block diagram shown in FIG. 3, the supervisor 13 includes the servo system integral value z (k) as described above. A mechanism for supplying the stable value of k) to the integrator 5 is provided. As described above, the integrator 15 integrates the deviation between the plate temperature target value r input from the differentiator 14 and the plate temperature y. When the plate temperature y reaches the temperature Tc-Tm shown in FIG. Then, the integral value (z) is forcibly set to a stable value of z (k) supplied from the supervisor 13. Thereby, high-speed cooling control without hunting phenomenon is achieved.

FIG. 4 shows an operation flow of the mechanism for supplying a stable value of the integrated value z (k) of the servo system of the supervisor 13.

As shown in FIG. 4, the plate temperature y
Is not higher than the target cooling temperature Tc (for example, 23 ° C.) of the wafer shown in FIG.
s) This mechanism assumes that the plate temperature y is settled at the cooling target temperature Tc, and sets the target value r (k) of the plate temperature to a value obtained by subtracting the equilibrium point temperature 25 ° C. from the cooling target temperature Tc. (Step S2). Note that, since the controller sets the origin of the target value r (k) to the equilibrium point temperature of 25 ° C., step S2 substantially means to set the target value r (k) to the cooling target temperature Tc.

The plate temperature y is shown in FIG. 2 (of the wafer).
If the temperature is higher than the cooling target temperature Tc (for example, 23 ° C.) by, for example, 0.2 ° C. or more (No in step S1), this mechanism assumes that the wafer is placed on the cooling plate, and sets the target value r (k) of the plate temperature to The temperature at the turning point shown in FIG. 2 (that is, the value obtained by further subtracting the predetermined temperature Tm from the value obtained by subtracting the equilibrium point temperature of 25 ° C. from the cooling target temperature Tc) is set (step S3). Thereafter, when the plate temperature reaches the turning point (Yes in step S4), the mechanism
The process proceeds to step S5, z z (k) as a stable value (k) = - by calculating _{(S 2 / S 1) ×} (r (k) / Ω 01) -0.65 (28), FIG this value The signal is output to the integrator 15 as shown in FIG. In the equation (28), the first term on the right side is the value of the integral value z (k) assuming that the plate temperature y has always been the set value Tc-Tm from the beginning _. S ₂ is the first and second element values of the switching matrix S shown in equation (21),
Ω ₀₁ in the above-mentioned equation (26)

[Equation 33] This is the first (leftmost) element value of the matrix. -0.65, the second term on the right-hand side of equation (28), is an adjustment value that serves to modify the plate temperature to be slightly lower than the set value Tc-Tm in order to further stabilize the control. It is.

A.2.5 Plate Temperature Trajectory Online Optimization Mechanism for Minimum Time Cooling and Settling of Wafer Temperature The supervisor 13 shown in FIG. 3 also has a mechanism for optimizing the plate temperature trajectory online as described above. Have. That is, this optimization mechanism of the supervisor 13 sets the wafer temperature to the cooling target temperature in the shortest time in accordance with the fluctuation of the cooling water temperature (thermal disturbance from the water cooling plate) and the initial wafer temperature (thermal disturbance from the wafer). The optimal plate temperature trajectory to determine online during the process.
More specifically, this mechanism compares the history of the thermal disturbance d (k) estimated by the disturbance estimation observer 12 shown in FIG. 3 with the thermal disturbance d _c (k) from the water cooling plate and the thermal disturbance from the wafer. d _w (k), and a three-dimensionally optimum plate temperature trajectory (that is, an optimum value of the temperature Tm that determines the turning point shown in FIG. 2) is determined for each of them by the procedure shown in FIG. . Thereby, it is possible to realize the shortest time cooling settling of the wafer temperature shown in FIG.

