JPH0861122A - Method and device for controlling engine - Google Patents

Abstract

PURPOSE: To enable the engine control stabler than the PI control by performing the filter processing with a time-lag of first order to the controlled variable to an object to be controlled. CONSTITUTION: In the case where x1 means torque deviation, x1 <(1)> means time differential, c means coefficient, ϕ means gain and Kf means dither signal, the sliding line constant S is obtained by a computing unit 3 with the computing S=cx1 +x1 <(1)> , and the gain ϕ is switched to α and β in response to the code of S.x1 so that S=0 by a gain unit 7. Code of the dither signal is switched by a variable switching unit 11 in response to the code of S, and while in the case where |x1 |<emin , Kf =0, and the filter processing with a time-lag of first order is performed by a filter unit 13 so as to obtain the manipulated variable (u) to an object 60 to be controlled.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an engine control method and apparatus including a throttle actuator as a control target and introducing a sliding mode control (SM control) in an engine test or the like.

[0002]

[Prior art]

<Symbols> Of the symbols appearing in the specification and drawings, the lower case s is the Laplace operator, and the upper case S is the sliding line constant. When the variables are generalized to A, the derivative of A with respect to time t (dA / d
The t) represents the A ^(1), 2-order derivative with respect to time t A a (d ² A / dt ²⁾ indicates the A ^(2), expressed as ∫A and differential (∫Adt) with respect to time t of the A. Further, when the deviation between the control command and the control amount is x ₁ , x ₁ ⁽¹⁾ [= dx ₁ / d
t] is expressed as x _2, and x ₁ ⁽²⁾ [= d ² x ₁ / dt ² ] is x ₂
Sometimes referred to as ⁽¹⁾ .

<Outline of Engine Test> In the engine test, opening and closing of a throttle valve of the engine is operated by controlling a throttle actuator by an engine control unit, and intake pressure, torque, and rotation speed (rotation speed) at that time are controlled.
And so on. Recently, due to global environmental problems, NOx and S
Ox regulations have become stricter, and gas emitted from engines has become a problem. Therefore, the sophistication of the engine performance is important, and along with this, the sophistication of the device for testing the engine is required.

Of the engine tests, the test for measuring exhaust gas is carried out by operating the engine by changing the torque and the rotational speed of the target engine in a predetermined pattern. As described above, the operation of the engine is performed by controlling the throttle actuator by the engine control device to open and close the throttle valve.

For example, when torque is controlled by an engine control device, a dynamometer connected to the engine.
While controlling the rotation speed to a target value with, the engine controller controls the throttle actuator to open and close the throttle valve to control the torque to the target value. On the contrary, when controlling the rotation speed with the engine control device, while controlling the torque with the dynamometer to the target value, the engine control device controls the throttle actuator to open and close the throttle valve to set the rotation speed to the target value. Control.

<Conventional Engine Control Device> Conventionally, an engine control device to which PI (proportional integral) control is mainly applied is used. FIG. 11 is a diagram showing a configuration example of this type of engine control device, and FIG. 12 is a block diagram of a control system.

A control target 60 of the engine control device 50 includes a throttle actuator 70, and a throttle valve 81 of an engine 80 is connected to the throttle actuator 70 via a wire 82 as described later.
A dynamometer 90 is connected to the engine 80. The throttle actuator 70 includes a motor 71 such as an AC servo motor, a gear 72 for reducing the rotation of the motor 71, a clutch 73 provided between the reduction gear 72 and the motor 71, and a pulley 74 connected to the reduction gear 72. . One end of a wire 82 is connected to the throttle valve 81 of the engine 80, and the other end of the wire 82 is wound around a pulley 74 of the throttle actuator 70. The wire 82 is passed through and supported by the outer 83. In the figure,
Reference numeral 84 is a spring for returning the throttle valve 81 to the initial state (throttle opening 0%). Therefore, the motor 71
The rotation of the pulley 74 rotates the wire 82 to wind or rewind the wire 82, thereby opening and closing the throttle valve 81.

In order to detect the engine torque T _or for feedback, the engine 80 and the dynamo 90 are used.
A torque detector 54 is provided between and. Further, since it is necessary to know the throttle opening θ of the throttle valve 81 for feedback, the throttle actuator 7
The zero pulley 74 is provided with a gear 55 to detect the actuator position, and this is used as a pseudo throttle opening θ.

The engine control unit 50 comprises a throttle actuator position command calculation unit 51, a throttle actuator position control unit 52, and a driver unit 53 for the motor 71. The calculation unit 51, as shown in FIG.
Deviation between torque command T _or ^* and current torque T _or x ₁ (= T
_or ^* from -T _or), to create a throttle actuator position command theta ^* by the PI control, it gives the control unit 52. As shown in FIG. 12, the control unit 52 creates an actuator speed command ω ^* by P (proportional) control from the deviation (θ ^* −θ) between the throttle actuator position command θ ^* and the current throttle actuator position θ. A motor control signal 56 is created by PI control from the deviation (ω ^* −ω) between the actuator speed command ω ^* and the actuator speed ω detected by the sensor, and is given to the driver 53. The driver 53 applies a current to the motor 71 according to the motor control signal 56 to rotate the motor 71.

Accordingly, in the conventional engine control device 50 shown in FIG. 11, when the amount of control the torque of the engine 80, the torque command T _or ^* and the current torque T _or the deviation (x ₁ = T _or ^* The throttle actuator position command θ ^* such that −T _or ) becomes zero is created by PI control, and the deviation (θ ^* −θ) between the throttle actuator position command θ ^* and the current throttle actuator position θ is zero. Such a motor control signal 56 is generated by P control and PI control, and the throttle actuator 70 is controlled via the driver 53.

In FIG. 12, AΘR is an actuator position control system, ASR is an actuator speed control system,
ATR is an engine torque control system. Further, K _T is a motor torque constant, 1 / J _s is a constant based on the total inertia of the rotating portion of the throttle actuator 70, and 1 / s is an integral element representing the conversion from the actuator speed ω to the throttle opening θ.

[0012]

However, the throttle actuator 70, the throttle valve 81, and the wire 82 directly connecting them have mechanically non-linear elements such as hysteresis elements and rattling elements, and mechanical friction. , These are disturbances to the control system. In addition, engine characteristics also change and are diverse.

Therefore, in the conventional engine control device 50 mainly for PI control, the control may be in an unstable state or a limit cycle state. That is, the controlled object 6
Since the characteristic of 0 can be expressed as shown in FIG. 13, when the hysteresis element of the wire 82 is large, a control response example as shown in FIG. 14 is obtained, and a hunting phenomenon occurs and it is unstable. FIG. 15 shows a control response example when the hysteresis element of the wire 82 is small.

In view of the above-mentioned problems of the prior art mainly on PI control, the present invention introduces a sliding mode control to provide a stable control response to hysteresis elements, rattling elements, and various engine characteristics. It is an object of the present invention to provide an engine control method and device capable of obtaining the above.

[0015]

According to a first aspect of the present invention, there is provided an engine control device comprising: a throttle actuator as a control object; and a gain for control of the control object. Variably controlled so that the sliding line constant of (1) goes to zero; and the operation amount for the controlled object is subjected to first-order lag filtering. An engine control method according to a second aspect of the present invention is an engine control method including a throttle actuator as a control target: variably controlling a gain for control of the control target such that a sliding line constant of the control target is directed to zero. Adding a dither signal to the operation amount for the controlled object so as to suppress a steady deviation due to disturbance;
Stopping the addition of the dither signal when the control deviation is within a permissible error range. Furthermore,
An engine control method according to a third aspect of the present invention is an engine control method including a throttle actuator as a control target: variably controlling a gain for control of the control target so that a sliding line constant of the control target is directed to zero; The sliding line constant is composed of a component proportional to the control deviation, a component proportional to the time derivative of the control deviation, and a component proportional to the time integral of the control deviation;
It is characterized by including. Further, in the engine control method according to the fourth aspect of the present invention, in addition to the third aspect of the present invention, a dither signal is added to an operation amount for the controlled object so as to suppress a steady deviation due to disturbance; Stop the addition when the control deviation is within the allowable error range;
Filtering the operation amount for the controlled object with a primary delay.

According to a fifth aspect of the present invention, there is provided an engine control device including a throttle actuator as a control object, wherein the throttle actuator transfer function is 1 / (1 + sT ₁ ) and the engine transfer function is 1 / (1 + sT ₂ ), c is 0 <c <(T ₁ + T
_{2) / (T 1 T 2} ), the deviation between the control commands the x ₁ L ^* and the controlled variable L, x ^{_{1 (1)}} the time differential of the deviation x _1, gain Φ for deviations x _1, the alpha alpha> _{c (T 1 + T 2)} -T 1 T 2 c 2 -
1. When β is β <c (T ₁ + T ₂ ) −T ₁ T ₂ c ² −1 and K _f is a dither signal value: a deviation x ₁ between the control command L ^* and the current control amount L is calculated. Means; a means for obtaining the sliding line constant S from the deviation x ₁ and a predetermined coefficient c by the operation S = c · x ₁ + x ₁ ⁽¹⁾ ; a product x of the deviation x ₁ and the sliding line constant S A means for obtaining ₁ · S; the positive / negative of the product x ₁ · S is judged, and the gain Φ is set to x ₁ · S
A means for switching to a predetermined value α when 0 and a predetermined value β when x ₁ · S <0; and a gain Φ multiplied by the torque deviation x ₁ and Φ · x ₁ being _one of the manipulated variables. Means to do;
Determining the sign of sliding line constant S, a dither signal value to a K _f when the S> 0, when the S <0 switched -K _f, with one of K _f · sign (S) of the manipulated variable Means; control command L ^* and the manipulated variable Φ · x ₁ and K _f · sign
Means the final control u for the control target to the basic manipulated variable u _B performs a filtering process of first order lag;; (S) and the added means for obtaining the basic manipulated variable u _B in advance with the deviation x ₁ By comparing with the defined allowable error e _min , -e _min <x ₁ <
and a means for making the dither signal value K _f zero when e _min ;
It is characterized by including.

