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F consolidated control using decoupling control theory
JSAE Review 22 (2001) 9}14
Engine-CVT-A/F consolidated control using decoupling control theory Takeshi Takiyama Department of Mechanical Engineering, Faculty of Engineering, Osaka City University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan Received 20 December 1999; received in revised form 17 July 2000
Abstract If an engine with an electric throttle valve control and CVT is "tted to the powertrain, fuel consumption becomes economical while the throttle valve angle and the gear ratio of CVT are controlled simultaneously. If the engine is operated with a lean air-fuel ratio (A/F), it is also e!ective for fuel economy. Therefore, combining A/F control with the simultaneous control of the throttle valve angle and the gear ratio becomes a more important method for controlling the powertrain of a car. Though these input-output relations were complicated, an adequate and convenient control method was required for the synthetic powertrain control. From such a point of view, Engine-CVT-A/F consolidated control using decoupling control theory was investigated. 2001 Society of Automotive Engineers of Japan, Inc. and Elsevier Science B.V. All rights reserved.
1. Introduction When CVT (Continuously Variable Transmission) is "tted to the engine, the gear ratio can be changed voluntary within the mechanical limit. Therefore, fuel consumption of the engine becomes economical while satisfying the driving style if the throttle valve angle of the engine (h) and the gear ratio of the CVT (R ) are controlled K simultaneously [1]. Then, it is expected that further improvement of fuel economy can be obtained if CVT is combined with a lean burn SI engine [2]. Thus, it is expected that such powertrain system will become common because of environmental regulations. However, though the optimum economical point changes according to air-fuel ratio (A/F), combining air-fuel ratio (A/F) with the present consolidated control of the throttle valve angle (h) and CVT gear ratio (R ) and controlling those K parameters simultaneously becomes an important method for the powertrain control [3]. Then, it is expected that fuel economy and exhaust gas treatment become highly optimum over wider operating conditions than present while satisfying the driving style, because the control parameter of the powertrain system will be extended by such consolidated control. As is well known, the present A/F control algorithm at transient state is compensated in terms of the dynamics behavior because the time response of the induction system is slow [4]. In addition to this, it is supposed that the A/F control algorithm becomes complicated because the operation of the SI engine without stoichiometric
A/F seems to be increasing recently. The A/F control algorithm is generally decided depending on the operating condition and the exhaust gas treatment method. However, it is considered that it is necessary for simplifying the A/F control algorithm to control A/F as conveniently as possible without considering the interaction among the many factors of the engine conditions. Therefore, when the vehicle speed control subsystem, the fuel optimizing control subsystem and the A/F control subsystem under the powertrain control system can be treated as an independent single input}output system rather than a multi input}output system, the independent design of the control system or the independent decision of the control algorithm becomes possible and convenient. Thus, it is expected that the control performance of the powertrain system will be improved for fuel economy and exhaust gas treatment, because the total powertrain control scheme becomes simple and synthetic. From such a point of view, Engine-CVT-A/F consolidated control using decoupling control theory was investigated as an insightful and simple synthesis method for the powertrain system.
