Source: http://www.google.com/patents/US7216006?dq=6462713
Timestamp: 2017-04-26 16:16:45
Document Index: 747883747

Matched Legal Cases: ['§371', 'Application No. 2001', 'Application No. 2001', 'Application No. 2001', 'Application No. 2001', 'Application No. 2001', 'Application No. 2001']

Patent US7216006 - Control system for a plant including a slide mode controller - Google PatentsSearch Images Maps Play YouTube News Gmail Drive More »Sign inPatentsA control system for a plant is provided. This control system can control the plant more stably, when the model parameters of the controlled object model which are obtained by modeling the plant, which is a controlled object, are identified and the sliding mode control is performed using the identified...http://www.google.com/patents/US7216006?utm_source=gb-gplus-sharePatent US7216006 - Control system for a plant including a slide mode controllerAdvanced Patent SearchTry the new Google Patents, with machine-classified Google Scholar results, and Japanese and South Korean patents.Publication numberUS7216006 B2Publication typeGrantApplication numberUS 11/345,994Publication dateMay 8, 2007Filing dateFeb 2, 2006Priority dateApr 20, 2001Fee statusPaidAlso published asCA2411520A1, CA2411520C, CN1275108C, CN1460201A, EP1293851A1, EP1293851A4, EP1293851B1, EP2261759A1, EP2261759B1, EP2261759B8, EP2261760A1, EP2261760B1, EP2264302A1, EP2264302B1, US7050864, US20030120360, US20060129250, WO2002086630A1Publication number11345994, 345994, US 7216006 B2, US 7216006B2, US-B2-7216006, US7216006 B2, US7216006B2InventorsYuji Yasui, Yoshihisa Iwaki, Jun TakahashiOriginal AssigneeHonda Giken Kogyo Kabushiki KaishaExport CitationBiBTeX, EndNote, RefManPatent Citations (51), Referenced by (12), Classifications (30), Legal Events (2) External Links: USPTO, USPTO Assignment, EspacenetControl system for a plant including a slide mode controller
US 7216006 B2Abstract
A control system for a plant is provided. This control system can control the plant more stably, when the model parameters of the controlled object model which are obtained by modeling the plant, which is a controlled object, are identified and the sliding mode control is performed using the identified model parameters. The model parameter identifier (22) calculates a model parameter vector (θ) by adding an updating vector (dθ) to a reference vector (θbase) of the model parameter. The updating vector (dθ) is corrected by multiplying a past value of at least one element of the updating vector by a predetermined value which is greater than “0” and less than “1”. The model parameter vector (θ) is calculated by adding the corrected updating vector (dθ) to the reference vector (θbase).
This application is a divisional of U.S. patent application Ser. No. 10/312,108 (allowed), filed Dec. 20, 2002, now U.S. Pat. No. 7,050,864 which was a 35 U.S.C. §371 filing of International Application Number PCT/JP02/03895 filed Apr. 19, 2002, which claims priority to Japanese Patent Application No. 2001-123344 filed on Apr. 20, 2001, Japanese Patent Application No. 2001-125648 filed on Apr. 24, 2001, Japanese Patent Application No. 2001-146144 filed on May 16, 2001, Japanese Patent Application No. 2001-179926 filed on Jun. 14, 2001, Japanese Patent Application No. 2001-184540 filed on Jun. 19, 2001, Japanese Patent Application No. 2001-343998 filed on Nov. 9, 2001 in Japan. The contents of the aforementioned applications are hereby incorporated by reference.
The present invention relates to a control system for a plant, and more particularly to a control system for controlling a plant with a sliding mode controller based on a sliding mode control theory which is one of robust control theories.
One known control system based on a sliding mode control theory is disclosed in Japanese Patent Laid-open No. Hei 9-274504, for example. The publication proposes a method of setting a hyperplane in the sliding mode control theory according to the convergence state of a controlled state quantity. According to the proposed method, the convergence response and convergence stability of the sliding mode control is improved.
Due to nonlinear characteristics and disturbance whose average value is not “0”, the identifying error does not become “0” even though substantially optimum model parameters have actually been obtained. Therefore, the model parameters which do not need to be corrected are occasionally corrected. As a result, a drift occurs in which the values of the model parameters gradually shift from their optimum values to some other values to make the control performed by the sliding mode controller unstable.
It is therefore an object of the present invention to provide a control system for a plant, which can control the plant more stably when the model parameters of the controlled object model which are obtained by modeling the plant, which is a controlled object, are identified and the sliding mode control is performed using the identified model parameters.
To achieve the above object, the present invention provides a control system for a plant, comprising identifying means and a sliding mode controller. The identifying means identifies a model parameter vector (θ) of a controlled object model of a plant which is obtained by modeling the plant. The sliding mode controller controls the plant using the model parameter vector identified by the identifying means. The identifying means comprises an identifying error calculating means, an updating vector calculating means, and an updating vector correcting means. The identifying error calculating means calculates an identifying error (ide) of the model parameter vector. The updating vector calculating means calculates an updating vector (dθ) according to the identifying error. The updating vector correcting means corrects the updating vector by multiplying a past value of at least one element of the updating vector by a predetermined value (DELTAi, EPSi) which is greater than “0” and less than “1”. The identifying means calculates the model parameter vector by adding the corrected updating vector to a reference vector (θbase, θ(0)) of the model parameter vector.
