- Email: [email protected]
A Novel Pushbelt CVT Actuation System and Control Strategy*
6th IFAC Symposium Advances in Automotive Control Munich, Germany, July 12-14, 2010
A Novel Pushbelt CVT Actuation System and Control Strategy ? L. He ∗ L. Li ∗ X. L. Zhang ∗ J. Song ∗ ∗
State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing, China (Tel: +10-627-97118; e-mail: [email protected]).
Abstract: The CVT hydraulic actuation system almost adopt pressure sensors to feedback the pulley cylinder pressure to traction control unit (TCU), which is complex structure, high cost and poor reliability. A new electro-hydraulic actuation system that gets rid of the pressure sensors will be described in detail. It is for the clamping force control of CVT to adopt the bang-bang control and use the piecewise optimal method to control the gear ratio. Then, the rapid control prototype (RCP) of CVT is produced to evaluate the new CVT actuation system. At last, the new electro-hydraulic actuation system and its control strategy are tested on vehicle. The experimental results also confirm that the new CVT hydraulic system is stability and rapid response to actuate the CVT variator. Keywords: CVT; Electro-hydraulic Actuation System; Control Strategy; RCP. 1. INTRODUCTION Over the last few decades, environmental concerns have made it imperative for the government of most of the nations to impose stringent regulations on the fuel consumption and exhaust emissions of the vehicles in order to reduce the polluting emissions and the green-house gasses [He, 2008]. In order to fulfill these requirements, car manufacturers have been obligated to dramatically reduce vehicles gas emissions and improve the fuel consumption in relatively short times. Thus, a great deal of research has been devoted to find new technical solutions, which may improve the emission performances of nowadays IC engine vehicles. So far, vehicular drivelines with an internal combustion engine, an electronic throttle valve, and a CVT can offer much freedom in controlling the engine speed and torque, which can be used to improve fuel economy by operating the engine in fuel-optimal operating points. According to some tests of automotive company, the CVT can reduce the fuel consumption of engine 3-14% than automatic transmission reputedly, and it is possible for fuel economy to increase 5-10% of CVT driveline in the future, therefore, the CVT is regarded as a promising approach that can reduce energy consumption and exhaust emissions [Francis, 2006]. Through the number of publications concerning CVT is exceptionally large; it is seldom that introduces a full electro-hydraulic actuation system including its control strategy completely. Moreover, most of the approaches control the clamping pressure at the secondary pulley and control the CVT speed ratio by steering the oil flow into the primary pulley cylinder [Spijker, 2006, Vanvuchelen, 1997]. Wade put forward firstly the CVT thrust control concept to control both pulley pressures simultaneously
[Wade, 1984]. After that, there were lots of the researches of CVT pressure control, but in the recent years, it is seldom relatively. Thereinto, Ryu developed a model-based control algorithm for the pressure control type CVT using the steady state characteristics of the ratio control valve. In a pressure control CVT system, the desired speed ratio is obtained by controlling the primary actuator pressure [Ryu, 2005]. In order to further improve the control performance, Adachi coupled their robust controller to a feedforward controller and modeled the two-degree-offreedom CVT control system as a first-order lag system with an uncertain time constant and time delay [Adachi, 2006]. Pesgens developed a new ratio controller for a metal pushing V-belt CVT with a hydraulic clamping system whose ratio controller guaranteed that at least one of the pressure set points was always minimal with respect to its constraints, while the other was raised above the minimum level to enable shifting [Pesgens, 2005]. However, in these hydraulic actuation systems [Srivastava, 2009, Tsukuda, 2006], the pressure controllers are augmented by a ratio controller to achieve the desired ratio response accurately. Therefore, the current actuation systems adopted pressure sensors to feed the pulley cylinder pressure back to TCU, which are complex structure, high cost and poor reliability [Song, 2008]. In this paper, a full electro-hydraulic actuation system that gets rid of the pressure sensors will be described in detail, and developed a clamping force controller using Bang-Bang control principle and a gear ratio control strategy using the piecewise optimum control concept for this CVT actuation system. Then, the CVT rapid control prototype was produced to evaluate the new control strategy. At last, both this electro-hydraulic actuation system and its control strategy were tested on board.
? This work was supported in part by the State Key Laboratory of Automotive Safety and Energy of China.
978-3-902661-72-2/10/$20.00 © 2010 IFAC
489
10.3182/20100712-3-DE-2013.00151
AAC 2010 Munich, Germany, July 12-14, 2010
2. CVT HYDRAULIC ACTUATION SYSTEM
is used to make a communication between the high level control and low level drive.