An engine control apparatus according to a sixth aspect of the present invention is an engine control apparatus including a throttle actuator as a control target, wherein a transfer function of the throttle actuator is 1
/ (1 + sT ₁ ), the transfer function of the engine is 1 / (1 + s
T ₂ ), 2ξω _n is 2ξω _n <(T ₁ + T ₂ ) / (T
₁ T ₂ ), x ₁ is the deviation between the control command L ^* and the controlled variable L, x ₁
⁽¹⁾ the time differential of the deviation x _1, the time integral of the deviation x ₁ to ∫X _1, gain [Phi ₁ for deviation x _1, integrating the Φ ₂ ∫x ₁
, The gain α ₁ is α ₁ > [(T ₁ + T ₂ ) −2ξω _n
T ₁ T ₂ ] 2ξω _n −1 + T ₁ T ₂ ω _n ² , β ₁ is β ₁ <
_{[(T 1 + T 2)} -2ξω n T 1 T 2] 2ξω n -1 + T 1 T 2
_Let ω _n ² and α ₂ be α ₂ > (T ₁ + T ₂ ) ω _n ² -2 ω ω _n ³ T
₁ T ₂ , β ₂ β ₂ <(T ₁ + T ₂ ) ω _n ² −2 ω ω _n ³ T ₁ T
₂ , when K _f is a dither signal value: means for obtaining a deviation x ₁ between the control command L ^* and the control amount L; S = x from the deviation x ₁ and the predetermined coefficients 2ξω _n and ω _n ^2. ₁ ⁽¹⁾ +2 ξ
means for determining the deviation x ₁ and the product S · x ₁ with sliding line constant S;; means and for determining the ^{_{ω n x 1 + ω n 2}} ∫x 1 comprising sliding line constant S by calculating the product S · x ₁
Positive and negative determination of the gain [Phi ₁ to the value alpha ₁ a predetermined when the S · x _1> 0, and means for switching to a value beta ₁ a predetermined when the S · x ₁ <0; gain [Phi ₁ Means to multiply deviation x ₁ by Φ · x ₁ as _one of the manipulated variables; and means to obtain product S · ∫x ₁ of integral ∫x _{1 of} deviation and sliding line constant S; and product S · ∫ The positive or negative of x ₁ is determined, and the gain Φ ₂ is set to a predetermined value α ₂ when S · ∫x ₁ > 0,
A means for switching to a predetermined value β ₂ when S · ∫x ₁ <0; a gain Φ ₂ is multiplied by the deviation integral ∫x ₁ , and Φ ₂
・ Means for making ∫ x _{1 one} of the manipulated variables; determining whether the sliding line constant S is positive or negative, and switching the dither signal value to K _f when S> 0 and to -K _f when S <0, K _f
・ Means for making sign (S) one of the manipulated variables; control command L
^* And the manipulated variables Φ ₁ · x ₁ , Φ ₂ · ∫ x ₁ and K _f · sign
Means for adding (S) to obtain a manipulated variable for the controlled object.

The seventh invention is, in addition to the sixth invention, a control command L ^* and manipulated variables Φ ₁ · x ₁ , Φ ₂ · ∫x ₁ and K _f · sig.
a means for filtering the operation amount obtained by adding n (S) to a final operation amount by a first-order lag filtering; the deviation x
₁ is compared with a predetermined allowable error e _min, and −e _min <
and a means for making the dither signal value K _f zero when x ₁ <e _min .

[0019]

Since the present invention is basically based on the sliding mode control, it is possible to stably control a controlled object including a backlash element and a hysteresis element with a small overshoot amount. In particular, chattering can be suppressed by performing a filter process with a first-order delay on the operation amount for the controlled object. Further, chattering can be suppressed by setting the dither signal added to the manipulated variable to zero according to the control deviation. By suppressing such chattering, it is possible to mitigate the adverse effect on the control caused by a change with time or a failure of the mechanical system included in the control target. Furthermore, by including a component proportional to the control deviation in the sliding line constant, a component proportional to the time derivative thereof, and a component proportional to the time integration, a steady deviation does not occur even if the dither signal is reduced.

<Principle of Sliding Mode Control with S = c · x ₁ + x ₁ ⁽¹⁾ > Referring to FIG. 2, a sliding mode using S = c · x ₁ + x ₁ ⁽¹⁾ as a sliding line constant S The principle of control will be briefly described. Generally, there is a deviation x ₁ between the control command L ^* and the control amount L, and there is a relation of x ₁ = L ^* −L. At this time, the differential deviation x ₁ the deviation x ₁ obtained by differentiating with respect to time _{^{t (1) [= dx 1}} / d
The relation between t] and the original deviation x ₁ can be represented by a phase plane as shown in FIG.

In the phase plane shown in FIG. 2, (x ₁ ,
A point satisfying x ₁ ⁽¹⁾ ) = (0,0) is in a stable state without a steady deviation. Therefore, the point (x ₁ , x ₁ ⁽¹⁾ ) is c · x
_It is conceivable that the control asymptotically moves to the stable state (0, 0) along the line ₁ + x ₁ ⁽¹⁾ = 0. Compared with the conventional PI control, when the controlled object includes backlash or hysteresis, , Control is stabilized. However, c> 0. That is, the sliding line constant S is set to S = c · x ₁ + x ₁
^It may be detected as ⁽¹⁾ and controlled so as to move toward S = c · x ₁ + x ₁ ⁽¹⁾ = 0. This is the sliding mode control, and the gain Φ for the deviation x ₁ is switched according to the sliding line constant S. In addition, a dither signal is added to the manipulated variable to suppress the steady-state deviation due to disturbance,
The value K _f is switched between positive and negative depending on the sliding line constant S.

For example, when the sliding line constant S is larger than zero on the phase plane shown in FIG.
Control so that the sliding line constant S is directed to a region smaller than zero, that is, a differential sliding line constant S obtained by differentiating the sliding line constant S with respect to time t.
⁽¹⁾ Gain Φ so that [= dS / dt] is S ⁽¹⁾ <0
_If the switching control of the dither signal value K _f is performed, the sliding line constant S becomes stable.

On the other hand, when the sliding line constant S is in a region smaller than zero on the phase plane shown in FIG. 2, control is performed so that the sliding line constant S is larger than zero, that is, the differential sliding line constant S.
⁽¹⁾ Gain Φ so that [= dS / dt] is S ⁽¹⁾ > 0
_If the switching control of the dither signal value K _f is performed, the sliding line constant S becomes stable.

Therefore, in the sliding mode control,
The control represented by the following equation (1) is performed so as to satisfy the above two conditions.

[0025]

[Equation 1]

<Error System of Controlled Object> As shown in FIG. 3, the characteristics of the throttle actuator 70 and the engine 80, which are the controlled objects 60 of the engine control device 1, are set to the first-order delay systems 1 / (1 + sT ₁ ) and 1 / (, respectively). When modeled by 1 + sT ₂ ), the error system of the controlled object 60 is expressed by the following equation (2). The reason is as follows. Note that the lowercase letter s is the Laplace operator, T ₁ and T ₂ are the time constants, u is the control input (operation amount) to the controlled object 60, x ₂ =
x ₁ ⁽¹⁾ , x ₂ ⁽¹⁾ = dx ₁ ⁽¹⁾ / dt = d ² x ₁ / dt ² .

[0027]

[Equation 2]

First, the transfer function L / u from the control input u of the controlled object 60 to the controlled variable L is expressed by the following equation (3).

[0029]

L / u = [1 / (1 + sT ₁ )] [1 / (1 + sT ₂ )] = 1 / [T ₁ T ₂ s ² + (T ₁ T ₂ ) s + 1] (Equation 3)

Now, let the state variable in the transfer function L / u be x
= L, it is expressed by the following equation (4), so the control amount L
L ^{(2) obtained} by second-order differentiating with respect to time t is expressed by the following equation (7) by L ^{(1) obtained} by differentiating the control amount L with respect to time and the control input u by using the Laplace transform theorem. .

[0031]

X = L = u / [T ₁ T ₂ s ² + (T ₁ + T ₂ ) s + 1] Equation (4)

[Formula 5] L ⁽¹⁾ = s · u / [T ₁ T ₂ s ² + (T ₁ + T ₂ ) s + 1] Equation (5)

## EQU6 ## u = L [T ₁ T ₂ s ² + (T ₁ + T ₂ ) s + 1] Equation (6)

[Formula 7] L ⁽²⁾ = s ² · u / [T ₁ T ₂ s ² ＋ (T ₁ + T ₂ ) s + 1) = (T ₁ T ₂ s ² ＋ (T ₁ + T ₂ ) s + 1) / (T ₁ T ₂ ) ・ u / T ₁ T ₂ s ² ＋ (T ₁ ＋ T ₂ ) s ＋ 1 − (T ₁ ＋ T ₂ ) / (T ₁ T ₂ ) ・ s ・ u / T ₁ T ₂ s ² ＋ (T _{1 + T 2) s + 1 -} [1 / (T 1 T 2)] · u / [T 1 T 2 s 2 + (T 1 + T 2) s + 1 = - [(T 1 + T 2) / (T 1 T 2)]・ L ⁽¹⁾ −L / (T ₁ T ₂ ) + u / (T ₁ T ₂ ) ... Formula (7)

[0032] Then the state variables x ₁ when the state variable x is changed, is represented by x ₁ = L ^* -L, the derivative with respect to time t x ₁ ⁽¹⁾ is x ₁ represented by the following formula (8) Be done. Furthermore, x ₁
⁽¹⁾ is the state variable x ₂ , and this state variable x ₂ is the time t
X ₂ ⁽¹⁾ differentiated with respect to is expressed by the following expression (9) from the expression (7). Therefore, from these equations (8) and (9), it can be seen that the above equation (2) represents the error system.