With this configuration, the updating vector is calculated according to the identifying error of the model parameter vector, and corrected by multiplying the past value of at least one element of the updating vector by the predetermined value which is greater than “0” and less than “1”. The corrected updating vector is added to the reference vector of the model parameter vector to calculate the model parameter vector. Accordingly, values of the elements of the updating vector are limited, thus stabilizing the model parameter vector in the vicinity of the reference vector. As a result, the drift of the model parameters is prevented, to thereby improve the stability of the sliding mode control performed by the sliding mode controller.
Preferably, the identifying error correcting means sets the identifying error to “0”, if the identifying error is in the predetermined range. With this configuration, the effect of the identifying error which is not to be reflected to the values of model parameters is eliminated, resulting in an increased effect of preventing the model parameters from drifting.
Preferably, the identifying error correcting means sets the identifying error (ide) to “0”, if the identifying error (ide) is in the predetermined range (−EIDNRLMT≦ide≦EIDNRLMT).
FIG. 1 is a schematic view of a throttle valve control system according to a first embodiment of the present invention;
The present invention will be explained below with reference to the drawings.
FIG. 1 schematically shows a configuration of a throttle valve control system according to a first embodiment of the present invention. An internal combustion engine (hereinafter referred to as “engine”) 1 has an intake passage 2 with a throttle valve 3 disposed therein. The throttle valve 3 is provided with a return spring 4 as a first energizing means for energizing the throttle valve 3 in a closing direction, and a resilient member 5 as a second energizing means for energizing the throttle valve 3 in an opening direction. The throttle valve 3 can be actuated by a motor 6 as an actuating means through gears (not shown). When the actuating force from the motor 6 is not applied to the throttle valve 3, an opening TH of the throttle valve 3 is maintained at a default opening THDEF (for example, 5 degrees) where the energizing force of the return spring 4 and the energizing force of the resilient member 5 are in equilibrium.
The motor 6 is connected to an electronic control unit (hereinafter referred to as “ECU”) 7. The operation of the motor 6 is controlled by the ECU 7. The throttle valve 3 is associated with a throttle valve opening sensor 8 for detecting the throttle valve opening TH. A detected signal from the throttle valve opening sensor 8 is supplied to the ECU 7.
DTH ( k + 1 ) = a1 × DTH ( k ) + a2 × DTH ( k - 1 ) + b1 × DUT ( k - d ) + c1 ( 1 ) where k is a parameter representing discrete time, and DTH(k) is a throttle valve opening deviation amount defined by the equation (2) shown below. DTH(k+1) is a throttle valve opening deviation amount at a discrete time (k+1).
FIG. 3 is a functional block diagram of the throttle valve control system which is realized by the ECU 7. The throttle valve control system as configured includes, an adaptive sliding mode controller 21, a model parameter identifier 22, a state predictor 23 for calculating a predicted throttle valve opening deviation amount (hereinafter referred to as “predicted deviation amount” or PREDTH(k)) where PREDTH(k) (=DTH(k+d)) after the dead time d has elapsed, and a target opening setting unit 24 for setting a target opening THR for the throttle valve 3 according to the accelerator pedal depression amount ACC.
e ( k ) = DTH ( k ) - DTHR ( k ) ( 4 ) σ ( k ) = e ( k ) + VPOLE × e ( k - 1 ) = ( DTH ( k ) - DTHR ( k ) ) + VPOLE × ( DTH ( k - 1 ) - DTHR ( k - 1 ) ) ( 5 ) where VPOLE is a switching function setting parameter that is set to a value which is greater than −1 and less than 1.
On a phase plane defined by a vertical axis representing the deviation e(k) and a horizontal axis representing the preceding deviation e(k−1), a pair of the deviation e(k) and the preceding deviation e(k−1) satisfying the equation of “σ(k)=0” represents a straight line. The straight line is generally referred to as a switching straight line. A sliding mode control is a control contemplating the behavior of the deviation e(k) on the switching straight line. The sliding mode control is carried out so that the switching function value σ(k) becomes 0, i.e., the pair of the deviation e(k) and the preceding deviation e(k−1) exists on the switching straight line on the phase plane, to thereby achieve a robust control against disturbance and the modeling error (the difference between the characteristics of an actual plant and the characteristics of a controlled object model). As a result, the throttle valve opening deviation amount DTH is controlled with good robustness to follow up the target value DTHR.
As described above, according to the sliding mode control, the deviation e(k) is converged to 0 at an indicated converging speed and robustly against disturbance and the modeling error by constraining the pair of the deviation e(k) and the preceding deviation e(k−1) on the switching straight line (the pair of e(k) and e(k−1) will be hereinafter referred to as “deviation state quantity”). Therefore, in the sliding mode control, it is important how to place the deviation state quantity onto the switching straight line and constrain the deviation state quantity on the switching straight line.