2. Experimental apparatus and objective model 2.1. Experimental apparatus Fig. 1 shows the schematic diagram of the experimental powertrain simulator and Table 1 provides the
0389-4304/01/$20.00 2001 Society of Automotive Engineers of Japan, Inc. and Elsevier Science B.V. All rights reserved. PII: S 0 3 8 9 - 4 3 0 4 ( 0 0 ) 0 0 0 9 7 - 7
JSAE20014002
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T. Takiyama / JSAE Review 22 (2001) 9}14
corresponding speci"cations and nomenclature. The sign &above a symbol represents the target value. The objective system is a driving simulator consisting of a 1300 cc SI engine equipped with a metal-V-belt CVT, a #ywheel of inertia equal to the vehicle mass (approx. 900 kg), an eddy current dynamometer that generates running resistance and its measurement and control system. In order to change the gear ratio of CVT (R ), a rack (R), which is
driven by the stepping motor, is actuated by wire to move
the shift cam that is linked to the shift-control valve. The throttle valve is also manipulated by the stepping motor through the wire. A/F (air fuel ratio) is varied by operating the fuel injection mass using ECU commanding voltage and A/F is measured at the exhaust manifold with a LAF (linear-A/F) sensor. This sensor can measure the excess air ratio from 0.6 to 1.6. k is then used as the symbol of the excess air ratio. The A/F lean limit of this SI engine is approximately j"1.3 (A/F"19) because the engine is of port-injection type and not equipped with any e!ective method for lean combustion. It was considered that this limit was no matter for this study. 2.2. Objective model An objective engine-CVT-A/F-Load model was developed for both the purpose of the decoupled system design and the strategic consolidated control investigation of the powertrain system. From the point of view of powertrain control, it was necessary to develop the objective model whose dynamic characteristic mostly agreed with the experimental simulator. Therefore, the objective Engine-CVT-A/F Load model, as shown in Fig. 2, was developed depending on the characteristics of the experimental rig such as the metal V-belt CVT static character. n was used as the output value instead of the vehicle U speed (<) because a bench-type apparatus was used.
Fig. 1. Schematic diagram of experimental equipment.
Table 1 Speci"cations of experimental rig and nomenclature Engine Swept volume Maximum power Maximum torque
(< ) (¸ max) (¹ max)
0.0013 58 105.9
m kW Nm
Tansmission & Final CVT gear ratio Final gear ratio
(R )
(R )
2.503}0.497 5.246 Car Body
Vehicle mass (Flywheel) Front project area Coe$. of drag Tire radius Coe$. of roll. resist. Mass density of air
(M) (A) (C ) (r ) (k ) (o)
900 1.82 0.35 0.264 0.018 1.205
kg m * m * kg/m
n : Dynamometer speed n : Wheel speed ¹ : Dynamometer torque ¹ : Wheel torque d: Gradient of road h: Throttle valve angle
s\ s\ N N rad rad
Others F : Running resistance * n : Engine speed R: Rack position ¹ : Load torque * V: Vehicle speed j: Air excess ratio &: Symbol of target value
N s\ mm N m/s !
T. Takiyama / JSAE Review 22 (2001) 9}14
11
Fig. 2. Objective model.
Then, a well known fuel #ow model [4] was adopted for A/F subsystem. Though the detail of matrix elements and the identi"cation results were omitted for want of space, good identi"cation results were obtained. Therefore, it was concluded that this objective model was appropriate for use as an Engine-CVT-A/F-Load model.
3. Design of decoupled system 3.1. Simplixcation of objective system Equation (2) denotes the system matrix P(s) of the multi input-output system of Eq. (1). The solution of "P(s)""0 should be negative for stable condition of the decoupled system. Then, Eq. (3) was obtained as the determinant "P(s)". x (t)"Ax(t)#Bu(t), (1)
y(t)"Cx(t),
P(s)"
A!sI B C
0
,
(2)
*g *g *n *j *h *R "P(s)"" +12#6¸s#(¸s), J¸¹ ¹ ¹ ¹ *j *¹ *j *¹ ! , (3) ;(1#sa¹ ) (1#s¹
*g *g *g *g s(0, Therefore,
*j *¹ *j *¹ ' . (4) *g *g *g *g The "rst term and the second term of the right side + , of Eq. (3) become negative (s(0). In the third term, the condition of Eq. (4) should be negative (s(0). However, though the parameter *¹ /*g of the objective system is
relatively bigger than the other parameter values, the decoupled system becomes unstable. Though the in#uence from A/F command (j ) to wheel speed (n ) can be compensated by the closed loop system because the time response was relatively long, the in#uence from throttle valve (h) to A/F output (j ) causes serious damage for A/F control because the time response is very quick. Therefore, it was considered that the in#uence from the induction system (h) to the A/F system (j ) should be decoupled to simplify the A/F control algorithm. Then, the system, regarding *¹ /*g "0, was considered as the objective decoupling system for the aim both of decoupling the in#uence from h to j and regarding the in#uence from j to n as a disturbance. Also, a dead time element did not appear in the decoupled system when pade approximation was substituted for the dead time factor. Therefore, a "fth order objective system, that eliminated the dead time factor, was considered as the objective decoupling system for simplicity of the designing method. Under these assumptions, Eq. (5) denotes the determinant and Eq. (6) denotes the stable condition for the decoupled system. This condition can always be satis"ed without any restriction. Therefore, the decoupled system always becomes stable. !*g *g *n *j *¹ *j *h *R *g *g "P(s)"" (1#sa¹ ) J¹ ¹ ¹ ¹