As shown in FIG. 5, the optimizing mechanism initially sets the temperature Tm (hereinafter referred to as “height of the turning point”) to a predetermined default value (for example, 1.5 ° C.) (step S11). ). Thereafter, the plate temperature is, for example, 0.2 ° C. lower than the wafer cooling target temperature Tc (for example, 23 ° C.) shown in FIG.
(Step S12: No), and the plate temperature is in a steady state (Ye in Step S13).
s) In some cases, the mechanism considers the current state to be a state between the time when the plate temperature becomes steady state in the previous wafer cooling process and the time when the next new wafer is placed, The thermal disturbance d _c (k) from the water cooling plate is calculated as an average value of the thermal disturbance d (k) estimated by the disturbance observer (step S14). Thereafter, the plate temperature has not yet become higher than the cooling target temperature Tc (for example, 23 ° C.) by 0.2 ° C. or more (No in step S12), but the plate temperature is no longer in a steady state (No in step S13).
If this is the case, the mechanism considers the current condition to be the time when a new wafer is initially placed on the cooling plate and when the effects of thermal disturbance from the wafer have not yet appeared on the plate temperature, Thermal disturbance d _c (k) from plate
Is set to the value of the thermal disturbance d _c (k) from the water-cooled plate determined in the last step S14 immediately before (step S1).
Five).

Thereafter, the plate temperature is set to the cooling target temperature Tc.
(For example, 23 ° C.) higher than 0.2 ° C. (Step S
At 12), the mechanism considers the current state as a state after a new wafer is placed on the cooling plate and the influence of thermal disturbance from the wafer appears on the plate temperature. , Thermal disturbance from the wafer d _w (k)
Is set to the maximum value of the thermal disturbance d (k) estimated so far (step S16). Then, the mechanism proceeds to step S17, and using a predetermined calculation formula, the thermal disturbance d from the wafer
based on the current value of _w thermal disturbance d _c from the current set value of _(k) and a water-cooled plate _(k), with a predetermined formula to calculate the height Tm turning point.

The calculation formula used in step S17 is determined by trial and error through simulation and experiment, and is, for example, as shown in the following formula (29).

(Equation 34)

The height Tm of the turning point calculated in step S17 until the plate temperature reaches the turning point after the wafer is placed (while the result is No in step S18).
To maintain. When the plate temperature reaches the turning point (Yes in step S18), the process returns to the first step S11, and the height Tm of the turning point is set to a default value.

A.3 Experimental Results The performance of the sliding mode controller described above was experimentally examined. In this experiment, the wafer cooling target temperature was set to 23.0 ° C, the initial wafer temperature was changed in the range of 70 to 180 ° C, and the cooling water temperature was changed in the range of 15 to 30 ° C. By measuring the temperature at 17 points,
Wafer cooling settling time including wafer surface temperature distribution (average of wafer surface temperature distribution is 23.00 ± 0.0
The time until the temperature falls within the range of 5 [° C.] was measured. The results are shown in Table 1 below.

[Table 1]

From this table, it can be seen that, when evaluated by the average value of the in-plane temperature distribution of the wafer, the controller almost satisfies the control system design specifications shown at the beginning of this embodiment.

As described above, according to the present embodiment in which the sliding mode controller according to the present invention having adaptability and robustness to a process system having a dead time is applied to a cooling plate for a semiconductor manufacturing apparatus, the cooling water temperature and Even when the initial temperature of the wafer changes and the dynamic characteristics change significantly, a short wafer cooling settling time that almost satisfies the desired specifications can be realized without adjusting the control parameters.

B. Second Embodiment The first embodiment described above is one in which the present invention is applied to a one-input one-output cooling plate, but the second embodiment is a multi-input multi-output system. The present invention is applied to a cooling plate. FIG. 6 shows a rough sectional structure (only one side from the center) of the cooling plate of the multi-input multi-output system in the second embodiment.

The cooling plate 100 shown in FIG.
It has a circular plane shape (the left end in the figure is the center position), and its plane area is divided into a plurality of zones, for example, three zones Z1 to Z3 (of course, it may be two zones or four or more zones). . For example, the first zone Z1 is a central circular zone, the second zone Z2 is a donut-shaped zone surrounding the first zone Z1, and the third zone Z3 is an outermost donut-shaped zone surrounding the second zone Z2. It is. These zones
Z1 to Z3 are respectively provided with thermoelectric conversion modules 3-1 to 3-3 which are independent from each other in terms of electric circuit, and temperature sensors 7-1 to 7-3 for detecting plate temperature.