The equivalent control input Ueq(k) is an input for constraining the deviation state quantity on the switching straight line. The reaching law input Urch(k) is an input for placing deviation state quantity onto the switching straight line. The adaptive law input Uadp(k) is an input for placing deviation state quantity onto the switching straight line while reducing the modeling error and the effect of disturbance. Methods of calculating these inputs Ueq(k), Urch(k), and Uadp(k) will be described below.
DUT ( k ) = 1 b1 { ( 1 - a1 - VPOLE ) DTH ( k + d ) + ( VPOLE - a2 ) DTH ( k + d - 1 ) - c1 + DTHR ( k + d + 1 ) + ( VPOLE - 1 ) DTHR ( k + d ) - VPOLE × DTHR ( k + d - 1 ) } = Ueq ( k ) ( 9 ) Urch ( k ) = - F b1 σ ( k + d ) ( 10 ) Uadp ( k ) = - G b1 ∑ i = 0 k + d Δ T σ ( i ) ( 11 ) where F and G respectively represent a reaching law control gain and an adaptive law control gain, which are set as described below, and ΔT represents a control period.
F>0 (12)
F<2−(ΔT/2)G (14)
where a1′, a2′, b1ζ, c1′ represent model parameters before a limit process described later is carried out, ide(k) represents an identifying error defined by the equations (17), (18), and (19) shown below, where DTHHAT(k) represents an estimated value of the throttle valve opening deviation amount DTH(k) (hereinafter referred to as “estimated throttle valve opening deviation amount”) which is calculated using the latest model parameter vector θ(k−1), and KP(k) represents a gain coefficient vector defined by the equation (20) shown below. In the equation (20), P(k) represents a quartic square matrix calculated from the equation (21) shown below.
DTHHAT
In accordance with the setting of coefficients λ1 and λ2 in the equation (21), the identifying algorithm from the equations (15) through (21) becomes one of the following four identifying algorithm:
“Quasi-static dynamic characteristics changes” mean slow-rate characteristics changes such as power supply voltage fluctuations or hardware degradations due to aging.
In order to satisfy the requirements B1 and B2, the coefficients λ1 and λ2 are set respectively to a given value λ and “0” so that the weighted Method-of-least-squares algorithm is employed.
idenl(k)=Fnl(ide(k)) (23)
θ(k)=θ(k−1)+KP(k)idenl(k) (15a)
DDTHRSQA
DDTHR
Since the throttle valve opening deviation amount DTH is controlled to the target value DTHR by the adaptive sliding mode controller 21, the target value DTHR in the equation (25) may be changed to the throttle valve opening deviation amount DTH. In this case, an amount of change DDTH in the throttle valve opening deviation amount DTH may be calculated, and the dead zone width parameter EIDNRLMT may be set according to the square average value DDTHRSQA obtained by replacing DDTHR in the equation (24) with DDTH.
By rewriting the equation (1) which defines the controlled object model, using the matrixes A, B and the vectors X(k), U(k), the following equation (30) is obtained.
If matrixes A′ and B′ are defined by the following equations (32), (33), using the model parameters a1′, a2′, b1′, and c1′ which are not subjected to the limit process, a predicted vector XHAT(k+d) is given by the following equation (34).
The first-row element DTHHAT(k+d) of the predicted vector XHAT(k+d) corresponds to the predicted deviation amount PREDTH(k), and is given by the following equation (35).
PREDTH ( k ) = DTHHAT ( k + d ) = α 1 × DTH ( k ) + α 2 × DTH ( k - 1 ) + β 1 × DUT ( k - 1 ) + β 2 × DUT ( k - 2 ) + ⋯ + β d × DUT ( k - d ) + γ 1 + γ2 + ⋯ + γ d ( 35 ) where α1 represents a first-row, first-column element of the matrix A′d, α2 represents a first-row, second-column element of the matrix A′d, βi represents a first-row, first-column element of the matrix A′d−iB′, and γi represents a first-row, second-column element of the matrix A′d−iB′.
PREDTH
Using the predicted deviation amount PREDTH(k) calculated from the equation (35), a predicted switching function value σpre(k) is defined by the following equation (36). The reaching law input Urch(k) and the adaptive law input Uadp(k) are calculated respectively from the following equations (10a) and (11a).
The model parameter c1′ is a parameter representing a deviation of the default opening THDEF and disturbance. Therefore, as shown in FIG. 8, the model parameter c1′ changes with disturbance, but can be regarded as substantially constant in a relatively short period. In the present embodiment, the model parameter c1′ is statistically processed, and the central value of its variations is calculated as a default opening deviation thdefadp. The default opening deviation thdefadp is used for calculating the throttle valve opening deviation amount DTH and the target value DTHR.