(5)
Therefore, 1 s"! (0 a¹
(6)
3.2. Decoupled system As is well known, decoupling control theory is used to obtain the pair of matrices +F, G, that were used at the
12
T. Takiyama / JSAE Review 22 (2001) 9}14
state feedback u"!Fx#Gw. Then, by such state feedback, the transfer function matrix of closed loop system was translated to a diagonal matrix that satis"es any diagonal element not being zero. The pair of matrices +F, G, can be obtained using an appropriate state transfer (z"S x). The detail of the state transfer was omitted @ for space reasons, please see the reference [5]. Then, the decoupled system is not stable if the decoupled system only consists of an integrator. Therefore, the decoupled system should be stable with the proper feedback system w"!fz#w using the voluntary feedback gain f. Consequently, Eq. (7) denotes the decoupled system. The relation between new inputs w , w , w and outputs n , n , j became independent as the single input}output system and a stable decoupled system was obtained.
n
n " j
1 f #s(f #s) 0
0 1 s#f
0
0
0 0 1 s#f
w w . w
(7)
In Eq. (7), f , f , f , f denote the feedback gains that are stable for each input-output subsystem of the decoupled system. Though these gains f can be determined for the time constant of each subsystem's input-output relation, they were determined to obtain the same time response of the experimental rig by simulation. Especially, many time response characters for w !n sub system can be obtained because that subsystem was a second order system. However, from the point of view of stability and convenient, f , f were determined at the multiple root on the real-axis.
4. Experimental result 4.1. Experimental condition Fig. 3 illustrates the condition of driving mode and A/F variable pattern. The experiment was carried out using those conditions. The A/F control algorithm was essentially decided by the operating condition or the treatment method for exhaust emission. However, the algorithm assumed that A/F vary stepwise (plan A) or continuously (plan B) from lean to stoichiometric for investigation the decoupling e!ect. To operate on the optimum fuel point, the engine speed, denoted in Eq. (8), was commanded as the target engine speed [3]. a and b are the inclination and the interception of the fuel optimum line, respectively. !b#(b#(2a/n) jI ¸ C. nJ " 2a
(8)
Fig. 3. Experimental condition: (A) driving mode; and (B) A/F plan.
Fig. 4. Schematic diagram of total system.
Fig. 4 shows the block diagram of the total objective system. Though the state values were required for the decoupled system, not every state was observed because of experimental restrictions. Though we tried to apply an observer system, it was very di$cult to apply this objective system because of a multi input-output coupled system. Therefore, the state values were obtained by forward calculation of the time response of the objective model, assuming the initial values of the objective model were the same as those of the experiment. The experimental values of h, R, j were used as the input values of the model calculation to obtain the state values. However, since the experimental signal of h had small scatter, the signal of h was "ltered through the "rst order digital "lter to eliminate the scatter signal. Then, the signal of j from the output of the decoupled system also had a di!erentiate signal because of h scatter. Though the enlargement of f was investigated to satisfy both the "ltering performance and the stabilizing performance at the same time, the signal of j was "nally "ltered at the input of the experimental rig from the point of view of the control performance. The symbol Fil. in Fig. 4 means these "lters. The output signals from the decoupled system were disturbed when h was saturated at WOT. Though some countermeasure method was investigated, "nally, the decoupled system was not used only while h was saturated at WOT. Thus, in such case, the system was only controlled by the ordinary closed loop without the decoupled system. The closed loop was operated by the PI control system, and the PI gains were exchanged whether the decoupled system was available or not. 4.2. Experimental results Figs. 5 and 6 represent the experimental results in condition of driving mode a. The left side part of each
T. Takiyama / JSAE Review 22 (2001) 9}14
13
the equation <"2pr n . Fuel optimum line (Ideal line) was linearised according to the engine power. The following issues were recognized:
Fig. 5. Experimental results using driving mode a and A/F Plan A.