B.0 Control System Design Specifications The zone-divided multi-input / output system shown in FIG.
In addition, dynamic characteristics and external thermal disturbance d_z1~ D_z3Is different)
Without adjusting the control parameters.
Make the traces (temperature rise / fall trajectory, load fluctuation trajectory, etc.) the same. However
The cooling plate 100 to be controlled is located in a zone
Are designed so that mutual interference between them can be ignored.
You. In the case of temperature control, three
Plate temperatures are equal (T_z1= T_z2= T_z3) Then other
The thermal disturbance from the zone is zero (d_z12= d _z23= d_z13= 0) and
Can be considered.

B.1 Configuration of Model Reference Adaptive Control System with Integral Hyperplane Added One of a plurality of zones Z1 to Z3 shown in FIG. 6 is set as a reference zone. For the reference zone, a discrete time sliding mode control system similar to that of the first embodiment is constructed and applied. For other zones,
As described in detail below, a state error system using a reference zone as a reference model is created, and a discrete-time sliding mode model reference adaptive control system is constructed and applied. In the construction of the model reference adaptive control system, an integral term of a state error between the target model and the reference model is designed in addition to a hyperplane in order to eliminate a steady-state error.

B.2 Control System Design B.2.1 Basic Design The target system (a zone other than the reference zone) is represented by a discrete-time state equation and an output equation of the following equation (30).

(Equation 35)

On the other hand, the reference model (reference zone) is expressed by the following (3)
It is expressed by the state equation and the output equation of the equation (1).

[Equation 36]

The following equation (32) is transformed with respect to equations (30) and (31) to create a state error system.

(37)

Here, Ω _m1 X _m1 = Ω ₁ X ₁ , Ω _m2 X _m2 = Ω ₂ X ₂ ,
Assuming…

(38) Becomes Thus, the state variable x (k) of the target system and the state variable x _m (k) of the reference model are represented by a regular matrix T,

[Equation 39] In a relationship. However, due to this linear transformation, both the characteristic equation and the transfer function matrix are invariant.

Here, when the expression (30) of the target system is converted using the expression (34), the target system represented by the following expression (35) represented by a new state variable x ′ (k) is created. You.

(Equation 40)

Specifically, if x _i , x _mi ; i = 1,2, the following is obtained.

[Equation 41]

Therefore, the state error is defined as in the following equation (37).

(Equation 42)

From this, the state error system is expressed by the following (38)
It is expressed like a formula.

[Equation 43]

Here, the switching hyperplane in the error space to which the integral term of the state error between the target system and the reference model is added, assuming that the sampling interval is h [s],

[Equation 44] Given by From σ (k) = σ (k + 1) =…,

[Equation 45] Therefore, assuming that the matrix SΓ ′ is a regular matrix, the equivalent input is as follows.

[Equation 46]

The sliding mode controller is represented by the following equation (42).

[Equation 47]

B.2.2 Block Diagram FIG. 7 shows a control block diagram of the present embodiment. In FIG. 7, block 200 is a reference zone (reference model).
Is a discrete-time sliding mode controller of
The configuration is the same as that shown in FIG. Block 300
Is a discrete-time sliding mode model reference adaptive controller in a zone other than the reference zone, and (4)
It is expressed by equation 2).

In the discrete time sliding mode model reference adaptive controller 300, the block 60
To 66 is (42) a section for generating a linear control input u _lf in the expression is a part for generating a non-linear control input u _NLF shown in block 54 to 59 is (42) below.

B.2.3 Application to Cooling Plate Having Three Zones The above-described control system is divided into three zones shown in FIG. 6, and a specific cooling system having different dynamic characteristics and external heat disturbance for each zone. Apply to plate 100. In FIG.
An ideal temperature locus of a plate in a wafer cooling process using the cooling plate 100 is shown. Here, the central first zone Z1 is defined as a reference zone. As shown in FIG. 8, the second zone Z2 has a control trajectory similar to the first zone Z1 because the thermal disturbance characteristic from the wafer is similar to the central first zone Z1. In the outermost third zone Z3, the temperature rise due to thermal disturbance is reduced by the edge effect.