Specifically, in the equations (15) through (21), by replacing θ(k) and θ(k)T with thdefadp, replacing ζ(k) and ζ(k)T with “1”, replacing ide(k) with ecl(k), replacing KP(k) with KPTH(k), replacing P(k) with PTH(k), and replacing λ1 and λ2 respectively with λ1′ and λ2′, the following equations (37) through (40) are obtained.
thdefadp
One of the four algorithms described above can be selected according to the setting of the coefficients λ1′ and λ2′. In the equation (39), the coefficient λ1′ is set to a given value other than 0 or 1, and the coefficient λ2′ is set to 1, thus employing the weighted method of least squares.
DTH(k)=TH(k)−THDEF+thdefadp (41)
In step S16, a process of stability determination of the sliding mode controller as shown in FIG. 29 is carried out. Specifically, the stability is determined based on a differential value of the Lyapunov function, and a stability determination flag FSMCSTAB is set. When the stability determination flag FSMCSTAB is set to “1”, this indicates that the adaptive sliding mode controller 21 is unstable.
If the stability determination flag FSMCSTAB is set to “1”, indicating that the adaptive sliding mode controller 21 is unstable, the switching function setting parameter VPOLE is set to a predetermined stabilizing value XPOLESTB (see steps S231 and S232 in FIG. 24), and the equivalent control input Ueq is set to “0”. That is, the control process by the adaptive sliding mode controller 21 is switched to a control process based on only the reaching law input Urch and the adaptive law input Uadp, to thereby stabilize the control (see steps S206 and S208 in FIG. 22).
In step S51, the identifying error ide(k) is calculated from the equation (17). Then, it is determined whether or not the value of a counter CNTIDST which is incremented in step S53 is greater than a predetermined value XCNTIDST that is set according to the dead time d of the controlled object (step S52). The predetermined value XCNTIDST is set, for example, to “3” according to a dead time d=2. Since the counter CNTIDST has an initial value of “0”, the process first goes to step S53, in which the counter CNTIDST is incremented by “1”. Then, the identifying error ide(k) is set to “0” in step S54, after which the process goes to step S55. Immediately after starting identifying the model parameter vector θ(k), no correct identifying error can be obtained by the equation (17). Therefore, the identifying error ide(k) is set to “0” according to steps S52 through S54, instead of using the calculated result of the equation (17).
Referring back to FIG. 12, the dead zone process as shown in FIG. 14 is carried out in step S56. In step S61 shown in FIG. 14, “n” in the equation (24) is set, for example, to “5” to calculate the square average value DDTHRSQA of an amount of change of the target throttle valve opening THR. Then, an EIDNRLMT table shown in FIG. 15 is retrieved according to the square average value DDTHRSQA to calculate the dead zone width parameter EIDNRLMT (step S62).
If the identifying error ide(k) is in the range between +EIDNRLMT and −EIDNRLMT, the corrected identifying error idenl(k) is set to “0” in step S66.
In step S71 shown in FIG. 16, flags FA1STAB, FA2STAB, FB1LMT, and FC1LMT used in this process are initialized to be set to “0”. In step S72, the limit process of the model parameters a1′ and a2′ shown in FIG. 17 is executed. In step S73, the limit process of the model parameter b1′ shown in FIG. 19 is executed. In step S74, the limit process of the model parameter c1′ shown in FIG. 20 is executed.
In FIG. 18, combinations of the model parameters a1′ and a2′ which are required to be limited are indicated by “x” symbols, and the range of combinations of the model parameters a1′ and a2′ which are stable are indicated by a hatched region (hereinafter referred to as “stable region”). The limit process shown in FIG. 17 is a process of moving the combinations of the model parameters a1′ and a2′ which are in the outside of the stable region into the stable region at positions indicated by “◯” symbols.
In step S81, it is determined whether or not the model parameter a2′ is greater than or equal to a predetermined a2 lower limit value XIDA2L. The predetermined a2 lower limit value XIDA2L is set to a negative value greater than “−1”. Stable corrected model parameters a1 and a2 are obtained when setting the predetermined a2 lower limit value XIDA2L to “−1”. However, the predetermined a2 lower limit value XIDA2L is set to a negative value greater than “−1” because the matrix A defined by the equation (26) to the “n”th power may occasionally become unstable (which means that the model parameters a1′ and a2′ do not diverge, but oscillate).
If a2′ is less than XIDA2L in step S81, the corrected model parameter a2 is set to the lower limit value XIDA2L, and an a2 stabilizing flag FA2STAB is set to “1”. When the a2 stabilizing flag FA2STAB is set to “1”, this indicates that the corrected model parameter a2 is set to the lower limit value XIDA2L. In FIG. 18, the correction of the model parameter in a limit process P1 of steps S81 and S82 is indicated by the arrow lines with “P1”.
In steps S84 and S85, it is determined whether or not the model parameter a1′ is in a range defined by a predetermined a1 lower limit value XIDA1L and a predetermined a1 upper limit value XIDA1H. The predetermined a1 lower limit value XIDA1L is set to a value which is equal to or greater than “−2” and lower than “0”, and the predetermined a1 upper limit value XIDA1H is set to “2”, for example.