(i) The dynamic characteristic performance was changed because the pole position of each subsystem were moved by the stabilization of the decoupled system. Therefore, the behavior of h was remarkably di!erent from that of non-decoupled system because the car speed control subsystem was a second order system. Therefore, it was considered that the objective system was satisfactorily decoupled. (ii) Some droop was recognized because the closed loop system was a "rst type system. However, the car speed < has relatively good agreement with the target speed
(9) (10) (11)
Fig. 7 represents the evaluation result while accelerating. The white bar indicates the performance only using the PI control without the decoupled system (PI). The gray bar indicates the performance using the gain scheduling feedforward compensation depending on the movement of h in addition to the former controller (FF). The black bar indicates the performance using the decoupled system (DCP). These values were translated to the relative values by a maximum value and the small value means an excellent evaluation. Fig. 6. Experimental results using driving mode a and A/F Plan B.
"gure represents the time response of each value for experimental rig, the right above part indicates the engine behavior and the right below part indicates the vehicle behavior. The vehicle speed was indicated using
(i) In the case of driving mode a, the black bar is almost the smallest value of all. Therefore, it was considered that the decoupled system most satisfactory operated the Engine-CVT-A/F consolidated control. (ii) The black bar of E< at plan B is relatively large. 4 The reason was that acceleration of the engine was slow because the operation of h was so moderate
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T. Takiyama / JSAE Review 22 (2001) 9}14
Fig. 7. Performance comparison result.
that attaining WOT became slow when the decoupled system was available. However, it was considered to be improved by the feedforward compensation. Since the lack of the engine power at lean mixture was also recognized, it was considered that improving of the combustion promotion was also e!ective and necessary. (iii) In the case of the driving mode b, good agreement with the target speed was not obtained because h was saturated at WOT and the engine was not able to generate the required power by nJ increas ing. However, it was considered to be improved by applying the total feedforward control system. 5. Conclusion 1. Investigation was carried out on the Engine-CVT-A/F consolidated control using decoupling control theory and good control performances were obtained. 2. Vehicle speed control subsystem, fuel optimizing control subsystem and A/F control sub-system under the powertrain control can be treated as the single input}output subsystem independently by decoupling control theory. Therefore, it is expected that the control performance for the powertrain system becomes so improbable that high fuel economy and high exhaust treatment can be obtained because it is
considered that the application of every kind of control theory and any control algorithm become simple and synthetic when the decoupled control system is available.
Acknowledgements The author wishes to express his gratitude to Prof. S. Morita of Osaka City University for his helpful discussion and M. Yasuoka of Nissan Motor Co., Ltd. for provision of the A/F variable equipment.
References [1] Takiyama, T., Morita, S., Analysis of improvement of fuel consumption by engine-CVT consolidated control, Proc. AVEC'96, Vol. 2, pp. 1159}1167 (1996). [2] Saitoh, K. et al., Development of `NEO DI(QG18DD)#HYPER CVTa (in Japanese with English summary), Nissan Technical Review, Vol. 44, pp. 13}16 (1999). [3] Takiyama, T., Engine-CVT consolidated control for variable A/F, CVT '99, September 1999, pp. 36}41. [4] Matumura, T., Nanyoshi, Y., New fuel metering technique for compensating wall #ow in a transient condition using the model-matching method, JSAE Rev. Vol. 10, No. 3, pp. 5}9 (1989). [5] Ogou, H., Mita, T., System control theory, Jikkyou Syuppan, pp. 180}194 (in Japanese).