As for the description of figure 1, it is easy to see that the variator of CVT transmits the power by the friction between pulley and pushbelt. Hereby, the variator need enough thrust to clamp both pulleys and pushbelt together during the operation. The hydraulic system is easy to be control, simple and low cost, in general, which was adopted to supply a pressure for the pulley of CVT variator. In Fig. 1, there is a hydraulic system sketch map to actuate the CVT pulley cylinder plunger [He, 2008].
CVT Stepper Motor
Secondary Solenoid
Clutch Solenoid
Oil Temp . Sensor
Speed Sensor
CAN Low-level Drive
Step Switches
PRND Switches
CVT Control Strategy of TCU
Steering Wheel Switches
Shifter Interlock Relay
Gear Shifter
Fig. 2. CVT components relation block diagram. 3.1 CVT control principle
Fig. 1. CVT hydraulic actuation system. According to the Fig. 1, it can be seen that the principle of CVT hydraulic system is: the outlet of gear pump connects directly to the secondary pulley cylinder whose pressure is steered by the secondary valve in the first oil circuit that is between secondary pulley cylinder and gear pump. The secondary valve is an overflow valve, whose spool position is adjusted by the synthetic force among pitot pressure of engine speed, the force of return spring, the outlet pressure of secondary solenoid valve and so on. The secondary solenoid valve is digital high speed on-off valve, whose inlet connects to the first oil circuit and whose outlet pressure is adjusted by the PWM duty cycle. For preventing the first oil circuit pressure is larger than the rating pressure, moreover, the first oil circuit connects to clutch oil circuit by the secondary exhaust valve which is equivalent to bypass outlet of first oil circuit. The primary pulley cylinder connects directly to the outlet of primary valve whose inlet connects directly to the first oil circuit, whose pressure is steered by a synthetic force among the pitot pressure of primary pulley speed, the force of return spring and the stepper motor that is controlled by target position and desired speed. 3. CVT CONTROL STRATEGY Before the description of CVT control, it is important that make a clear of the frame of CVT electrical hardware. Fig. 2 is a full aggregation of CVT control hardware. From the Fig. 2, it can be known that the whole CVT control system is subdivided into two parts, high level control system and low level drive system. The high level control supplies mostly the control strategy of CVT, that is to say, is equivalent to the cerebrum. And the low level system take mainly charge of driving these electrical components, e.g., Stepper motor and solenoids. CAN buses 490
As a rule, about the CVT control principle, it is chosen to use pressure control instead of flow control, whose reasons is presented by Serrarens [Serrarens, 2008]. Due to the special structure of variator, it can be seen that the slip between pulley and pushbelt is not beyond the rating security slip ratio, if either of two pulleys clamping force is enough to prevent this slip. In general, the secondary pulley is selected as the control objective to supply enough clamping force to guarantee that the slip of variator is limited within rating value. When the secondary pulley clamping force is in the range of set-point, it is considered that the operating state of variator is safe. Now the primary pulley clamping force is controlled to let the gear ratio of variator change the target one. That is to say, the secondary pulley cylinder pressure is used to provide enough clamping force to transmit the torque of engine, and the primary pulley cylinder pressure is controlled to adjust the gear ratio of variator. 3.2 Clamping force control strategy The clamping force control of variator is directly relative to the safety, endurable performance, life of CVT variator, which is important for CVT control. In reality, the control method of the secondary pulley cylinder pressure often adopts the accurate feedback pressure control usually. It is easy to deduce the clamping force Fs of secondary pulley for the actually transmitted torque, which is denoted by Tp cos β Fs = (1) 2µRp Where, Tp is the input torque of primary pulley, generally, this value is equivalent to the engine torque Te , Nm; β is the half sheave angle of pulley, rad; µ is the friction coefficient between the pulley and pushbelt, Rp is the deformed belt pitch radius, m. In practice, a safety margin is applied. For this purpose, in determining the minimum clamping force, the actual torque is increased with 30% of the maximal primary torque Tp,max . The minimum clamping force then is determined from |Tp | + 0.3Tp,max cos β F30% = (2) 2µRp
AAC 2010 Munich, Germany, July 12-14, 2010