[0033]

## EQU00008 ## x ₁ ⁽¹⁾ = -L ⁽¹⁾ = x ₂ ... Expression (8)

[Formula 9] x ₂ ⁽¹⁾ = -L ⁽²⁾ = (T ₁ + T ₂ ) / (T ₁ T ₂ )] L ⁽¹⁾ + L (T ₁ T ₂ ) -u / (T ₁ T _{2 ) = - (T 1 + T} 2) / (T 1 T 2)] · x 2 - (x 1 -L *) / (T 1 T 2) -u / (T 1 T 2) ...... (9)

FIG. 4 shows a system in which the controlled object 60 in FIG. 3 is replaced by the error system represented by the above equation (2).

<Restrictions in Sliding Mode Control> Next, the previous equation (1) representing the sliding mode control is given.
think about. Differential sliding line constant S ⁽¹⁾
X ₂ = x ₁ ⁽¹⁾ = S−c · x ₁ is used to calculate
Moreover, as the control input u, u = Φ · x ₁ + K _f · sign
By substituting (S), the following equation (10) is obtained using the equation (2) of the error system.

[0036]

[Equation 10] S ⁽¹⁾ = c · x ₁ ⁽¹⁾ + x ₁ ⁽²⁾ = c · x ₁ ⁽¹⁾ + x ₂ ⁽¹⁾ = c · x ₂ − (T ₁ + T ₂ ) / (T ₁ + T ₂ ) ・ x ₂ − (x ₁ −L ^* ) / (T ₁ T ₂ ) − [Φ · x ₁ + K _f · sign (S)] / (T ₁ T ₂ ) = [c− (T ₁ + T ₂ ) / (T ₁ + T ₂ ) (S−c ・ x ₁ ) − (x ₁ −L ^* ) / (T ₁ T ₂ ) − [Φ × x ₁ + K _f · sign (S)] / (T _{1 T 2) = S [c- (} T 1 + T 2) / (T 1 T 2) -x 1 [c 2 -c (T 1 + T 2) / (T 1 T 2) + 1 / (T 1 T 2) _{+ Φ / (T 1 T 2} )] - [K f · sign (S) -L *] / (T 1 T 2) ...... (10)

Therefore, S · S ⁽¹⁾ is given by the following equation (11).

[0038]

[Equation 11] S · S ⁽¹⁾ = S ² [c− (T ₁ + T ₂ ) / (T ₁ T ₂ ) −x ₁ · S c ² −c (T ₁ + T ₂ ) / (T ₁ T ₂ ) + 1 / (T ₁ T ₂ ) + Φ / (T ₁ T ₂ ) −SK _f · sign (S) −L ^* ] …… Equation (11)

To satisfy the condition S · S ⁽¹⁾ <0,
From Expression (11), it is sufficient to satisfy the following conditions 1 to. c <(T ₁ + T ₂ ) / (T ₁ T ₂ ). When x ₁ · S> 0, Φ = α> c (T ₁ + T ₂ ) −
T ₁ T ₂ c ² −1. When x ₁ · S <0, Φ = β <c (T ₁ + T ₂ ) −
T ₁ T ₂ c ² −1. K _f > | L ^* | _max , that is, the dither signal value K _f is larger than the maximum absolute value of the control command L ^* . When S> 0, K _f · sign (S) = + K _f ,
Be _{K f - K f · sign (} S) = in the case of S <0.

<Problems and Countermeasures when u = Φ · x ₁ + K _f · sign (S)> If only Φ · x ₁ + K _f · sign (S) is the control input u to the controlled object 60, sliding Since the gain Φ switches to α and β depending on the sign of the mode control state x ₁ · S, chattering occurs. Further, since the dither signal value K _f for suppressing disturbance is switched between positive and negative (+ K _f and −K _f ) depending on the sign of the sliding line constant S, chattering increases. Since _Kf > | L ^* | _max , this tendency is strong.

Therefore, the occurrence of chattering is suppressed by the following measures (i) to (iii). (I) The control command L ^* is added to the manipulated variable (control input) in a feedforward manner, and u _B = Φ · x ₁ + K _f · sign
(S) + L ^* is the basic manipulated variable. As a result, the third term on the right side of the equation (11) is only −S · K _f · sign (S), and K _f can be a small value such that K _f > 0.
Chattering is alleviated. (Ii) Further, the basic operation amount u _B is subjected to a filter process with a first-order delay to obtain the final operation amount u. This makes it difficult for the manipulated variable u to change with respect to the switching of the gain Φ and the sign change of the dither signal value K _f , and chattering is further alleviated. (iii) Further, when the absolute value of the control deviation x ₁ (= L ^* -L) is less than the predetermined allowable error _emin , the dither signal value K _{f is set} to K.
Change from _f > 0 to _Kf = 0. This further reduces chattering near the stable state (0,0) on the phase plane shown in FIG.

[0042] The sliding line constants S described previously ^{_{<S = x 1 (1)}} + 2ξω n x 1 + ω n 2 ∫x 1 principle of the sliding mode control _{to> S = c · x 1 +} x 1 (1) and In the above control, a steady deviation of T ₁ T ₂ / (1 + Φ) occurs when K _f = 0. That is, the control deviation x with respect to the disturbance f _d
1 (= L ^* −L), where e = x ₁ , the following equation (14) is obtained from the equation (2) of the error system by the following derivation process.
It is represented by. However, u = Φ · e + K _f · sign (S) +
L ^* , lowercase s is the Laplace operator, e ⁽¹⁾ = se, e
⁽²⁾ = s ² e.

[0043]

Equation 12] ^{e (2) = - (T} 1 + T 2) / (T 1 T 2) e (1) - 1 / (T 1 T 2) e- 1 / (T 1 T 2) u + 1 / (T ₁ T ₂ ) L ^* ＋ f _d …… Equation (12)

[Equation 13] e [s ² + s (T ₁ + T ₂ ) / (T ₁ T ₂ ) + 1 / (T ₁ T ₂ ) = − 1 / (T ₁ T ₂ ) (Φ · e + K _f · sign (S) ＋ L ^* ) ＋ 1 / (T ₁ T ₂ ) L ^* ＋ f _d …… Equation (13)

[Equation 14] e = -K _f · sign (S) / (T ₁ T ₂ ) + f _d / s ² + s (T ₁ + T ₂ ) / (T ₁ T ₂ ) + (1 + Φ) / (T ₁ T ₂ ) ... Formula (14)

In the equation (14), if K _f = 0,
The error for the disturbance f _d is T ₁ T ₂ / (1 + Φ) according to the following equation (15) from the Laplace final value theorem in consideration of the step disturbance f _dm / s. However, the magnitude of the disturbance is normalized so that f _dm = 1.

[0045]

(Equation 15)

To eliminate this steady-state deviation T ₁ T ₂ / (1 + Φ), a dither signal of ± K _f (K _f > 0) is necessary, which was a factor of increasing chattering as described above.

Therefore, the control deviation x ₁ and its time derivative x ₁
^In addition to ⁽¹⁾ , by introducing an integral deviation ∫x ₁ (= ∫x ₁ dt) obtained by integrating the control deviation x ₁ with respect to time t, it is possible to express these relationships in a three-dimensional phase space as shown in FIG. You can

Then, consider the secondary vibration type in the phase space of FIG.
S = x₁ ⁽¹⁾+ 2ξω_nx₁+ Ω _n ²∫x₁The slide
It is detected as the swing line constant S, and this line is S = x
₁ ⁽¹⁾+ 2ξω_nx₁+ Ω_n ²∫x₁Control to go to = 0
Deviation x₁Gain for₁And its integral deviation ∫x₁Against
Gain Φ₂Switch between and. This allows the dither signal
Value K_fIs K_fEven if = 0, the disturbance f_dStationary bias for
The difference does not occur. The reason for this and the coefficient 2ξω
_nCondition, gain Φ₁And Φ₂The switching conditions of will be described.

<Regarding 2ξω _n , Φ ₁ and Φ ₂ > S · S ^{(1) in the} above-mentioned sliding mode control formula ^{(1)
_{Is, S = x 1 (1)}} + 2ξω n since it is ^{_{x 1 + ω n 2 ∫x 1}} , x 1 (2) = x 2 (1), x 1 (1) = it is x ₂ and Equation Considering (9), the following expression (16) is obtained.