Engine-CVT-A/F consolidated control using decoupling control theory Takeshi Takiyama Department of Mechanical Engineering, Faculty of Engineering, Osaka City University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan Received 20 December 1999; received in revised form 17 July 2000
Abstract If an engine with an electric throttle valve control and CVT is "tted to the powertrain, fuel consumption becomes economical while the throttle valve angle and the gear ratio of CVT are controlled simultaneously. If the engine is operated with a lean air-fuel ratio (A/F), it is also e!ective for fuel economy. Therefore, combining A/F control with the simultaneous control of the throttle valve angle and the gear ratio becomes a more important method for controlling the powertrain of a car. Though these input-output relations were complicated, an adequate and convenient control method was required for the synthetic powertrain control. From such a point of view, Engine-CVT-A/F consolidated control using decoupling control theory was investigated. 2001 Society of Automotive Engineers of Japan, Inc. and Elsevier Science B.V. All rights reserved.
1. Introduction When CVT (Continuously Variable Transmission) is "tted to the engine, the gear ratio can be changed voluntary within the mechanical limit. Therefore, fuel consumption of the engine becomes economical while satisfying the driving style if the throttle valve angle of the engine (h) and the gear ratio of the CVT (R ) are controlled K simultaneously [1]. Then, it is expected that further improvement of fuel economy can be obtained if CVT is combined with a lean burn SI engine [2]. Thus, it is expected that such powertrain system will become common because of environmental regulations. However, though the optimum economical point changes according to air-fuel ratio (A/F), combining air-fuel ratio (A/F) with the present consolidated control of the throttle valve angle (h) and CVT gear ratio (R ) and controlling those K parameters simultaneously becomes an important method for the powertrain control [3]. Then, it is expected that fuel economy and exhaust gas treatment become highly optimum over wider operating conditions than present while satisfying the driving style, because the control parameter of the powertrain system will be extended by such consolidated control. As is well known, the present A/F control algorithm at transient state is compensated in terms of the dynamics behavior because the time response of the induction system is slow [4]. In addition to this, it is supposed that the A/F control algorithm becomes complicated because the operation of the SI engine without stoichiometric
A/F seems to be increasing recently. The A/F control algorithm is generally decided depending on the operating condition and the exhaust gas treatment method. However, it is considered that it is necessary for simplifying the A/F control algorithm to control A/F as conveniently as possible without considering the interaction among the many factors of the engine conditions. Therefore, when the vehicle speed control subsystem, the fuel optimizing control subsystem and the A/F control subsystem under the powertrain control system can be treated as an independent single input}output system rather than a multi input}output system, the independent design of the control system or the independent decision of the control algorithm becomes possible and convenient. Thus, it is expected that the control performance of the powertrain system will be improved for fuel economy and exhaust gas treatment, because the total powertrain control scheme becomes simple and synthetic. From such a point of view, Engine-CVT-A/F consolidated control using decoupling control theory was investigated as an insightful and simple synthesis method for the powertrain system.