If a1′ is less than XIDA1L in step S84, the corrected model parameter a1 is set to the lower limit value XIDA1L and an a1 stabilizing flag FA1STAB is set to “1” in step S86. If a1′ is greater than XIDA1H in step S85, the corrected model parameter a1 is set to the upper limit value XIDA1H and the a1 stabilizing flag FA1STAB is set to “1” in step S87. When the a1 stabilizing flag FA1STAB is set to “1”, this indicates that the corrected model parameter a1 is set to the lower limit value XIDA1L or the upper limit value XIDA1H. In FIG. 18, the correction of the model parameter in a limit process P2 of steps S84 through S87 is indicated by the arrow lines with “P2”.
In step S90, it is determined whether or not the sum of the absolute value of the corrected model parameter a1 and the corrected model parameter a2 is less than or equal to a predetermined stability determination value XA2STAB. The predetermined stability determination value XA2STAB is set to a value close to “1” but less than “1” (e.g., “0.99”).
If the answer to step S90 is negative (NO), it is determined whether or not the corrected model parameter a1 is less than or equal to a value obtained by subtracting the predetermined a2 lower limit value XIDA2L from the predetermined stability determination value XA2STAB in step S91 (since XIDA2L is less than “0”, XA2STAB−XIDA2L is greater than XA2STAB). If the corrected model parameter a1 is equal to or less than (XA2STAB−XIDA2L), the corrected model parameter a2 is set to (XA2STAB−|a1|) and the a2 stabilizing flag FA2STAB is set to “1” in step S92.
If the corrected model parameter a1 is greater than (XA2STAB−XIDA2L) in step S91, the corrected model parameter a1 is set to (XA2STAB−XIDA2L) in step S93. Further in step S93, the corrected model parameter a2 is set to the predetermined a2 lower limit value XIDA2L, and the a1 stabilizing flag FA1STAB and the a2 stabilizing flag FA2STAB are set to “1” in step S93.
In FIG. 18, the correction of the model parameter in a limit process P3 of steps S91 and S92 is indicated by the arrow lines with “P3”, and the correction of the model parameter in a limit process P4 in steps S91 and S93 is indicated by the arrow lines with “P4”.
In steps S101 and S102, it is determined whether or not the model parameter b1′ is in a range defined by a predetermined b1 lower limit value XIDB1L and a predetermined b1 upper limit value XIDB1H. The predetermined b1 lower limit value XIDB1L is set to a positive value (e.g., “0.1”), and the predetermined b1 upper limit value XIDB1H is set to “1”, for example.
If b1′ is less than XIDB1L in step S101, the corrected model parameter b1 is set to the lower limit value XIDB1L, and a b1 limiting flag FB1LMT is set to “1” in step S104. If b1′ is greater than XIDB1H in step S102, then the corrected model parameter b1 is set to the upper limit value XIDB1H, and the b1 limiting flag FB1LMT is set to “1” in step S103. When the b1 limiting flag FB1LMT is set to “1”, this indicates that the corrected model parameter b1 is set to the lower limit value XIDB1L or the upper limit value XIDB1H.
In steps S111 and S112, it is determined whether or not the model parameters c1′ is in a range defined by a predetermined c1 lower limit value XIDC1L and a predetermined c1 upper limit value XIDC1H. The predetermined c1 lower limit value XIDC1L is set to “−60”, for example, and the predetermined c1 upper limit value XIDC1H is set to “60”, for example.
If c1′ is less than XIDC1L in step S111, the corrected model parameter c1 is set to the lower limit value XIDC1L, and a c1 limiting flag FC1LMT is set to “1” in step S114. If c1′ is greater than XIDC1H in step S112, the corrected model parameter c1 is set to the upper limit value XIDC1H, and the c1 limiting flag FC1LMT is set to “1” in step S113. When the c1 limiting flag FC1LMT is set to “1”, this indicates that the corrected model parameter c1 is set to the lower limit value XIDC1L or the upper limit value XIDC1H.
In step S206, it is determined whether or not the stability determination flag FSMCSTAB set in the process shown in FIG. 29 is “1”. When the stability determination flag FSMCSTAB is set to “1”, this indicates that the adaptive sliding mode controller 21 is unstable.
If FSMCSTAB is “0” in step S206, indicating that the adaptive sliding mode controller 21 is stable, the control inputs Ueq, Urch, and Uadp which are calculated in steps S203 through S205 are added, thereby calculating the control input Usl in step S207.
If FSMCSTAB is “1” in step S206, indicating that the adaptive sliding mode controller 21 is unstable, the sum of the reaching law input Urch and the adaptive law input Uadp is calculated as the control input Usl. In other words, the equivalent control input Ueq is not used for calculating the control input Usl, thus preventing the control system from becoming unstable.
In step S231, it is determined whether or not the stability determination flag FSMCSTAB is “1”. If FSMCSTAB is “1” in step S231, indicating that the adaptive sliding mode controller 21 is unstable, the switching function setting parameter VPOLE is set to a predetermined stabilizing value XPOLESTB in step S232. The predetermined stabilizing value XPOLESTB is set to a value which is greater than “−1” but very close to “−1” (e.g., “−0.999”).