[0050]

[Expression 16] S · S ⁽¹⁾ = S · d (x ₁ ⁽¹⁾ ＋2 ξω _n x ₁ ＋ ω _n ² ∫ x ₁ ) / dt = S ・ x ₁ ⁽²⁾ ＋2 ξω _n x ₁ ⁽¹⁾ + ω _n ² x ₁ = S ・-(T ₁ + T ₂ ) / (T ₁ T ₂ ) x ₂ − 1 / (T ₁ T ₂ ) x ₁ + 1 / (T ₁ T ₂ ) L ^* − 1 / (T ₁ + T ₂ ) u + 2ξω _n x ₂ + ω _n ² x ₁ ] = S ・-(T ₁ + T ₂ ) / (T ₁ T ₂ ) x ₂ +2 ξω _n x ₂ −1 / (T ₁ T ₂ ) x ₁ + ω _n ² x ₁ − 1 / (T ₁ T ₂ ) u + 1 / (T ₁ T ₂ ) L ^* ] …… Equation (16)

From equation (16), x ₂ = S-2ξω _n x ₁ −ω
_n ² ∫ x ₁ (= x ₁ ⁽¹⁾ ), and u = Φ ₁ ·
Considering x ₁ + Φ ₂ · ∫x ₁ + K _f · sign (S) + L ^* , the following equation (17) is obtained. Note that L ^* is the equation (16)
In order to compensate the term [1 / (T ₁ T ₂ )] L ^{* in} a feedforward manner, the manipulated variable u is added.

[0052]

[Expression 17] S · S ⁽¹⁾ = S · − (T ₁ + T ₂ ) / (T ₁ T ₂ ) + 2ξω _n (S−2ξω _n x ₁ −ω _n ² ∫ x ₁ ) + −1 / ( T ₁ T ₂ ) ＋ ω _n ² x ₁ − 1 / (T ₁ T ₂ ) u + 1 / (T ₁ T ₂ ) L ^* ] = S ・ − (T ₁ + T ₂ ) / (T ₁ T ₂ ) + 2ξω _{n (S-2ξω n x 1} -ω n 2 ∫x 1) + -1 / (T 1 T 2) + ω n 2 x 1 - 1 / (T 1 T 2) (Φ 1 · x 1 + Φ 2 · ∫ x ₁ ＋ K _f・ sign (S) ＋ L ^* ) + 1 / (T ₁ T ₂ ) L ^* ＝ [− (T ₁ + T ₂ ) / (T ₁ + T ₂ ) ＋2 ξω _n S ² + − (T ₁ + T ₂ ) / (T ₁ T ₂ ) ＋ 2ξω _n (−2ξω _n ) ＋ −1 / (T ₁ T ₂ ) ＋ ω _n ² −Φ ₁ / (T ₁ T ₂ ) S ・ x ₁ ＋ − (T ₁ + T ₂ ) / (T ₁ T ₂ ) +2 ξω _n (−ω _n ² ) −Φ ₂ / (T ₁ T ₂ ) S ・ ∫x ₁ − K _f・ sign (S) / (T ₁ T ₂ ) S …… Formula (17)

From the equation (17), in order to satisfy S · S ⁽¹⁾ <0, it is sufficient to satisfy the following conditions ^{(1) to (3)} . From the term of S ² , 2ξω _n <(T ₁ + T ₂ ) / (T
₁ T ₂ ). As long as this holds, ω _n ² is arbitrary. Φ ₁ = α ₁ in the case of than the term of the _{S · x 1 S · x 1} >0>
_{[(T 1 + T 2)} -2ξω n T 1 T 2] 2ξω n -1 + T 1 T 2
Be ω _n ² . When S · x ₁ <0, Φ ₁ = β ₁ <[(T ₁ + T ₂ ).
_{-2ξω n T 1 T 2] 2ξω} n -1 + T 1 T 2 ω n be ^2. From S · ∫x ₁ term, if S · ∫x ₁ > 0, Φ ₂ =
α ₂ > (T ₁ + T ₂ ) ω _n ² −2 ξω _n ³ T ₁ T ₂ . When S · ∫x ₁ <0, Φ ₂ = β ₂ <[(T ₁ +
T ^₂₎ ω _{n 2} be a -2ξω _n ³ T ₁ T _2. From the term of S, if S> 0, then K _f · sigh (S)> 0
That is, if + K _f and S <0, then K _f · sign (S) <0, that is, −
K _f , However, if the allowable error is e _min, and if | x ₁ | <e _min , then K _f = 0.

<Regarding Steady State Deviation> The error system of the controlled object 60 when the disturbance f _d is added is expressed by the above equation (2).
Since it is sufficient to add the term of the disturbance f _d to, the following expression (18) is given.

[0055]

(Equation 18)

U = Φ₁・ X₁+ Φ₂・ ∫x₁+ K_f・ Sign
(S) + L^*And using Laplace's theorem,
From the error system of equation (18), the disturbance f_dControl over
Deviation x₁ Is e = x₁Then, through the following derivation process,
It is expressed by equation (22).

[0057]

[Number 19] ^{e (2) = - (T} 1 + T 2) / (T 1 T 2) e (1) - 1 / (T 1 T 2) e- 1 / (T 1 T 2) u + 1 / (T ₁ T ₂ ) L ^* + f _d …… Equation (19)

[0058]

[Equation 20] e s ² + s (T ₁ + T ₂ ) / (T ₁ T ₂ ) + 1 / (T ₁ T ₂ )] = − 1 / (T ₁ T ₂ ) Φ ₁ · e + Φ ₂ · (e / S) + _Kf · sign (S) + L ^* ] + 1 / (T ₁ T ₂ ) L ^* + f _d …… Equation (20)

[0059]

(Equation 21) e s ² + s (T ₁ + T ₂ ) / (T ₁ T ₂ ) + 1 / (T ₁ T ₂ ) + Φ ₁ / (T ₁ T ₂ ) + Φ ₂ / (T ₁ T ₂ s) = − 1 / (T ₁ + T ₂ ) K _f · sign (S) + f _d …… Equation (21)

[0060]

[Equation 22] e = −K _f · sign (S) / (T ₁ T ₂ ) + f _d / s ² + s (T ₁ + T ₂ ) / (T ₁ T ₂ ) + (1 + Φ ₁ ) / (T ₁ T ₂ ) ＋ Φ ₂ / (T ₁ T ₂ s) …… Equation (22)

When K _f = 0 in the equation (22), the error e with respect to the disturbance f _d is given by the following equation (23). Therefore, the error e with respect to the step disturbance f _dm / s becomes zero from the following equation (24) according to Laplace's final theorem, and a steady deviation due to the disturbance does not occur. However, the magnitude of the disturbance is normalized so that f _dm = 1.

[0062]

[Equation 23] e / f _d = s / s ² + s (T ₁ + T ₂ ) / (T ₁ T ₂ ) + (1 + Φ ₁ ) / (T ₁ T ₂ ) + Φ ₂ / (T ₁ T ₂ s) …… Formula (23)

[0063]

[Equation 24]

[0064]

The engine control device of the present invention will be described in detail below with reference to the accompanying drawings.

<First Embodiment> Referring to FIG. 1, as a first embodiment of the present invention, the construction of an engine control device in which S = c · x ₁ + x ₁ ⁽¹⁾ is a sliding constant S will be described. In FIG. 1, the engine control device 1 includes a torque deviation calculation unit 2, a sliding line constant calculation unit 3, a gain unit 7, a dither signal value variable switching unit 11, and an addition unit 12.
And a filter unit 13. Further, the calculation unit 3 includes a coefficient multiplication unit 4, a differential calculation unit 5, and an addition unit 6. Also,
The gain unit 7 includes a gain switching determination data calculation unit 8, a gain switching unit 9, and a multiplication unit 10. Each of these parts 2
13 can be realized by a computer and its software.

The control target 60, which is shown in detail in FIG. 11, includes a throttle actuator 70 and an engine 80. The throttle actuator 70 is simulated by a first-order lag system and has 1 / (1 + sT ₁ ) as a transfer function.
The engine 80 is also simulated with a first-order lag system, 1 / (1 + s
T ₂ ). However, s is a Laplace operator, and T ₁ and T ₂ are time constants.

In FIG. 1, the calculation unit 2 uses the torque command T _or
The deviation x ₁ (= T _or ^* -T _or ) between ^* and the current torque T _or is calculated and given to the sliding line constant calculation unit 3, the gain unit 7, the dither signal value switching unit 11 and the addition unit 12, respectively. The torque command T _or ^* is given from the outside such as a computer used in the engine testing device. The current torque T _or is the torque detector 54 shown in FIG.
Etc.

The calculation unit 3 calculates the torque deviation x ₁ (= T _or ^* -
The sliding line constant S is obtained from the calculation S = c · x ₁ + x ₁ ⁽¹ ) from T _or ) and is given to the gain unit 7 and the dither signal value variable switching unit 9. Where x ₂ =
x ₁ ⁽¹⁾ , that is, x ₂ is a differential torque deviation (x ₂ = x ₁ ⁽¹⁾ = dx ₁ / dt) obtained by differentiating x ₁ with respect to time t. c is a coefficient, and the time constants T ₁ , T _{2 of the} controlled object 60
Is set in the range of 0 <c <(T ₁ + T ₂ ) / (T ₁ + T ₂ ).

For the above-described calculation, the calculation unit 3 has a multiplication unit.
4, the differential operation unit 5, and the addition unit 6 operate as follows.
It Multiplier 4 calculates torque deviation x₁X coefficient x
₁And the differential operation unit 5 calculates s / (1 + sT₃) Become a transmission
Torque deviation x by function₁To its differential torque deviation x₁
⁽¹⁾Then, the addition unit 6 adds these and the sliding
Glein constant S (= c · x₁+ X₁ ⁽¹⁾). What
Oh, s is the Laplace operator, T₃ Is the time constant.