2. Experimental apparatus and objective model 2.1. Experimental apparatus Fig. 1 shows the schematic diagram of the experimental powertrain simulator and Table 1 provides the
0389-4304/01/$20.00 2001 Society of Automotive Engineers of Japan, Inc. and Elsevier Science B.V. All rights reserved. PII: S 0 3 8 9 - 4 3 0 4 ( 0 0 ) 0 0 0 9 7 - 7
JSAE20014002
10
T. Takiyama / JSAE Review 22 (2001) 9}14
corresponding speci"cations and nomenclature. The sign &above a symbol represents the target value. The objective system is a driving simulator consisting of a 1300 cc SI engine equipped with a metal-V-belt CVT, a #ywheel of inertia equal to the vehicle mass (approx. 900 kg), an eddy current dynamometer that generates running resistance and its measurement and control system. In order to change the gear ratio of CVT (R ), a rack (R), which is
driven by the stepping motor, is actuated by wire to move
the shift cam that is linked to the shift-control valve. The throttle valve is also manipulated by the stepping motor through the wire. A/F (air fuel ratio) is varied by operating the fuel injection mass using ECU commanding voltage and A/F is measured at the exhaust manifold with a LAF (linear-A/F) sensor. This sensor can measure the excess air ratio from 0.6 to 1.6. k is then used as the symbol of the excess air ratio. The A/F lean limit of this SI engine is approximately j"1.3 (A/F"19) because the engine is of port-injection type and not equipped with any e!ective method for lean combustion. It was considered that this limit was no matter for this study. 2.2. Objective model An objective engine-CVT-A/F-Load model was developed for both the purpose of the decoupled system design and the strategic consolidated control investigation of the powertrain system. From the point of view of powertrain control, it was necessary to develop the objective model whose dynamic characteristic mostly agreed with the experimental simulator. Therefore, the objective Engine-CVT-A/F Load model, as shown in Fig. 2, was developed depending on the characteristics of the experimental rig such as the metal V-belt CVT static character. n was used as the output value instead of the vehicle U speed (<) because a bench-type apparatus was used.
Fig. 1. Schematic diagram of experimental equipment.
Table 1 Speci"cations of experimental rig and nomenclature Engine Swept volume Maximum power Maximum torque
(< ) (¸ max) (¹ max)
0.0013 58 105.9
m kW Nm
Tansmission & Final CVT gear ratio Final gear ratio
(R )
(R )
2.503}0.497 5.246 Car Body
Vehicle mass (Flywheel) Front project area Coe$. of drag Tire radius Coe$. of roll. resist. Mass density of air
(M) (A) (C ) (r ) (k ) (o)
900 1.82 0.35 0.264 0.018 1.205
kg m * m * kg/m
n : Dynamometer speed n : Wheel speed ¹ : Dynamometer torque ¹ : Wheel torque d: Gradient of road h: Throttle valve angle
s\ s\ N N rad rad
Others F : Running resistance * n : Engine speed R: Rack position ¹ : Load torque * V: Vehicle speed j: Air excess ratio &: Symbol of target value
N s\ mm N m/s !
T. Takiyama / JSAE Review 22 (2001) 9}14
11
Fig. 2. Objective model.
Then, a well known fuel #ow model [4] was adopted for A/F subsystem. Though the detail of matrix elements and the identi"cation results were omitted for want of space, good identi"cation results were obtained. Therefore, it was concluded that this objective model was appropriate for use as an Engine-CVT-A/F-Load model.
3. Design of decoupled system 3.1. Simplixcation of objective system Equation (2) denotes the system matrix P(s) of the multi input-output system of Eq. (1). The solution of "P(s)""0 should be negative for stable condition of the decoupled system. Then, Eq. (3) was obtained as the determinant "P(s)". x (t)"Ax(t)#Bu(t), (1)
y(t)"Cx(t),
P(s)"
A!sI B C
0
,
(2)
*g *g *n *j *h *R "P(s)"" +12#6¸s#(¸s), J¸¹ ¹ ¹ ¹ *j *¹ *j *¹ ! , (3) ;(1#sa¹ ) (1#s¹
*g *g *g *g s(0, Therefore,
*j *¹ *j *¹ ' . (4) *g *g *g *g The "rst term and the second term of the right side + , of Eq. (3) become negative (s(0). In the third term, the condition of Eq. (4) should be negative (s(0). However, though the parameter *¹ /*g of the objective system is
relatively bigger than the other parameter values, the decoupled system becomes unstable. Though the in#uence from A/F command (j ) to wheel speed (n ) can be compensated by the closed loop system because the time response was relatively long, the in#uence from throttle valve (h) to A/F output (j ) causes serious damage for A/F control because the time response is very quick. Therefore, it was considered that the in#uence from the induction system (h) to the A/F system (j ) should be decoupled to simplify the A/F control algorithm. Then, the system, regarding *¹ /*g "0, was considered as the objective decoupling system for the aim both of decoupling the in#uence from h to j and regarding the in#uence from j to n as a disturbance. Also, a dead time element did not appear in the decoupled system when pade approximation was substituted for the dead time factor. Therefore, a "fth order objective system, that eliminated the dead time factor, was considered as the objective decoupling system for simplicity of the designing method. Under these assumptions, Eq. (5) denotes the determinant and Eq. (6) denotes the stable condition for the decoupled system. This condition can always be satis"ed without any restriction. Therefore, the decoupled system always becomes stable. !*g *g *n *j *¹ *j *h *R *g *g "P(s)"" (1#sa¹ ) J¹ ¹ ¹ ¹