If FSMCSTAB is “0”, indicating that the adaptive sliding mode controller 21 is stable, an amount of change DDTHR(k) in the target value DTHR(k) is calculated from the following equation (46) in step S233.
In step S234, a VPOLE map is retrieved according to the throttle valve opening deviation amount DTH and the amount of change DDTHR calculated in step S233 to calculate the switching function setting parameter VPOLE. As shown in FIG. 25A, the VPOLE map is set so that the switching function setting parameter VPOLE increases when the throttle valve opening deviation amount DTH has a value in the vicinity of “0”, i.e., when the throttle valve opening TH is in the vicinity of the default opening THDEF, and the switching function setting parameter VPOLE has a substantially constant value regardless of changes of the throttle valve opening deviation amount DTH, when the throttle valve opening deviation amount DTH has values which are not in the vicinity of “0”. The VPOLE map is also set so that the switching function setting parameter VPOLE increases as the amount of change DDTHR in target value increases as indicated by the solid line in FIG. 25B, and the switching function setting parameter VPOLE increases as the amount of change DDTHR in the target value has a value in the vicinity of “0” as indicated by the broken line in FIG. 25B, when the throttle valve opening deviation amount DTH has a value in the vicinity of “0”.
SUMSIGMA(k)=SUMSIGMA(k−1)+σpre×ΔT (47)
In step S261, it is determined whether or not the stability determination flag FSMCSTAB is “1”. If the stability determination flag FSMCSTAB is “0”, indicating that the adaptive sliding mode controller 21 is stable, the control gain F is set to a normal gain XKRCH in step S262, and the reaching law input Urch is calculated from the following equation (48), which is the same as the equation (10 a), in step S263.
Urch=−F×σpre/b1 (48)
If the stability determination flag FSMCSTAB is “1”, indicating that the adaptive sliding mode controller 21 is unstable, the control gain F is set to a predetermined stabilizing gain XKRCHSTB in step S264, and the reaching law input Urch is calculated according to the following equation (49), which does not include the model parameter b1, in step S265.
Urch=−F×σpre (49)
In step S271, it is determined whether or not the stability determination flag FSMCSTAB is “1”. If the stability determination flag FSMCSTAB is “0”, indicating that the adaptive sliding mode controller 21 is stable, the control gain G is set to a normal gain XKADP in step S272, and the adaptive law input Uadp is calculated from the following equation (50), which corresponds to the equation (11a), in step S273.
Uadp=−G×SUMSIGMA/b1 (50)
If the stability determination flag FSMCSTAB is “1”, indicating that the adaptive sliding mode controller 21 is unstable, the control gain G is set to a predetermined stabilizing gain XKADPSTB in step S274, and the adaptive law input Uadp is calculated according to the following equation (51), which does not include the model parameter b1, in step S275.
Uadp=−G×SUMSIGMA (51)
Dσpre=σpre(k)−σpre(k−1) (52)
SGMSTAB=Dσpre×σpre(k) (53)
In step S283, it is determined whether or not the stability determination parameter SGMSTAB is less than or equal to a stability determining threshold XSGMSTAB. If SGMSTAB is greater than XSGMSTAB, it is determined that the adaptive sliding mode controller 21 may possibly be unstable, and an unstability detecting counter CNTSMCST is incremented by “1” in step S285. If SGMSTAB is less than or equal to XSGMSTAB, the adaptive sliding mode controller 21 is determined to be stable, and the count of the unstability detecting counter CNTSMCST is not incremented but maintained in step S284.
In step S286, it is determined whether or not the value of the unstability detecting counter CNTSMCST is less than or equal to a predetermined count XSSTAB. If CNTSMCST is less than or equal to XSSTAB, the adaptive sliding mode controller 21 is determined to be stable, and a first determination flag FSMCSTAB1 is set to “0” in step S287. If CNTSMCST is greater than XSSTAB, the adaptive sliding mode controller 21 is determined to be unstable, and the first determination flag FSMCSTAB1 is set to “1” in step S288. The value of the unstability detecting counter CNTSMCST is initialized to “0”, when the ignition switch is turned on.
In step S289, a stability determining period counter CNTJUDST is decremented by “1”. It is determined whether or not the value of the stability determining period counter CNTJUDST is “0” in step S290. The value of the stability determining period counter CNTJUDST is initialized to a predetermined determining count XCJUDST, when the ignition switch is turned on. Initially, therefore, the answer to step S290 is negative (NO), and the process immediately goes to step S295.
If the count of the stability determining period counter CNTJUDST subsequently becomes “0”, the process goes from step S290 to step S291, in which it is determined whether or not the first determination flag FSMCSTAB1 is “1”. If the first determination flag FSMCSTAB1 is “0”, a second determination flag FSMCSTAB2 is set to “0” in step S293. If the first determination flag FSMCSTAB1 is “1”, the second determination flag FSMCSTAB2 is set to “1” in step S292.
In step S294, the value of the stability determining period counter CNTJUDST is set to the predetermined determining count XCJUDST, and the unstability detecting counter CNTSMCST is set to “0”. Thereafter, the process goes to step S295.