B.2.3.1 Modeling As described above, it is assumed that the cooling plate 100 is designed so that mutual interference between zones can be ignored. Further, as shown in FIG. 8, since the control objective is to make the plate temperatures of the respective zones equal (T _z1 = T _z2 = T _z3 ), thermal disturbances d _z12 = d _z23 = d _z13 from other zones = 0. Therefore, the dynamic characteristics of each zone were identified by treating each zone as a single input / output system.
The dynamic characteristics of the first to third zones Z1 to Z3 are respectively given, for example, by the following equations (43) to (45).

[Equation 48]

[0095] Further, with respect to thermal disturbance d _z1 size of to d _z3 also the heat transfer coefficient of d _w in equation (15) in the first embodiment λα _w S _w from the wafer to be given to each zone Z1 to Z3, 1st zone Z1
For example, it is 4.14 [% / ° C], that of the second zone Z2 is 3.70 [% / ° C], and that of the third zone Z3 is 2.00 [% / ° C].
It differs from zone to zone.

2.3.2 Control System Design Parameters The controller in the first zone Z1, which is the reference zone,
The design is performed in the same manner as in the embodiment (however, the hyperplane design uses a pole placement method to obtain an overshoot waveform). On the other hand, the controllers in the second and third zones Z2 and Z3 perform the method described in item 2 of the second embodiment. The respective design parameters and control inputs are as follows, for example.

The design parameters and control inputs of the first zone Z1 are, for example,

[Equation 49] become that way.

The design parameters and control inputs of the second zone Z2 are, for example,

[Equation 50] become that way.

The design parameters and control inputs of the third zone Z3 are, for example,

(Equation 51) become that way.

B.2.3.3 Supervisor in Second and Third Zones Regarding the third zone Z3, thermal disturbance from the wafer is much smaller than that of the first zone (reference zone) Z1, and the temperature rise is small. Immediately after the wafer is placed, the state error e (k) becomes excessive. As a result, the operation amount of the third zone Z3 immediately after the mounting of the wafer becomes excessive (the power consumption also increases). Therefore,
It is desirable to apply the following supervisor to the third zone Z3.

(Equation 52) In addition, the same supervisor can be applied to the second zone Z2.

B.3 Experiment FIG. 9 shows the result of an experiment conducted using a controller having the above-described design parameters (including the above-described supervisors in the second and third zones). In this experiment,
Wafer initial temperature is 150 ° C, cooling water temperature is 25 ° C (flow rate 3.0
[l / min]). Then, by measuring the temperature at 17 points in the wafer surface and the temperature in three zones of the plate, the settling time including the temperature distribution in the wafer surface was measured (the target wafer cooling temperature was 23.0 [° C.]). From FIG. 9, it was found that the temperature distribution of the plate caused by the large thermal disturbance from the wafer was quickly eliminated during the process. Further, although not shown in FIG.
Before reaching 3.0 [° C], it converged to ± 0.2 [° C] or less. In addition, the initial temperature of the wafer is 40 ° C, and the cooling water temperature is 25 ° C.
(Flow rate 3.0 [l / min])
The same good results as those shown in the above were obtained.

As described above, according to the second embodiment in which the present invention is applied to the cooling plate for a semiconductor manufacturing apparatus which is a multi-input / output system with little mutual interference, the difference in the dynamic characteristics of each zone and the It is possible to quickly converge the temperature distribution between the zones to a sufficiently small value without adjusting the control parameters with respect to the difference in the magnitude of the thermal disturbance applied to.

C. Third Embodiment In the first and second embodiments, the dead time is modeled by the Paddy approximation, and a discrete-time sliding mode control system is configured. However, with this approach,
The robustness cannot be further improved due to a modeling error that does not satisfy the matching condition by the Paddy approximation (chattering occurs). Therefore, in the third embodiment, the control system design method according to the present invention in which the paddy approximation error is compensated is adopted, and the robustness is further improved. Specifically, a control system is designed using a paddy approximation error-compensated disturbance observer described below.

C.1 Paddy Approximation Error-Compensated Disturbance Observer A paddy approximation error e _{pd is} obtained by converting the paddy approximation model into a discrete time system at a sampling interval h [s] in the equation (14) of the first embodiment. When configuring a disturbance observer with (k) added,

(Equation 53) Becomes Here, e _pd (k) is represented by the following equation (59) as an output of the Paddy approximation error system.