(5)
Therefore, 1 s"! (0 a¹
(6)
3.2. Decoupled system As is well known, decoupling control theory is used to obtain the pair of matrices +F, G, that were used at the
12
T. Takiyama / JSAE Review 22 (2001) 9}14
state feedback u"!Fx#Gw. Then, by such state feedback, the transfer function matrix of closed loop system was translated to a diagonal matrix that satis"es any diagonal element not being zero. The pair of matrices +F, G, can be obtained using an appropriate state transfer (z"S x). The detail of the state transfer was omitted @ for space reasons, please see the reference [5]. Then, the decoupled system is not stable if the decoupled system only consists of an integrator. Therefore, the decoupled system should be stable with the proper feedback system w"!fz#w using the voluntary feedback gain f. Consequently, Eq. (7) denotes the decoupled system. The relation between new inputs w , w , w and outputs n , n , j became independent as the single input}output system and a stable decoupled system was obtained.
n
n " j
1 f #s(f #s) 0
0 1 s#f
0
0
0 0 1 s#f
w w . w
(7)
In Eq. (7), f , f , f , f denote the feedback gains that are stable for each input-output subsystem of the decoupled system. Though these gains f can be determined for the time constant of each subsystem's input-output relation, they were determined to obtain the same time response of the experimental rig by simulation. Especially, many time response characters for w !n sub system can be obtained because that subsystem was a second order system. However, from the point of view of stability and convenient, f , f were determined at the multiple root on the real-axis.
4. Experimental result 4.1. Experimental condition Fig. 3 illustrates the condition of driving mode and A/F variable pattern. The experiment was carried out using those conditions. The A/F control algorithm was essentially decided by the operating condition or the treatment method for exhaust emission. However, the algorithm assumed that A/F vary stepwise (plan A) or continuously (plan B) from lean to stoichiometric for investigation the decoupling e!ect. To operate on the optimum fuel point, the engine speed, denoted in Eq. (8), was commanded as the target engine speed [3]. a and b are the inclination and the interception of the fuel optimum line, respectively. !b#(b#(2a/n) jI ¸ C. nJ " 2a
(8)
Fig. 3. Experimental condition: (A) driving mode; and (B) A/F plan.
Fig. 4. Schematic diagram of total system.
Fig. 4 shows the block diagram of the total objective system. Though the state values were required for the decoupled system, not every state was observed because of experimental restrictions. Though we tried to apply an observer system, it was very di$cult to apply this objective system because of a multi input-output coupled system. Therefore, the state values were obtained by forward calculation of the time response of the objective model, assuming the initial values of the objective model were the same as those of the experiment. The experimental values of h, R, j were used as the input values of the model calculation to obtain the state values. However, since the experimental signal of h had small scatter, the signal of h was "ltered through the "rst order digital "lter to eliminate the scatter signal. Then, the signal of j from the output of the decoupled system also had a di!erentiate signal because of h scatter. Though the enlargement of f was investigated to satisfy both the "ltering performance and the stabilizing performance at the same time, the signal of j was "nally "ltered at the input of the experimental rig from the point of view of the control performance. The symbol Fil. in Fig. 4 means these "lters. The output signals from the decoupled system were disturbed when h was saturated at WOT. Though some countermeasure method was investigated, "nally, the decoupled system was not used only while h was saturated at WOT. Thus, in such case, the system was only controlled by the ordinary closed loop without the decoupled system. The closed loop was operated by the PI control system, and the PI gains were exchanged whether the decoupled system was available or not. 4.2. Experimental results Figs. 5 and 6 represent the experimental results in condition of driving mode a. The left side part of each
T. Takiyama / JSAE Review 22 (2001) 9}14
13
the equation <"2pr n . Fuel optimum line (Ideal line) was linearised according to the engine power. The following issues were recognized:
Fig. 5. Experimental results using driving mode a and A/F Plan A.