To steer the clamping force accurately, it is important for CVT system to get the precise value of pulley cylinder pressure through the pressure sensors, which will be more complex, the cost will be higher and the reliability will be worse, after the pressure sensors were put into the hydraulic system. Considering the pump is driven directly by the engine crank, the pressure of hydraulic system is lower only within the range of low speed of engine. If utilizing properly all available power to provide the maximum clamping force, on this condition, it also can be enough thrust to prevent the slip of variator during the operation. At the same time, the pressure change of this hydraulic system is in direct proportion to the demand increment of pulley clamping force, that is to say, along with engine output power increasing, engine speed is higher, the pressure of hydraulic system is also higher, which can suffice the increment of clamping force demand with the output torque increasing. Thus, the hydraulic system pressure control is divided into two states: one is low pressure serve state (LPSS), where the hydraulic system only provides the lowest pressure on current condition as soon as possible, but the LPSS pressure is larger than the basic demand pressure to prevent the variator slip; the other is high pressure serve state (HPSS), where the hydraulic system provides the highest pressure potentially to confirm the requirement of clamping force in the emergency. According to the above analysis, the hydraulic system is usually in the LPSS. The LPSS of hydraulic system will be changed into the HPSS utilizing properly all available power, when the emergency occurs, e.g., the low engine speed and the kickdown acceleration. The control operation is very similar with the Bang-Bang control that has been an intuitive assumption for some time that if a control system is being operated from a limited source of power then the system can be moved from one state to another in the shortest time by at all times utilizing properly all available power. Under the condition of neglecting the clutch system, according to CVT hydraulic system principle of the figure 1, it is easy to obtain the state equation of actuation system: x˙ t = A(t)x(t) + B(t)u(t)
(3)
T
u(t) = [ u1 u2 u3 ]
(4) T
x(t) = [ x1 x2 x3 x4 x5 x6 x7 x8 x9 ] 0 0 0 At Ase Kso 0 ms ms 0 0 Vum 0 0 0 K sm B(t) = 0 0 mra 0 0 0 Kt 0 0 Arr 0 0 0 0 0 0 · ¸ A1 A2 A(t) = A3 A4
(5)
0 K s m s A1 (t) = −Kqs 0 0
1 0 Ds As ms ms 0 0 1 0
0 0
0 0 0 0 D
0 0 Kra ra 0 mra mra 0 0 Kss 0 ms 0 0 0 0 0 0
0
0 0 0 0 A2 (t) = 0 0 0 0 0 0 0 1 0 0 0 Krs 0 1 0 0 A3 (t) = mr 0 0 0 0 0 0 0 −Krd Ksn Ksc 0 0 0 0 0 0 Kr Dr 0 0 A4 (t) = mr mra K 0 Kcr 0 qr 0 0 Krd Krn Krc −Krd Krc
(8)
(9)
(10)
(11)
Where x1 is the secondary valve spool position, x˙ 1 = x2 ; x3 is the secondary cylinder pressure;x4 is the primary assistant spool position; x˙ 4 = x5 ; x6 is the primary spool position; x˙ 6 = x7 ; x8 is the primary cylinder pressure; x9 is the gear ratio of variator; ms , Ks , Ds is the mass, stiff and damp of secondary spool respectively, only changing the suffix into r9 and ra, these will be the primary spool and its assistant spool; Kt is the pitot tube pressure coefficient; As e and Arr is the pitot actuation area of secondary spool and primary spool respectively; Kso is the secondary pressure coefficient; Vum is the gear pump parameter; Ksm is the stepper motor coefficient; Kss is the gear ratio actuation coefficient to secondary spool; Kqs is the secondary valve flow pressure coefficient; Krs is the stiff of primary valve between main spool and assistant spool; Asc and Arc is the secondary and primary cylinder piston area; Krd , Ksn and Krn are all the gear ratio rate coefficient relative with cylinder pressure; Krc is the gear ratio coefficient. Due to the Bang-bang control principle, yields Performance index: Ztf min J = dt (12) u
0
Control constraints: |ui (t)| ≤ 1, (6)
i = 1, 2, 3
Hamilton function: H[x, u, λ] = 1 + xT AT λ + uT B T λ
(13) (14)
For the minimum of Hamilton function, the optimal control: u∗i (t) = −sgn[B T λ(t)]i , i = 1, 2, 3 (15) (7)
491
Where the sgn is a sign function. According to canonical equations:
AAC 2010 Munich, Germany, July 12-14, 2010
∂H = x˙ = Ax + Bu ∂λ ∂H λ˙ = = −AT λ ∂x
(16) (17)
PI controller to get the desired position of stepper motor. And then the new real gear ratio is produced by CVT driveline. Go around and around, the new ratio backs to compare with new desired ratio. /CZ2QYGT4GIKQP
Yields: T
λ(t) = e−A t λ0
(18)
Where λ0 = λ(0) is the initial value of adjoint vector. Substituting Eq. (18) into Eq. (15), resulting in: T
u∗i (t) = −sgn(B T eA t λ0 )
(19)
Te /Nm 150 125
75
The gear ratio control is important for CVT performance. As for the above mentioned, the pressure of primary cylinder is for the gear ratio control. Whenever the secondary cylinder is in any clamping forces state, there is always a primary clamping force corresponding to the secondary clamping force in the any gear ratio. For any gear ratio, only need to adjust the primary clamping force correspondingly. As we all know, during the travel, the vehicle speed changes very slow compared with the engine speed, CVT gear ratio and throttle position. That is to say, it can be assumption for the vehicle speed to be a constant when the gear ratio was adjusted to let engine speed adapt to the current vehicle speed under the condition of current throttle position. Therefore, the intent of gear ratio adjustment is to let engine operate on the optimal operation points, at the same time, this optimal engine speed also is fit for the current vehicle speed and throttle position. So the optimal gear ratio i0 can be defined: nd imax > imax n DN n nd d imin ≤ ≤ imax itarget = (20) n n DN DN n d imin ≤ imin nDN