(Equation 54) here,

[Equation 55] Is obtained by converting the control target system (formula (1) of the first embodiment) into a discrete time system.

FIG. 10 shows a Paddy approximation error-compensated disturbance observer.
1 shows the configuration of the server. In FIG. 10, block 400
The Paddy approximation error-compensated disturbance observer shown in the above equation (58)
And the block 80 therein is represented by the above equation (59).
Paddy approximation error system. This paddy approximation error
Approximation error e calculated by system 80_pd(k) and control target 1
Based on the output Y (k) of 1 and shown in accordance with the above equation (58)
State variable x as₁, X _TwoAnd the disturbance d are estimated.

C.2 Sliding Mode Control System Design From the equation (3) described in the first embodiment, a sliding mode controller is designed in the same manner as in the first embodiment. It should be noted here that the sliding mode control is fundamentally different from the linear control.

[Equation 56] Instead of the state-space model consisting of

[Equation 57] Therefore, the proposed method for compensating for the Paddy approximation error in the output equation has no effect on the configuration of the sliding mode control system.

The design parameters and control inputs are as follows (60)
~ (62). However, the design of the switching hyperplane uses the pole placement method to obtain a desired transient response characteristic.

[Equation 58]

C.3 Simulation The third embodiment (sliding mode controller using a paddy approximation error-compensated disturbance observer) and the third embodiment
For the first embodiment (sliding mode controller using a disturbance observer without a paddy approximation error compensation function), a simulation was performed by giving a step-like target input r and a step-like disturbance d. The disturbance suppression term β (k) is set to β (k) ≡0 in all cases. Table 2 shows a comparison between the simulation results of the two controllers.

[Table 2]

As can be seen from Table 2, robust stability is further improved by using a paddy approximation error-compensated disturbance observer.

D. Fourth Embodiment When the paddy approximation error system (paddy approximation error compensation) used in the third embodiment is applied to an actual process, a process that is a distributed constant system is approximated by a lumped constant dead time system. Due to modeling errors, not always good enough performance is obtained. Therefore, in the fourth embodiment, the real process expression used for the paddy approximation error system is changed to a model using a finite dimensional approximation of the dead time (that is, only the paddy approximation error compensation is calculated as “first order delay + dead time , But using a finite-dimensional approximation).
Thereby, the process can be represented with higher accuracy.

The details are as follows.

That is, (5) in the third embodiment
9) equation of y _real (k), to the finite-dimensional approximation of the dead time representation. A finite dimensional approximation of the dead time is as follows.

[Equation 59]

Further, by converting the above equation (63) into a state equation and discretizing it at a sampling interval h [s],

[Equation 60] Is obtained. The new Paddy approximation error system is

[Equation 61] Becomes

E. Fifth Embodiment In the above-described first embodiment, as described above, the observer gain G performs pole placement in a simulation by trial and error. This is the same in the third embodiment.

Therefore, in the fifth embodiment, as described below, an appropriate (substantially optimum) pole of the disturbance estimation observer is obtained by the optimum pole arrangement algorithm.
Thereby, the observer gain G can be obtained.

E.1 Control System Design A control system using both the sliding mode control and the observer is configured. The control target (for example, the one given as in the equation (1)) is based on the description of the first embodiment. As can be seen, a parameter estimation uncertainty is used instead of a normal observer because the parameter uncertainty is included.

Further, in the fifth embodiment,
Not only does Paddy approximate the dead time (not only applying a first-order Paddy approximation to the dead time component of equation (1)),
2 shows an optimal pole assignment algorithm of an observer described in a discrete-time system.

E.2 Discrete Time Sliding Mode Control E.2.1 Configuration of Type 1 Servo System The target value r (k) and the output y (k) are added to the state variables of the expression representing x (k + 1) in the expression (14). The sliding mode servo control system is designed by using an expansion system to which the integral value z (k) of the difference from ()) is added.

(Equation 62) Here, the switching function σ (k) is defined as follows.

[Equation 63] The unobservable state variables x ₁ (k) and x ₂ (k) are estimated by a disturbance estimation observer.