(i) The dynamic characteristic performance was changed because the pole position of each subsystem were moved by the stabilization of the decoupled system. Therefore, the behavior of h was remarkably di!erent from that of non-decoupled system because the car speed control subsystem was a second order system. Therefore, it was considered that the objective system was satisfactorily decoupled. (ii) Some droop was recognized because the closed loop system was a "rst type system. However, the car speed < has relatively good agreement with the target speed
(9) (10) (11)
Fig. 7 represents the evaluation result while accelerating. The white bar indicates the performance only using the PI control without the decoupled system (PI). The gray bar indicates the performance using the gain scheduling feedforward compensation depending on the movement of h in addition to the former controller (FF). The black bar indicates the performance using the decoupled system (DCP). These values were translated to the relative values by a maximum value and the small value means an excellent evaluation. Fig. 6. Experimental results using driving mode a and A/F Plan B.
"gure represents the time response of each value for experimental rig, the right above part indicates the engine behavior and the right below part indicates the vehicle behavior. The vehicle speed was indicated using
(i) In the case of driving mode a, the black bar is almost the smallest value of all. Therefore, it was considered that the decoupled system most satisfactory operated the Engine-CVT-A/F consolidated control. (ii) The black bar of E< at plan B is relatively large. 4 The reason was that acceleration of the engine was slow because the operation of h was so moderate
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T. Takiyama / JSAE Review 22 (2001) 9}14
Fig. 7. Performance comparison result.
that attaining WOT became slow when the decoupled system was available. However, it was considered to be improved by the feedforward compensation. Since the lack of the engine power at lean mixture was also recognized, it was considered that improving of the combustion promotion was also e!ective and necessary. (iii) In the case of the driving mode b, good agreement with the target speed was not obtained because h was saturated at WOT and the engine was not able to generate the required power by nJ increas ing. However, it was considered to be improved by applying the total feedforward control system. 5. Conclusion 1. Investigation was carried out on the Engine-CVT-A/F consolidated control using decoupling control theory and good control performances were obtained. 2. Vehicle speed control subsystem, fuel optimizing control subsystem and A/F control sub-system under the powertrain control can be treated as the single input}output subsystem independently by decoupling control theory. Therefore, it is expected that the control performance for the powertrain system becomes so improbable that high fuel economy and high exhaust treatment can be obtained because it is
considered that the application of every kind of control theory and any control algorithm become simple and synthetic when the decoupled control system is available.
Acknowledgements The author wishes to express his gratitude to Prof. S. Morita of Osaka City University for his helpful discussion and M. Yasuoka of Nissan Motor Co., Ltd. for provision of the A/F variable equipment.
References [1] Takiyama, T., Morita, S., Analysis of improvement of fuel consumption by engine-CVT consolidated control, Proc. AVEC'96, Vol. 2, pp. 1159}1167 (1996). [2] Saitoh, K. et al., Development of `NEO DI(QG18DD)#HYPER CVTa (in Japanese with English summary), Nissan Technical Review, Vol. 44, pp. 13}16 (1999). [3] Takiyama, T., Engine-CVT consolidated control for variable A/F, CVT '99, September 1999, pp. 36}41. [4] Matumura, T., Nanyoshi, Y., New fuel metering technique for compensating wall #ow in a transient condition using the model-matching method, JSAE Rev. Vol. 10, No. 3, pp. 5}9 (1989). [5] Ogou, H., Mita, T., System control theory, Jikkyou Syuppan, pp. 180}194 (in Japanese).