The gain section 7 has a sliding line constant S.
And torque deviation x₁Product of S and x₁Ask for this value gay
Sx₁Gain if> 0
Φ is Φ = α> c (T₁+ T₂) -T₁T₂c²As -1
Luk deviation x₁Multiply by S ・ x₁ If <0, set gain Φ
Φ = β <c (T₁+ T₂) + T₁T₂c²Torque as -1
Deviation x₁Multiply by Φ ・ x₁Is added as one of the manipulated variables
Give to part 12.

In the gain section 7, the calculation section 8, the gain switching section 9, and the multiplication section 10 operate as follows for the above-described calculation. The calculation unit 8 performs a calculation for multiplying the torque deviation x ₁ (= T _or ^* -T _or ) by the sliding line constant S, and gives the obtained product x ₁ · S to the gain switching unit 9 as gain switching determination data. The gain switching unit 9 determines the sign of the gain switching determination data x ₁ · S, and when x ₁ · S> 0, Φ = α> c (T ₁ + T ₂ ) −T ₁ T ₂ c ² −1, x ₁ · S
When <0, Φ = β <c (T ₁ + T ₂ ) −T ₁ T ₂ c ² −1. x ₁
When S = 0, either α or β may be taken, but the previous value may be maintained. Note that the sampling time has a hysteresis factor because of digital control. The multiplication unit 10 uses the gain Φ (= α or β) as the torque deviation x ₁ (= T _or ^* -T
_or )) and Φ · x ₁ as _one of the manipulated variables
Give to 2.

The dither signal value variable switching unit 11 basically has a sliding line constant S (= c · x ₁ + x ₁ ⁽¹⁾ ).
The value of the dither signal is + K _f or −K _f (K
_f > 0), and K _f · sign (S) is given to the adder 12 as one of the manipulated variables. However, whether or not the absolute value | x ₁ | of the torque deviation x ₁ is less than a preset allowable range e _min is determined by comparing x ₁ and e _min, and | x ₁ | <e
_{In the case of min, that} is, −e _min <x ₁ <e _min , K _f is changed to 0. That is, the dither signal is substantially not output to the adder 12. Where K _f · sign (S)
Needless to say, if S> 0, + K _f , S <
In the case of 0 is -K _f. When the _{S = 0 + K f, -K} f
It does not matter which of the two is used, but it is good to keep the previous code. Note that the sampling time has a hysteresis factor because of digital control.

The addition unit 12 calculates Φ × ₁ and K _f · sign
(S) is added and the first basic manipulated variable (= Φ · x ₁ + K _f
・ Sign (S)) and further add the torque command T _or ^* in a feedforward manner to obtain Φ ・ x ₁ + K _f・ sign (S) + T
_or ^* is given to the filter unit 13 as the second basic manipulated variable u _B.

The filter unit 1 has a second basic manipulated variable u _B of 1
First-order lag filtering is performed by the transfer function of / (1 + sT ₄ ), and as a result, u is given as a final manipulated variable to the throttle actuator 70 of the controlled object 60 through a driver to drive the motor. In addition, s is a Laplace operator and T ₄ is a time constant.

In the engine control unit 1 of the first embodiment (FIG. 1) described above, basically, the sliding line constant S is calculated from the torque deviation x ₁ , its time derivative x ₁ ⁽¹⁾ and the coefficient c by S = C · x ₁ + x ₁ ⁽¹⁾ is detected and S and x
_The gain Φ for the torque deviation x ₁ is switched between α and β according to the sign of the product S · x ₁ of ₁ , and the dither signal is changed to K _f · sign (S), that is, K _f according to the sign of S. Switch to -K _f . At this time, the adder 12 adds the torque deviation x ₁ to the manipulated variable u in a feed-forward manner to reduce the dither signal value K _f . Therefore, chattering due to code switching of the dither signal is reduced. Further, by performing a first-order lag filtering process on the manipulated variable u by the filter unit 13, abrupt fluctuation of the control input to the controlled object 60 is suppressed with respect to gain switching and code switching of the dither signal. Therefore, chattering due to these is reduced. Furthermore, when | x ₁ | <e _min , the dither signal value variable switching unit 11 changes the dither signal value from K _f > 0 to K _f = 0. Therefore,
Within the allowable error e _min , that is, the stable state (0,
In the vicinity of 0), there is no chattering due to the dither signal, and the control response becomes stable.

FIG. 6 and FIG. 7 show the step response results of the torque T _or of the engine control device 1 incorporating the sliding mode control according to the first embodiment. Further, for comparison, FIG. 8 shows a step response result of the torque T _or of the engine control device 50 using the conventional PI control. As can be seen from these figures, a better control response can be obtained in the present invention than in the conventional case. However, the conditions are as follows. (I) In FIG. 6, T ₁ = 0.002 seconds, T ₂ = 1 second, T
₄ = 0.05 _{seconds, K f = 0.2, α =} 8~12, β = -
And 6-10, the torque command the e _min T _or ^* of 0.78
%. (Ii) In FIG. 7, T ₁ = 0.002 seconds, T ₂ = 1 second, T ₄
= 0.13 _{seconds, K f = 0.2, α =} 8~12, β = -6
And ~-10, e _min a torque command T _or ^* of 0.78%
And (iii) In FIG. 8, T ₂ = 1 second, K _P in PI control,
K _I was set to K _P = 5 and K _I = 5, respectively.

In the first embodiment described above, the engine control device 1 sets the torque T _or as the control amount, and the torque command T _or ^*.
Is used as a control command, but if the control amount is the rotational speed or intake pressure and the control command is replaced with a rotational speed command, an intake pressure command, or the like, the throttle actuator 70 is controlled to control the rotational speed of the engine 80 or The intake pressure can be controlled.

<Second Embodiment> Next, referring to FIG. 9, as a second embodiment of the present invention, S = x ₁ ⁽¹⁾ + 2ξω _n x ₁ + ω _n ²
The configuration of the engine control device in which ∫ x ₁ is the sliding line constant will be described. In FIG. 9, the engine control unit 21 includes a torque deviation calculation unit 22, a sliding line constant calculation unit 23, a first gain unit 29, and a second gain unit 29.
The gain unit 33, the dither signal value switching unit 37, and the adding unit 38. Further, the calculation unit 23 includes a differential calculation unit 24, a coefficient multiplication unit 25, an integration calculation unit 26, a coefficient multiplication unit 27, and an addition unit 28. Further, the first gain unit 29 is a calculation unit 30 for the gain switching determination data.
And a gain switching unit 31 and a multiplication unit 32. The second gain unit 33 is a calculation unit 3 for the gain switching determination data.
4, a gain switching unit 35, and a multiplication unit 36. Each of these units 22 to 38 can be configured by a computer and its software.

The controlled object 60 includes the throttle actuator 70 and the engine 80 as in the first embodiment of FIG. 1, and the transfer function of the throttle actuator 70 is 1 /
(1 + sT ₁ ), the transfer function of the engine 80 is 1 / (1+
sT ₂ ).

In FIG. 9, the calculation unit 22 uses the torque command T
deviation x between _or ^* and the current torque T _or which is the control amount x
₁ (= T _or ^* -T _or ) is obtained and given to the sliding line constant calculation unit 23, the first gain unit 29, and the second gain unit 33. The torque command T _or ^* is given from the outside such as a computer used in the engine test apparatus, and the current torque T _or is the torque detector 54 shown in FIG.
Etc.

The calculation unit 23 calculates the torque deviation x ₁ (= T _or ^* -T
_or )), S = x ₁ ⁽¹⁾ + 2ξω _n x ₁
+ Ω _n ² ∫ x _{1 is} calculated to obtain the sliding line constant S, and the first gain unit 29 and the second gain unit 33 are obtained.
And the dither signal value switching unit 37. Where x ₁
⁽¹⁾ is a differential torque deviation obtained by differentiating with respect to time t of the torque deviation _{x 1 (= dx 1 / dt} ), x 2 are Displayed (x ₂ = x ₁ ⁽¹⁾⁾ to. ∫ x ₁ is the torque deviation x ₁ at time t
Is integrated torque deviation (= ∫x ₁ dt). Further, ξ and ω _n are coefficients representing the damping rate (ξ) and the velocity (ω _n ) of the secondary vibration type, and the time constant T of the controlled object 60.
₁ and T ₂ , 2ξω _n <(T ₁ + T ₂ ) / (T ₁ T ₂ ).
It is set in the range that satisfies.

For the above calculation, the calculation unit 23 for the sliding line constant S comprises a differential calculation unit 24, a coefficient multiplication unit 25, an integration calculation unit 26, a coefficient multiplication unit 27, and an addition unit 28. The differential operation part 24 obtains the differential torque deviation x ₁ ⁽¹⁾ (= x ₂ ) from the torque deviation x ₁ by the transfer function of s / (1 + sT ₃ ). The coefficient multiplication unit 25 multiplies the torque deviation x ₁ by the coefficient 2ξω _n to obtain 2ξω _n x ₁ .
The integral calculator 26 has 1 / s as a transfer function, and the torque deviation x
_The integrated torque deviation ∫x ₁ is obtained from ₁ , and the coefficient multiplication unit 27 multiplies the integrated torque deviation ∫x ₁ by the coefficient ω _n ² to obtain ω _n ² ∫x 1.
Ask for ₁ . The addition unit 28 adds these to obtain the sliding line constant S as S = x ₁ ⁽¹⁾ + 2ξω _n x ₁ + ω _n ² ∫
Calculate as x ₁ .