In step S295, the stability determination flag FSMCSTAB is set to the logical sum of the first determination flag FSMCSTAB1 and the second determination flag FSMCSTAB2. The second determination flag FSMCSTAB2 is maintained at “1” until the value of the stability determining period counter CNTJUDST becomes “0”, even if the answer to step S286 becomes affirmative (YES) and the first determination flag FSMCSTAB1 is set to “0”. Therefore, the stability determination flag FSMCSTAB is also maintained at “1” until the value of the stability determining period counter CNTJUDST becomes “0”.
In step S253, a gain parameter PTH(k) is calculated from the following equation (56):
XDEFADPW
The equation (56) is obtained by setting λ1′ and λ2′ in the equation (39) respectively to a predetermined value XDEFADP and “1”.
In the first embodiment described above, the controlled object model is defined by the equation (1) including the dead time d, and the predicted deviation amount PREDTH after the elapse of the dead time d is calculated with the state predictor 23, to thereby control the controlled object model which includes the dead time. Accordingly, it is necessary to execute calculations corresponding to the state predictor 23 in the CPU, and the amount of calculations executed by the CPU becomes large. In the second embodiment, in order to reduce the calculation load on the CPU, the controlled object model is defined by the following equation (1a) where the dead time d is set to “0”, and the modeling error caused by setting the dead time d to “0” is compensated by the robustness of the adaptive sliding mode control.
In order to further reduce the calculation load on the CPU, the fixed gain algorithm is employed as the algorithm for identifying the model parameters.
Using the adaptive sliding mode controller 21 a offers the same advantages as described above in the first embodiment, and achieves the robustness of the control system against the dead time of the controlled object. Therefore, it is possible to compensate for the modeling error that is caused by setting the dead time d to “0”.
The equations (9b), (10b), and (11b) are obtained by setting the dead time d to “0” in the equations (9), (10), and (11).
In the present embodiment, the following requirements B4 and B5 are required to be satisfied, in addition to the requirements B1 through B3 which should be satisfied like the first embodiment should be satisfied.
In order to satisfy the requirement B4, the coefficients λ1 and λ2 are set respectively to “1” and “0”, to thereby employ the fixed gain algorithm. Accordingly, the square matrix P(k) is made constant, and the calculation of the equation (21) can be omitted. As a result, the amount of calculations can greatly be reduced.
According to the algorithm thus simplified, the amount of calculations can be reduced. However, the identifying ability is also slightly reduced. Further, the equation (15) for calculating the model parameter vector θ(k) can be rewritten to the following equation (15b) and has an integral structure of the identifying error ide(k). Therefore, the identifying error ide(k) is likely to be integrated to the model parameters to cause the drift of the model parameters.
θ ( k ) = θ ( 0 ) + KP ( 1 ) ide ( 1 ) + KP ( 2 ) ide ( 2 ) + ⋯ + KP ( k ) ide ( k ) ( 15 b ) where θ(0) represents an initial vector having elements of initial values of the model parameters.
θ ( k ) = θ ( 0 ) + DELTA k - 1 × KP ( 1 ) ide ( 1 ) + DELTA k - 2 × KP ( 2 ) ide ( 2 ) + ⋯ + DELTA × KP ( k - 1 ) ide ( k - 1 ) + KP ( k ) ide ( k ) ( 15 c ) where DELTA represents a forgetting coefficient vector having forgetting coefficients DELTAi (i=1 through 4) as elements, as indicated by the following equation.
The forgetting coefficients DELTAi are set to a value between 0 and 1 (0<DELTAi<1) and have a function to gradually reduce the influence of past identifying errors. One of the coefficient DELTA3 which is relevant to the calculation of the model parameter b1, and the coefficient DELTA4 which is relevant to the calculation of the model parameter c1 is set to “1”. In other words, one of the forgetting coefficients DELTA3 and DELTA4 is made noneffective. By setting one or more of the elements of the forgetting coefficient vector DELTA to “1”, it is possible to prevent a steady-state deviation between the target value DTHR and the throttle valve opening deviation amount DTH from occurring. If both of the coefficients DELTA3 and DELTA4 are set to “1”, the effect of preventing the model parameters from drifting becomes insufficient. Accordingly, it is preferable to set only one of the coefficients DELTA3 or DELTA4 to “1”.
If the equation (15) is rewritten into a recursive form, the following equations (15d) and (15e) are obtained. A process of calculating the model parameter vector θ(k) from the equations (15d) and (15e) instead of the equation (15) is hereinafter referred to as a δ correcting method, and dθ(k) defined by the equation (15e) is referred to as “updating vector”.
θ(k)=θ(0)+dθ(k) (15d)
dθ(k)=DELTA×dθ(k−1)+KP(k)ide(k) (15e)
In step S16 a, a process of determining the stability of the sliding mode controller as shown in FIG. 41 is carried out. Specifically, the stability of the sliding mode controller is determined using the switching function value σ instead of the predicted switching function value σpre, and the stability determination flag FSMCSTAB is set. The process performed when the stability determination flag FSMCSTAB is set to “1” is the same as that the first embodiment.