D2.2 Design of Equivalent Control System In the sliding mode of the discrete time system, σ (k) =
From σ (k + 1) = σ (k + 2) = ・ ・ ・, the equivalent control input u _eq (k) is
If we don't consider disturbances,

[Equation 64] And the equivalent control equation is expressed by the following equation (71).

[Equation 65] The design of the switching hyperplane applies a pole arrangement method that can designate the poles λ ₁ and λ ₂ of the equivalent control system to desired characteristics.

D1.3 Design of Sliding Mode Controller The control input u (k) is represented by the following equation (72).
It is assumed that it is composed of two independent control inputs, u _eq (k) and a non-linear control input u _nl (k).

[Equation 66] Here, H _max is the maximum estimated value of the disturbance. At this time,
Conditions in which sliding mode exists

[Equation 67] To be satisfied.

FIG. 3 is a block diagram summarizing the above. The supervisor is configured to supply an appropriate integrated value z (k) when the control input u (k) becomes close to the target value r (k) even when the control input u (k) is saturated in a transient state. R (k) supplied at that time is a small real number α
(Eg, arbitrarily or set to a value deemed appropriate by some simulation)

[Equation 68] It is represented as

E.3 Discrete Time Disturbance Estimation Observer In the expression representing x (k + 1) in the expression (14), if the disturbance estimation observer is formed, the following expressions (76) to (80) are obtained.
become that way.

[Equation 69] here,

[Equation 70] Is the disturbance superimposed on the input

[Equation 71] State estimates, including

[Equation 72] Is the output estimate. Also, observer gain G
Is determined by an optimum pole arrangement algorithm described below.

E.4 Optimum Pole Assignment Algorithm for Disturbance Estimation Observer The optimum pole assignment algorithm in this embodiment is based on the real system (1) and the disturbance estimation observers (76) to (80).
Using the phase curve and the gain curve of the equation, the pole p = [p ₁ p ₂
p ₃ ] is an algorithm that finds a numerically optimal solution of ^T in a three-stage search of the following (i) to (iii). Where p
The search range of

[Equation 73] And

(I) Consideration of sensitivity to noise The search condition in the first stage is created from the viewpoint of limiting the estimation speed of the disturbance estimation observer so as not to be too high (the estimation speed of the disturbance estimation observer). Is too high, the state of the system cannot be accurately estimated due to the influence of noise or the like). Specifically, by considering the sensitivity of the switching function sigma (k) with respect to noise, using a small positive real gamma _n with (e.g., optionally or value set to a value deemed appropriate by one simulation) Thus, it is expressed as the following equation (85).

[Equation 74] Here, δ _max is the maximum value of the noise component.

(Ii) Phase shift at each frequency π / h Only poles satisfying the above equation (85) will be considered. The search condition in the second stage is created from the viewpoint of limiting the estimation speed of the disturbance estimation observer so as not to be too low. (If the estimation speed of the disturbance estimation observer is too low, And the state of the system cannot be accurately estimated). Specifically, even if the estimation speed of the disturbance estimation observer is increased (that is, even if the poles are close to the center of the unit circle in the z-region), the discrete system at each frequency π / h Phase shift

[Equation 75] And phase shift of disturbance estimation observer

[Equation 76] The fact that the absolute value of the difference from the difference does not _fall below a certain positive value ψ _min is used. Therefore, the present search condition is expressed by the following equation (86) using a certain small positive real number γ _p (for example, a value arbitrarily set to a value considered appropriate by a certain simulation). .

[Equation 77]

[0126 (iii) The consider only poles satisfying the gain above (85) and (86) below at each frequency _{1 / L ≦ ω ≦ ω g} . The search condition in the third stage is to search for an optimum one (specifically, one that can minimize the error of state estimation due to Paddy approximation) from the appropriate estimation speed of the disturbance estimation observer. It was created from the point of view. Specifically, the gain of the discretized real system near 1 / L, which is an important frequency band of the dead time system

[Equation 78] And the gain of the disturbance estimation observer

[Expression 79] Is used. Then, the pole that minimizes J is optimized. Here, ω _g is a value that depends on h and L / T.

[Equation 80]

E.5 Specific Example As a control target represented by the expression (1), for example, the following expression (8)
Consider 8).