The first gain unit 29 has a torque deviation x ₁ and a sliding line constant S (= x ₁ ⁽¹⁾ + 2ξω _n x ₁ + ω _n
² ∫ x ₁ ) and the product x ₁ · S is obtained, and this value is used as the gain switching determination data. When x ₁ · S> 0, the gain Φ ₁ is
₁ = α ₁ > [(T ₁ + T ₂ ) −2ξω _n T ₁ T ₂ ] · 2ξω _n
-1+ (T ₁ T ₂₎ multiplied by the torque deviation x ₁ as omega _n ^2,
When x ₁ · S <0, the gain Φ ₁ is Φ ₁ = β ₁ <[(T ₁ +
T ₂ ) −2ξω _n T ₁ T ₂ ] · ₂ ξω _n −1+ (T ₁ T ₂ ) ω _n
^The torque deviation x ₁ is multiplied by ² and Φ ₁ · x ₁ is given to the adder 38 as _one of the manipulated variables.

For the above calculation, the first gain unit 29
Is composed of a gain switching determination data calculation unit 30, a gain switching unit 31, and a multiplication unit 32. That is, the arithmetic unit 30 calculates the product x ₁ · T of the torque deviation x ₁ and the sliding line constant S.
S is obtained and given to the gain switching unit 31 as gain switching determination data. Gain switcher 31 determines the sign of _{x 1 · S, x 1 ·} S> Gain [Phi ₁ and alpha ₁ if 0
When x ₁ · S <0, the gain Φ ₁ is given to the multiplication unit 32 as β ₁ . The multiplication unit 32 multiplies the torque deviation x ₁ by the gain Φ ₁ , and Φ ₁ · x ₁ = α ₁ · x ₁ or Φ ₁ · x ₁ = β
₁ · x ₁ is given to the addition unit 38 as _one of the manipulated variables.

Here, α ₁ is α ₁ > [(T ₁ + T ₂ ) -2.
ξω _n T ₁ T ₂ ] · 2ξω _n −1+ (T ₁ T ₂ ) ω _n ² is preset. Also, β ₁ is β ₁ <[(T ₁ + T ₂ ) −
2ξω _n T ₁ T ₂ ] · 2ξω _n −1+ (T ₁ T ₂ ) ω _n ² is preset. In the case of x ₁ · S = 0, either Φ ₁ = α ₁ or Φ ₁ = β ₁ may be used, but the previous value should be maintained. The sampling time for digital control has an element of hysteresis.

The second gain section 33 uses the integrated torque deviation ∫x
₁ and sliding line constant S (= x ₁ ⁽¹⁾ + 2ξω _{n
^{x 1 + ω n 2 ∫x 1}} ) the product S · ∫x ₁ with determined, this value and gain switching determination data, S · ∫x _1> Gain [Phi ₂ to Φ ₂ = α ₂ if 0> [(T ₁ + T ₂ ) ω _n ² -2ξω _n ³ T ₁
Multiply the torque deviation ∫ x ₁ as T ₂ , and in the case of S · ∫ x ₁ <0, the gain Φ ₂ is Φ ₂ = β ₂ <[(T ₁ + T ₂ ) -2ξω _n ³
Multiply the torque deviation ∫ x ₁ as T ₁ T ₂ to obtain Φ ₂ · ∫ x ₁
Is given to the addition unit 38 as one of the manipulated variables.

The second gain unit 33 is used for the above calculation.
Is composed of a gain switching determination data calculation unit 34, a gain switching unit 35, and a multiplication unit 36. That is, the calculation unit 34 obtains a product S · ∫x ₁ of the integrated torque deviation ∫x ₁ and the sliding line constant S, and supplies it to the gain switching unit 35 as gain switching determination data. The gain switching unit 35 is S ・ ∫
The sign of x ₁ is determined, and if S · ∫x ₁ > 0, the gain Φ _{2 is set} to α ₂ , and if S · ∫x ₁ <0, the gain Φ _{2 is set} to β ₂ and given to the multiplication unit 36. . The multiplication unit 36 multiplies the integrated torque deviation ∫x ₁ by the gain Φ ₂ to obtain Φ ₂ · ∫x ₁ = α ₂ ·
∫x ₁ or Φ ₂ · ∫x ₁ = β ₂ · ∫x ₁ is given to the addition unit 38 as _one of the manipulated variables.

Here, α ₂ is α ₂ > (T ₁ + T ₂ ) ω _n ² −
It is preset in the range of 2ξω _n ³ T ₁ T ₂ . Further, β ₂ is preset in the range of β ₂ <(T ₁ + T ₂ ) ω _n ² −2 ξω _n ³ T ₁ T ₂ . When S · ∫x ₁ = 0, Φ ₂ = α ₂ or Φ
_It does not matter which of ₂ = β ₂ is used, but it is better to keep the previous value. The sampling time for digital control has an element of hysteresis.

The dither signal value switching section 37 is provided with a sliding
Longin constant S (= x₁ ⁽¹⁾+ 2ξω_nx₁+ Ω_n ²∫
x₁), The value of the dither signal is + K_fOr
-K_f(K _f> 0), K_f・ Operate sign (S)
It is given to the addition unit 38 as one of the quantities. However, if S> 0
K_f・ Sign (S) = K_f, K when S <0_f・ Sign
(S) =-K_fIs. + K when S = 0_f, -K_fIzu
It doesn't matter, but it is good to keep the previous code. What
The sampling time for digital control is
It has a cis element.

The adder 38 uses Φ ₁ · x ₁ and Φ ₂ · ∫x
₁ and K _f · sign (S) are added, and the torque command T _or
^* Is added in a feed-forward manner, and as a result u = Φ ₁ ·
x ₁ + Φ ₂ · ∫x ₁ + K _f · sign (S) + T _or ^* is given to the throttle actuator 70 of the controlled object 60 as an operation amount through an appropriate driver to drive the motor.

Engine control of the second embodiment (FIG. 9) described above
In the control device 21, S = x₁ ⁽¹⁾+ 2ξω_nx₁+ Ω_n ²∫x₁
The sliding line constant S is calculated as
x₁Gain for₁Product S · x₁Α according to the sign of₁
And β₁, And integrated torque deviation ∫x₁To
Gain Φ₂Product S · ∫ x₁Α according to the sign of₂When
β₂By switching between the
Original phase space (x₁, X ₁ ⁽¹⁾∫x₁) With S = x₁ ⁽¹⁾+2
ξω_nx₁+ Ω_n ²∫x₁Asymptotically lower along the line = 0
The control to move to the constant state (0, 0, 0) is performed. So
As a result, the dither signal value K_fIs zero (K_f= 0)
However, steady deviation due to disturbance does not occur. The operation amount u
Torque command T_or ^*Feed-forward
Therefore, the dither signal value K_fTo be able to reduce
However, the increase in chattering is suppressed.

Also in the second embodiment described above, the engine control unit 21 sets the torque T _or as the control amount, and the torque command T _or.
^{Although *} is the control command, if the control amount is the number of revolutions or the intake pressure, and if the control command is replaced with the number of revolutions command or the intake pressure command, etc., the throttle actuator 70 is controlled to control the number of revolutions of the engine 80. The intake pressure can be controlled.

<Third Embodiment> Next, an engine control apparatus according to a third embodiment of the present invention will be described with reference to FIG.
An engine control device 41 shown in FIG. 10 is a modification of the engine device 21 of the second embodiment shown in FIG. 9 in the following two points. The filter section 13 is provided on the output side of the adder section 38 as in the first embodiment of FIG. 1 to reduce the occurrence of chattering. Instead of the switching portion 37 of the dither signal value, a variable switching unit 11 of the same dither signal value to the first embodiment of FIG. 1 is provided, eliminating the occurrence of chattering due to switching of the dither signal value less than the tolerance e _min.

Therefore, the engine control unit 4 shown in FIG.
The configuration and operation of No. 1 are apparent from the description of the first and second embodiments above, but will be described below as a precaution, just in case.

In FIG. 10, the engine control device 41 includes a torque deviation calculation unit 22, a sliding line constant calculation unit 23, a first gain unit 29, a second gain unit 33, and a variable dither signal value. Switching unit 11 and addition unit 3
8 and a filter unit 13. Furthermore, the calculation unit 2
3 is composed of a differential calculation unit 24, a coefficient conversion unit 25, an integration calculation unit 26, a coefficient multiplication unit 27, and an addition unit 28. The first gain unit 29 includes a gain switching determination data calculation unit 30, a gain switching unit 31, and a multiplication unit 32. The second gain unit 33 includes a gain switching determination data calculation unit 34. , Gain switching unit 35, and multiplication unit 36
Consists of Each of these units 22 to 38 can be configured by a computer and its software.

The controlled object 60 includes the throttle actuator 70 and the engine 80 as in the embodiments of FIGS. 1 and 9, and the transfer function of the throttle actuator 70 is 1 /
(1 + sT ₁ ), the transfer function of the engine 80 is 1 / (1+
sT ₂ ).

In FIG. 10, the calculation unit 22 calculates the deviation x ₁ between the torque command T _or ^* and the current torque T _or which is the control amount thereof.
(= T _or ^* -T _or ) is obtained and given to the sliding line constant calculation unit 23, the first gain unit 29, and the second gain unit 33. The torque command T _or ^* is given from the outside such as a computer used in the engine test apparatus, and the current torque T _or is the torque detector 54 shown in FIG.
Etc.