In step S31 a, the gain coefficient vector KP(k) is calculated from the equation (20a). Then, the estimated throttle valve opening deviation amount DTHHAT(k) is calculated from the equations (18) and (19 a) in step S32 a. In step S33 a, a process of calculating ide(k) as shown in FIG. 35 is carried out to calculate the identifying error ide(k). In step S33 b, the updating vector dθ(k) is calculated from the equation (15e). Then, a θbase table shown in FIG. 34 is retrieved according to the throttle valve opening deviation amount DTH to calculate the reference model parameter vector θbase in step S33 c. In the θbase table, reference model parameters a1base, a2base, and b1base are set. When the throttle valve opening deviation amount DTH has a value close to “0” (i.e., when the throttle opening TH is in the vicinity of the default opening THDEF), the reference model parameters a1base and b1base decrease and the reference model parameter a2base increases. The reference model parameter c1base is set to “0”.
In the present embodiment, the predetermined value XCNTIDST in step S52 is set to “2”, for example, because the dead time d of the controlled object model is set to “0”.
FIG. 37 is a flowchart showing a process of calculating the switching function value σ which is carried out in step S201 a shown in FIG. 36. The process shown in FIG. 37 is different from the process shown in FIG. 23 in that steps S222 through S226 shown in FIG. 23 are changed respectively to steps S222 a through S226 a. In step S222 a, the switching function value σ(k) is calculated from the equation (5). Steps S223 a through S226 a are the steps obtained by replacing “σpre” in steps S223 through S226 shown in FIG. 23 with “σ”. Accordingly, the switching function value σ(k) is subjected to the limit process in the same manner as the process shown in FIG. 23.
SUMSIGMAa(k)=SUMSIGMAa(k−1)+σ×ΔT (47a)
Dσ=σ(k)−σ(k−1) (52a)
SGMSTAB=Dσ×σ(k) (53a)
The second reference value V2BASE is added to bias the central value of the first control quantity U1 which is the output of the adaptive sliding mode controller 122. In the first embodiment, there is no component corresponding to the adder 106, and hence the second reference value V2BASE substantially equals “0” (i.e., U1=U2=Usl). In the present embodiment, the second reference value V2BASE is set to such a value that the opening of the flow rate control valve 111 is 50%, for example.
θ ( k ) = EPS k θ ( 0 ) + EPS k - 1 × KP ( 1 ) ide ( 1 ) + EPS k - 2 × KP ( 2 ) ide ( 2 ) + ⋯ + EPS × KP ( k - 1 ) ide ( k - 1 ) + KP ( k ) ide ( k ) ( 15 g ) where EPS represents a forgetting coefficient vector having forgetting coefficients EPSi (i=1 through 4) as its elements, as indicated by the following equation.
Like the forgetting coefficients DELTAi, the forgetting coefficients EPS1, EPS2, and EPS4 are set to a value between “0” and “1” (0<EPSi<1) and have a function to gradually reduce the influence of past identifying errors.
In the ε correcting method, the coefficient EPS3 which is relevant to the calculation of the model parameter b1 must be set to “1” for the following reasons. In the ε correcting method, the all values of the model parameters becomes closer to zero, as the identifying error ide(k) becomes less. Since the model parameter b1 is applied to the denominator of the equations (9b), (10b), and (11b), the input Usl applied to the controlled object diverges as the model parameter b1 becomes closer to “0”.
θ(k)=EPS×θ(k−1)+KP(k)ide(k) (15h)
According to the control system for a plant of the present invention, one or more model parameters of a controlled object model which is obtained by modeling the plant as a controlled object, are identified, and the sliding mode control using the identified model parameters can be stabilized. Specifically, the present invention is applicable to the control of an actuating device of a throttle valve that controls an amount of air supplied to an internal combustion engine, a combustion system including an internal combustion engine, a chemical plant, or the like. The present invention contributes to improve stability of control when controlling the above controlled object with the sliding mode control. Further, the present invention is also applicable to the control of an engine having an crank shaft mounted vertically, such as an outboard engine for driving a ship.
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Ltd.Method and device for primary frequency regulation based on bang-bang control* Cited by examinerClassifications U.S. Classification700/54, 700/32, 701/85, 700/52, 700/71, 123/337, 700/37, 123/398, 123/376International ClassificationG05B13/02, F02D41/14, F02D9/08, F02D31/00, G06F17/00, F02D11/02, F02D35/00, G05B23/02, G05B11/01, G05B13/04Cooperative ClassificationG05B13/042, F02D41/1403, F02D35/0007, G05B13/047, G05B13/048European ClassificationG05B13/04B, G05B13/04D, G05B13/04C, F02D41/14B4, F02D35/00B, G05B23/02BLegal EventsDateCodeEventDescriptionOct 6, 2010FPAYFee paymentYear of fee payment: 4Oct 8, 2014FPAYFee paymentYear of fee payment: 8RotateOriginal ImageGoogle Home - Sitemap - USPTO Bulk Downloads - Privacy Policy - Terms of Service - About Google Patents - Send FeedbackData provided by IFI CLAIMS Patent Services