[0128]

[Equation 81] In the above equation (88), a control system for obtaining the above-described optimum pole arrangement algorithm is designed. Here, for example, the sampling interval h = 0.05 [s].

First, a switching hyperplane is designed. The desired characteristics include poles λ1 and λ2 of the equivalent control system.
Is placed at 0.970 ± 0.023j. This allows

(Equation 82) Becomes Then, β (k) = 0.

Next, the pole of the disturbance estimation observer is obtained by the optimum pole arrangement algorithm. The design parameters in this case are as follows.

[Equation 83] With these setting parameters, the optimum pole p and the observer gain G are calculated by the above equations (81) to (87).

[Equation 84] Becomes

As described above, when the pole of the disturbance estimation observer is obtained from the optimum pole algorithm as described above, and the observer gain is obtained using the pole (design of the disturbance estimation observer), even if a paddy approximation error occurs, The state of the real system can be estimated not only in a relatively low frequency range but also in a relatively high frequency range.

Further, if the observer gain is obtained by using the poles obtained from the optimum pole algorithm as described above, it is easier to obtain the observer gain from the poles obtained by performing the pole arrangement by trial and error. Observer gain curve close to the gain curve can be obtained. That is, it is easy to design a suitable disturbance estimation observer.

Although the embodiments of the present invention have been described above, these embodiments are exemplifications for describing the present invention, and are not intended to limit the scope of the present invention only to these embodiments. The present invention can be implemented in various other forms. The temperature control of the cooling plate shown in FIGS. 1 and 6 is only an example to which the present invention is applied, and the present invention can be applied to various other process systems.

[Brief description of the drawings]

FIG. 1 is a schematic sectional view of an example of a cooling plate.

FIG. 2 shows the temperature of a wafer 5 (hereinafter referred to as “wafer temperature”) aimed at controlling the temperature of a cooling plate and the surface plate 4
FIG. 5 is a diagram showing a locus of a temporal change in the temperature (hereinafter, referred to as a plate temperature) and the input power (hereinafter, referred to as an operation amount) of the thermoelectric conversion module 3.

FIG. 3 is a block diagram of a discrete-time sliding mode control system with a disturbance observer according to one embodiment of the present invention.

FIG. 4 is a diagram showing a flow of operation of a mechanism for supplying a stable value of a servo integrated value z (k) of the supervisor 3;

FIG. 5 is a diagram showing a flow of operation of a mechanism for optimizing a plate temperature trajectory of the supervisor 3 online.

FIG. 6 is a schematic sectional view of a cooling plate of a multi-input multi-output system according to a second embodiment.

FIG. 7 shows a basic control block diagram of the second embodiment.

8 is a diagram showing an ideal temperature trajectory of the cooling plate 100 shown in FIG. 6 in a wafer cooling process of the plate.

FIG. 9 is a diagram showing an experimental result of testing the performance of the second embodiment.

FIG. 10 is a block diagram showing a configuration of a paddy approximate error compensation disturbance observer.

[Explanation of symbols]

1, 100 cooling plate (control target system) 11 control target 12 disturbance observer 13 supervisor 14 to 23 discrete-time sliding mode controller 200 discrete-time sliding mode controller for reference zone (reference system) 300 discrete-time sliding mode model reference for other zones Type adaptive controller 400 Paddy approximation error compensation disturbance observer 80 Paddy approximation error system

 ──────────────────────────────────────────────────続 き Continued on the front page F term (reference) 5H004 GA03 GA10 GA17 GB01 GB20 HA01 HB01 JA04 JA22 JB08 JB22 JB24 KA32 KA33 KA71 KA72 KA74 KB05 KC17 KC34 KC35 KC45 LA01 LA03 LA12 LA13 LA15 LA19

Claims (14)