The calculation unit 23 calculates the torque deviation x ₁ (= T _or ^* -T
_or )), S = x ₁ ⁽¹⁾ + 2ξω _n x ₁
+ Ω _n ² ∫ x _{1 is} calculated to obtain the sliding line constant S, and the first gain unit 29 and the second gain unit 33 are obtained.
And the variable switching unit 11 for the dither signal value. here,
x ₁ ⁽¹⁾ is a differential torque deviation obtained by differentiating with respect to time t of the torque deviation _{x 1 (= dx 1 / dt} ), x 2 are Displayed ^{_{(x 2 = x 1 (1}} )) to. ∫x ₁ is an integrated torque deviation (= ∫x ₁ dt) obtained by integrating the torque deviation x ₁ with respect to time t. Further, ξ and ω _n are coefficients representing the damping rate (ξ) and the velocity (ω _n ) of the secondary vibration type, and 2ξω _n <(T ₁ + T ₂ ) by the time constants T ₁ and T ₂ of the controlled object 60. ) / (T
₁ T ₂ ) is set within the range.

For the above-mentioned calculation, the calculation unit 23 of the sliding line constant S comprises a differential calculation unit 24, a coefficient multiplication unit 25, an integration calculation unit 26, a coefficient multiplication unit 27, and an addition unit 28. The differential operation part 24 obtains the differential torque deviation x ₁ ⁽¹⁾ (= x ₂ ) from the torque deviation x ₁ by the transfer function of s / (1 + sT ₃ ). The coefficient multiplication unit 25 multiplies the torque deviation x ₁ by the coefficient 2ξω _n to obtain 2ξω _n x ₁ .
The integral calculator 26 has 1 / s as a transfer function, and the torque deviation x
_The integrated torque deviation ∫x ₁ is obtained from ₁ , and the coefficient multiplication unit 27 multiplies the integrated torque deviation ∫x ₁ by the coefficient ω _n ² to obtain ω _n ² ∫x 1.
Ask for ₁ . The addition unit 28 adds these to obtain the sliding line constant S as S = x ₁ ⁽¹⁾ + 2ξω _n x ₁ + ω _n ² ∫
Calculate as x ₁ .

The first gain unit 29 has a torque deviation x ₁ and a sliding line constant S (= x ₁ ⁽¹⁾ + 2ξω _n x ₁ + ω _n
² ∫ x ₁ ) and the product x ₁ · S is obtained, and this value is used as the gain switching determination data. When x ₁ · S> 0, the gain Φ _{1 is set} to Φ ₁
= Α ₁ > [(T ₁ + T ₂ ) −2ξω _n T ₁ T ₂ ] 2ξω _n −1
+ (T ₁ + T ₂ ) ω _n ² and the torque deviation x ₁ is multiplied to obtain x ₁
・ When S <0, the gain Φ ₁ is Φ ₁ = β ₁ <[(T ₁ +
T ₂ ) −2ξω _n T ₁ T ₂ ] / 2ξω _n −1+ (T ₁ + T ₂ ).
The torque deviation x ₁ is multiplied as ω _n ² , and Φ ₁ · x ₁ is given to the addition unit 38 as _one of the manipulated variables.

For the above calculation, the first gain unit 29
Is composed of a gain switching determination data calculation unit 30, a gain switching unit 31, and a multiplication unit 32. That is, the arithmetic unit 30 calculates the product x ₁ · T of the torque deviation x ₁ and the sliding line constant S.
S is obtained and given to the gain switching unit 31 as gain switching determination data. Gain switcher 31 determines the sign of _{x 1 · S, x 1 ·} S> 0 in the case of the gain [Phi ₁ and _{α 1, x 1 · S <} 1 gain [Phi ₁ beta if 0 To the multiplication unit 32. The multiplying unit 32 multiplies the torque deviation x ₁ by the gain Φ ₁ to obtain Φ ₁ · x ₁ = α ₁ · x ₁ or Φ ₁ · x ₁ = β ₁
X1 is given to the addition unit 38 as _one of the manipulated variables.

Here, α ₁ is α ₁ > [(T ₁ + T ₂ ) -2.
ξω _n T ₁ T ₂ ] · 2ξω _n −1+ (T ₁ T ₂ ) ω _n ² is preset. Also, β ₁ is β ₁ <[(T ₁ + T ₂ ) −
2ξω _n T ₁ T ₂ ] · 2ξω _n −1+ (T ₁ T ₂ ) ω _n ² is preset. In the case of x ₁ · S = 0, either Φ ₁ = α ₁ or Φ ₁ = β ₁ may be used, but the previous value should be maintained. Note that the sampling time has a hysteresis factor because of digital control.

The second gain section 33 uses the integrated torque deviation ∫x
₁ and sliding line constant S (= x ₁ ⁽¹⁾ + 2ξω _{n
^{x 1 + ω n 2 ∫x 1}} ) the product S · ∫x ₁ with determined, this value and gain switching determination data, S · ∫x _1> Gain [Phi ₂ to Φ ₂ = α ₂ if 0> (T ₁ + T ₂ ) ω _n ² -2ξω _n ³ T ₁ T
₂ is multiplied by the torque deviation ∫x _1, and when S · ∫x ₁ <0, the gain Φ ₂ is Φ ₂ = β ₂ <(T ₁ + T ₂ ) ω _n ² −2ξω _n ³
Multiply the torque deviation ∫ x ₁ as T ₁ T ₂ to obtain Φ ₂ · ∫ x ₁
Is given to the addition unit 38 as one of the manipulated variables.

The second gain unit 33 is used for the above calculation.
Is composed of a gain switching determination data calculation unit 34, a gain switching unit 35, and a multiplication unit 36. That is, the calculation unit 34 obtains a product S · ∫x ₁ of the integrated torque deviation ∫x ₁ and the sliding line constant S, and supplies it to the gain switching unit 35 as gain switching determination data. The gain switching unit 35 is S ・ ∫
The sign of x ₁ is determined. If S · ∫x ₁ > 0, the gain Φ _{2 is set} to α ₂ , and if S · ∫x ₁ <0, the gain Φ _{2 is set.}
Is given to the multiplication unit 36 as β ₂ . The multiplication unit 36 multiplies the integrated torque deviation ∫x ₁ by the gain Φ ₂ to obtain Φ ₂ · ∫x ₁ = α _2.
・ ∫x ₁ or Φ ₂ · ∫x ₁ = β ₂ · ∫x ₁ is the manipulated variable 1
It is given to the addition unit 38 as one.

Here, α ₂ is α ₂ > (T ₁ + T ₂ ) ω _n ² −
It is preset in the range of 2ξω _n ³ T ₁ T ₂ . Further, β ₂ is preset in the range of β ₂ <(T ₁ + T ₂ ) ω _n ³ −2ξω _n ³ T ₁ T ₂ . When S · ∫x ₁ = 0, Φ ₂ = α ₂ or Φ
_It does not matter which of ₂ = β ₂ is used, but it is better to keep the previous value. Note that the sampling time has a hysteresis factor because of digital control.

The dither signal value variable switching unit 11 basically has a sliding line constant S (= x ₁ ⁽¹⁾ + 2ξω _n x ₁
+ Switched to the value of the dither signal + K _f or -K _f (K _f> 0), depending on the sign of ω _n ² ∫x _1), to the adder 38 K _f · sign the (S) as one of the control output give. However, it is determined whether the absolute value | x ₁ | of the torque deviation x ₁ is less than a preset allowable range e _min by comparing x ₁ and _emin, and | x
_{If 1} | <e _{min, that} is, -e _{m in} <x ₁ <e _min , then K _f
Change it to = 0. That is, the dither signal is substantially not output to the adder 12. Where K _f · sign
Needless to say, the meaning of (S) is + if S> 0.
In the case of K _f, S <0 is -K _f. + When S = 0
K _f, but may either -K _f, it is preferable to maintain the previous sign. Note that the sampling time has a hysteresis factor because of digital control.

The adder 38 calculates Φ ₁ · x ₁ and Φ ₂ · ∫x
₁ and K _f · sign (S) are added to obtain the first basic manipulated variable (= Φ ₁ · x ₁ + Φ ₂ · ∫x ₁ + K _f · sign (S)), and the torque command T _or ^* In a feedforward manner,
Φ ₁ · x ₁ + Φ ₂ · ∫x ₁ + K _f · sign (S) + T _or ^* is given to the filter unit 13 as the second basic manipulated variable u _B.

The filter unit 13 performs first-order lag filtering on the second basic manipulated variable u _{B using} a transfer function of 1 / (1 + sT ₄ ), and as a result, u is used as the final manipulated variable through the driver as appropriate through the control target 60. To the throttle actuator 70 to drive the motor. In addition, s is a Laplace operator and T ₄ is a time constant.

Engine of the third embodiment (FIG. 10) described above
In the control device 41, S = x₁ ⁽¹⁾+ 2ξω_nx₁+ Ω_n ²∫x
₁The sliding line constant S is calculated as
Difference x₁ Gain for₁Product S · x₁According to the sign of
α₁And β₁, And integrated torque deviation ∫x
₁Gain for₂Product S · ∫ x₁Α according to the sign of
₂And β₂By switching between the
Similarly, the three-dimensional phase space (x₁,
x₁ ⁽¹⁾∫x₁) With S = x₁ ⁽¹⁾+ 2ξω_nx₁+ Ω_n ²∫x₁
Asymptotically stable (0,0,0) along the line = 0
The control is carried out to move to. As a result, the dither signal value
K_fIs zero (K_f= 0), steady deviation due to disturbance
There is no difference. In addition, the torque command T is added to the operation amount u._or ^*To
Dithered by adding feed-forward
Issue value K_fTo make chattering smaller and increase chattering
Is suppressed.

Further, in the engine control unit 41 of the third embodiment, similarly to the first embodiment, the filter amount of the operation amount u is filtered by the first-order lag by the filter unit 13 to perform gain switching and dither signal sign switching. On the other hand, the rapid fluctuation of the control input to the controlled object 60 is suppressed. Therefore, chattering due to these is reduced. Furthermore, when | x ₁ | <e _min , the dither signal value variable switching unit 11 changes the dither signal value from K _f > 0 to K _f = 0. Therefore, within the allowable error e _min , that is, the stable state (0,
In the vicinity of (0, 0), chattering due to the dither signal is eliminated, and the control response is stabilized.

Also in the above-described third embodiment, the engine control unit 41 sets the torque T _or as the control amount, and the torque command T _or.
^{Although *} is the control command, if the control amount is the number of revolutions or the intake pressure, and if the control command is replaced with the number of revolutions command or the intake pressure command, etc., the throttle actuator 70 is controlled to control the number of revolutions of the engine 80. The intake pressure can be controlled.

[0112]

Since the present invention is an engine control method and apparatus based on sliding mode control, it is possible to stably control an object to be controlled including a backlash element and a hysteresis element with a small overshoot amount. is there.

In particular, chattering can be suppressed by subjecting the operation amount to the controlled object to the filter processing of the first-order delay. Further, since the dither signal added to the manipulated variable is set to zero according to the control deviation, chattering can be suppressed. By suppressing such chattering, it is possible to mitigate the adverse effect on the control caused by a change with time or a failure of the mechanical system included in the control target.

Furthermore, by including a component proportional to the control deviation in the sliding line constant, a component proportional to the time derivative thereof, and a component proportional to the time integration,
Even if the dither signal is reduced, steady deviation does not occur.

[Brief description of drawings]

FIG. 1 is a diagram showing a configuration of an engine control device according to a first embodiment of the present invention.

FIG. 2 is a diagram showing the principle of sliding mode control.

FIG. 3 is a diagram showing a control target.

FIG. 4 is a block diagram showing an error system to be controlled.

FIG. 5 is a diagram showing the principle of another example of sliding mode control.

FIG. 6 is a diagram showing an example of a control response according to the first embodiment.

FIG. 7 is a diagram showing another control response example according to the first embodiment.

FIG. 8 is a diagram showing an example of a conventional control response.

FIG. 9 is a diagram showing a configuration of an engine control device according to a second embodiment of the present invention.

FIG. 10 is a diagram showing a configuration of an engine control device according to a third embodiment of the present invention.

FIG. 11 is a diagram showing a configuration of an engine control device according to a conventional example.

FIG. 12 is a block diagram of a control system of a conventional example.

FIG. 13 is a block diagram of a control target of a conventional example.

FIG. 14 is a diagram showing a control response example in the case where the wire has a large hysteresis in the conventional example.

FIG. 15 is a diagram showing an example of a control response when the wire hysteresis is small in the conventional example.

[Explanation of symbols]

 1, 21, 41 Engine control device 2, 22 Torque deviation calculation unit 3, 23 Sliding line constant calculation unit 4, 25, 27 Coefficient calculation unit 5, 24 Differential calculation unit 6, 28 Addition unit 7, 29, 33 Gain Parts 8, 10, 30, 32, 34, 36 Multipliers 9, 31, 35 Gain switching unit 11 Dither signal value variable switching unit 12, 38 Adder unit 13 Filter unit 26 Integral calculation unit 37 Dither signal value switching unit

Claims (7)

[Claims] 1. An engine control method including a throttle actuator as a control target: variably controlling a gain for the control of the control target so that a sliding line constant of the control target approaches zero; an operation amount for the control target. First-order lag filtering;
An engine control method comprising: 2. An engine control method including a throttle actuator as a control target: variably controlling a gain for control of the control target so that a sliding line constant of the control target is directed to zero; an operation amount for the control target. To add a dither signal so as to suppress a steady deviation due to disturbance;
Discontinue when the control deviation is within the allowable error range. 3. An engine control method including a throttle actuator as a control target: variably controlling a gain for control of the control target so that a sliding line constant of the control target is directed to zero; the sliding line constant is controlled. An engine control method comprising: a component proportional to a deviation, a component proportional to a time derivative of the control deviation, and a component proportional to a time integral of the control deviation. 4. The engine control method according to claim 3, wherein a dither signal is added to an operation amount for the controlled object so as to suppress a steady deviation due to a disturbance; the addition of the dither signal is allowed by the control deviation. An engine control method comprising: stopping when within an error range; applying a first-order lag filtering to the operation amount for the controlled object. 5. In an engine control device including a throttle actuator as a control target, the transfer function of the throttle actuator is 1 / (1 + sT ₁ ), the transfer function of the engine is 1 / (1 + sT ₂ ), and c is 0 <c <(T ₁ + T ₂ )
/ (T ₁ T _2), the deviation between the control commands the x ₁ L ^* and the controlled variable L, x ^{_{1 (1)}} the time differential of the deviation x _1, gain Φ for deviations x _1, the alpha alpha> c ( _{T 1 + T 2) -T 1} T 2 c 2 -
1. When β is β <c (T ₁ + T ₂ ) −T ₁ T ₂ c ² −1 and K _f is a dither signal value: a deviation x ₁ between the control command L ^* and the current control amount L is calculated. Means; a means for obtaining the sliding line constant S from the deviation x ₁ and a predetermined coefficient c by the operation S = c · x ₁ + x ₁ ⁽¹⁾ ; a product x of the deviation x ₁ and the sliding line constant S A means for obtaining ₁ · S; the positive / negative of the product x ₁ · S is judged, and the gain Φ is set to x ₁ · S
A means for switching to a predetermined value α when 0 and a predetermined value β when x ₁ · S <0; and a gain Φ multiplied by the torque deviation x ₁ and Φ · x ₁ being _one of the manipulated variables. Means to do;
Determining the sign of sliding line constant S, a dither signal value to a K _f when the S> 0, when the S <0 switched -K _f, with one of K _f · sign (S) of the manipulated variable Means; control command L ^* and the manipulated variable Φ · x ₁ and K _f · sign
Means the final control u for the control target to the basic manipulated variable u _B performs a filtering process of first order lag;; (S) and the added means for obtaining the basic manipulated variable u _B in advance with the deviation x ₁ By comparing with the defined allowable error e _min , -e _min <x ₁ <
and a means for making the dither signal value K _f zero when e _min ;
An engine control device comprising: 6. An engine control device including a throttle actuator as a control target, wherein the transfer function of the throttle actuator is 1 / (1 + sT ₁ ), the transfer function of the engine is 1 / (1 + sT ₂ ), and 2ξω _n is 2ξω _n <(T ₁
+ T ₂ ) / (T ₁ T ₂ ), x ₁ is the control command L ^* and control amount L
Deviation between, x ₁ ⁽¹⁾ the time differential deviation x _1, the time integral of the deviation x ₁ to ∫x _1, gain [Phi ₁ for deviation x _1, [Phi
₂ is the gain for integral ∫ x ₁ , α ₁ is α ₁ > [(T ₁ +
T ₂ ) −2ξω _n T ₁ T ₂ ] 2ξω _n −1 + T ₁ T ₂ ω _n ² , β
₁ is β ₁ <[(T ₁ + T ₂ ) −2ξω _n T ₁ T ₂ ] 2ξω _n −
1 + T ₁ T ₂ ω _n ² , α ₂ is α ₂ > (T ₁ + T ₂ ) ω _n ² -2ξ
_Let ω _n ³ T ₁ T ₂ , β ₂ be β ₂ <(T ₁ + T ₂ ) ω _n ² −2 ω ω _n
^{When 3} T ₁ T ₂ and K _f are used as dither signal values: means for obtaining a deviation x ₁ between the control command L ^* and the control amount L; deviation x ₁
And the predetermined coefficients 2ξω _n and ω _n ² from S = x ₁ ⁽¹⁾
_{+ 2ξω n x 1 + ω n} 2 ∫x 1 comprising calculating means for calculating a sliding line constant S by; means for determining the product S · x ₁ between deviation x ₁ and sliding line constant S; product S
A means for judging whether x ₁ is positive or negative and switching the gain Φ ₁ to a predetermined value α ₁ when S · x ₁ > 0, and to a predetermined value β ₁ when S · x ₁ <0; A means for multiplying the deviation x ₁ by the gain Φ ₁ and using Φ · x ₁ as _one of the manipulated variables; a means for obtaining the product S · ∫x ₁ of the deviation integral ∫x ₁ and the sliding line constant S; The positive / negative of S · ∫x ₁ is determined, and when the gain Φ ₂ is S · ∫x ₁ > 0, a predetermined value α ₂ is set,
A means for switching to a predetermined value β ₂ when S · ∫x ₁ <0; a gain Φ ₂ is multiplied by the deviation integral ∫x ₁ , and Φ ₂
・ Means for making ∫ x _{1 one} of the manipulated variables; determining whether the sliding line constant S is positive or negative, and switching the dither signal value to K _f when S> 0, and to -K _f when S <0. K _f ·
means for making sign (S) one of the manipulated variables; control command L ^*
And the manipulated variables Φ ₁ · x ₁ , Φ ₂ · ∫ x ₁ and K _f · sign
(S) is added to obtain a manipulated variable with respect to the controlled object. 7. The control command L ^* and the manipulated variables Φ ₁ · x ₁ , Φ ₂ ·
Means for applying a first-order lag filtering process to the final manipulated variable to obtain the final manipulated variable by adding ∫ x ₁ and K _f · sign (S); and the deviation x ₁ and a predetermined allowable error _emin 7. The engine control device according to claim 6, further comprising: a unit that sets the dither signal value K _f to zero when −e _min <x ₁ <e _min .