[Claims] 1. A discrete-time sliding mode controller designed for a model of a linear transfer function representing a control target, wherein the model is a linear approximation obtained by linearly approximating a dead time element of the control target. A disturbance observer for estimating state variables and disturbances of the model from inputs and outputs of the controlled object; and estimating the state variables from given target values, outputs of the controlled object, and the disturbance observer. A discrete-time sliding mode control device for a process system having a dead time, comprising: a sliding mode calculation unit configured to calculate a control input to the control target based on the value. 2. The sliding mode operation unit includes an integrator for integrating a deviation between the target value and an output of the controlled object to calculate the control input, based on an output of the controlled object. A stable value supply mechanism that calculates a stable value for an integral value of a deviation between the target value and the output of the controlled object, and sets the output of the integrator to the stable value at a predetermined time during the process. The control device according to claim 1, further comprising: 3. The control device according to claim 1, further comprising an online optimization mechanism for optimizing the target value based on a history of the estimated value of the disturbance from the disturbance observer during the process. 4. The system according to claim 1, wherein the disturbance observer has an approximation error system for calculating an approximation error between the dead time element and a linear approximation expression obtained by linearly approximating the dead time. The control device according to claim 1, wherein the state variable and the disturbance are estimated based on an error and an input and an output of the control target. 5. The control device according to claim 1, wherein the disturbance observer has a gain determined by a predetermined optimum pole assignment algorithm. 6. A discrete time sliding mode control device designed for a model representing one reference system selected from a plurality of single input / output systems constituting a multi-input multi-output control target, A discrete-time sliding mode controller designed for a model representing each system other than the reference system in the plurality of single input / output systems, and a discrete-time sliding mode controller for each of the other systems Is a discrete time sliding mode control device for a multi-input multi-output process system, which is a model reference type control device using the reference system model as a reference model. 7. A discrete-time sliding mode method designed for a model of a linear transfer function representing a control target, wherein the model is a linear approximation formula that linearly approximates a dead time element of the control target. A disturbance observing step of estimating a state variable and a disturbance of the model from an input and an output of the controlled object, and a given target value, an output of the controlled object and the state variable from the disturbance observing step. A discrete mode sliding mode control method for a process system having a dead time, comprising: a sliding mode calculating step of calculating a control input to the control target based on the estimated value. 8. A step of performing discrete-time sliding mode control on a model representing one reference system selected from a plurality of single input / output systems constituting a multi-input multi-output control target; Performing discrete-time sliding mode control on a model representing each system other than the reference system in the single input / output system of the above, and discrete-time sliding mode control on each of the other systems. Performing a discrete-time sliding mode control method on a multi-input multi-output process system that controls a model reference form using the reference system model as a reference model. 9. A discrete-time sliding mode method designed for a model of a linear transfer function representing a control target, wherein the model is a linear approximation formula that linearly approximates a dead time element of the control target. A disturbance observing step of estimating a state variable and a disturbance of the model from an input and an output of the controlled object, and a given target value, an output of the controlled object and the state variable from the disturbance observing step. A computer program for causing a computer to execute a discrete time sliding mode control method for a process system having a dead time, comprising: a sliding mode calculation step of calculating a control input to the control target based on the estimated value. 10. A discrete-time sliding mode control for a model representing one reference system selected from a plurality of single input / output systems constituting a multi-input multi-output control target; Performing discrete-time sliding mode control on a model representing each system other than the reference system in the single input / output system of the above, and discrete-time sliding mode control on each of the other systems. A computer program for causing a computer to execute a discrete-time sliding mode control method for a process system of a multi-input multi-output system that controls a model reference form using the model of the reference system as a reference model. 11. A model of a linear transfer function representing a controlled object, in which a state variable and a disturbance of a model including a linear approximation obtained by linearly approximating a dead time element of the controlled object are disturbed. An observer design method comprising: calculating a pole of a disturbance observer estimated from an input and an output using a predetermined optimum pole allocation algorithm; and determining a gain of the disturbance observer using the calculated pole. 12. A model of a linear transfer function representing a controlled object, in which a state variable and a disturbance of a model including a linear approximation obtained by linearly approximating a dead time element of the controlled object are disturbed. A computer program for causing a computer to execute a calculation step of calculating a pole of a disturbance observer estimated from an input and an output. 13. The computer program according to claim 12, wherein the calculating step calculates the pole based on a condition created from the viewpoint of limiting the estimated speed of the disturbance observer. 14. The computer program according to claim 12, further comprising causing a computer to execute a step of determining a gain of the disturbance observer using the calculated pole.