50
α
nd
Engine Map
PI Control Stepper motor
io =
nDN
nd nDN
id Desired -
+
Ratio
ia CVT Driveline
VS
Fig. 3. Gear ratio control course. Fig. 3 describes the control course of gear ratio, which includes three parts: Firstly, get the optimal ratio using equation (16); secondly, based on vehicle conditions, calculate desired gear ratio; at last, after getting the error between actual gear ratio and desired gear ratio, use the 492
F
B
A
25 1000
2000
3000
4000
5000
ne /rpm
Fig. 4. Gear ratio optimal control path to engine. During the desired gear ratio calculation, the piecewise optimum control was adopted. If the kickdown was triggered, the powertrain adopts the maximum power control. See red triangle track in the figure 4. If the throttle position change rate exceeded the set-point, the powertrain uses sport mode control. See magenta rhombus track in the Fig. 4. At last, adopt the optimal fuel economy control, that is to say, the desired ratio is the optimal ratio. See blue circle track in the figure 4. Through the piecewise optimal control of gear ratio, consequently, vehicle obtained compromise characters between fuel economy and drivability. 4. TEST ON BOARD To validate the forementioned CVT control strategy, the CVT RCP was produced. The CVT RCP and new control strategy were installed into a car, which is tested in ECE cycle on road. The results of road test are shown from Fig. 5 to 7. Figure 5 depicts the result to compare between actual engine speed and desired engine speed. It is easy to see for this test that the actual engine speed could track the desired speed preferably. In the park condition, nevertheless, it is obvious there is being speed difference between the actual speed and desired speed, which is due to being some loads in idle, e.g. air conditioner. At the same time, the engine speed increased abruptly during the course of shifting on park condition, since the clutch had been clamped a little before the start, for quickly starting. Engine speed [1000rpm]
Where nDR is the primary pulley speed, nDN is the secondary pulley speed, imin , imax are the minimum and maximum values of gear ratio of CVT.
G
T
C
100
3.3 Gear ratio control strategy
E
D
2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0
Actual engine Speed Desired engine Speed
50
100 Time [s]
150
200
Fig. 5. Actual & desired engine speeds compare.
Engine speed deflection ratio
AAC 2010 Munich, Germany, July 12-14, 2010
ACKNOWLEDGEMENTS
0.3
The research was supported by the Tongji-Continental Powertrain Technology Laboratory that was subsidized by Continental Company. Wendelin Kluegl contributes to this project, who is a chief technology officer of powertrain in Regensburg Germany. These supports are gratefully acknowledged.
0.2 0.1 0 -0.1 -0.2
0
50
100
Time [s]
150
200
REFERENCES
Fig. 6. Actual & desired engine speed deflection. Fig. 6 shows the result of engine speed deflection rate between the actual nd the desired. It can be seen that the deflection rate is larger when park and starting, where the largest exceeded 30%. During the start, the clutch didn’t engage completely, and the control strategy didn’t permit the gear ratio to change, hence the actual engine speed could not track the desired. Usually, the deflection rate is very small and is under the 5%. And then, the average ratio is about 6.28%. So it can be concluded that the new CVT control can let engine track the desired speed better.
Gear ratio
2.5 Actual gear ratio Desired gear ratio
2
1.5 1 0.5 0
50
100
Time [s]
150
200
Fig. 7. Actual & desired gear ratio compare. In Fig. 7, there is a result to compare actual gear ratio and desired gear ratio, which show the actual can follow the desired properly. Since the desired gear ratio change along with throttle position and vehicle speed, but the clutch do not lockup and the gear ratio of variator can not change, the actual gear ratio couldnt track the desired during starting. During the others conditions, the actual ratio was consistent with the desired. Therefore the piecewise optimum algorithm could apply into CVT gear ratio control. 5. CONCLUSION Through the verification on car, the new CVT hydraulic system for no pressure sensor could actuate the variator of CVT, and it is stability and rapid response. At the same time, the new system is lower cost than others CVT hydraulic actuation system using pressure sensors. For bang-bang control algorithm, it is very fit for the clamping force control of the new CVT hydraulic actuation system to limit the slip ratio of variator within the rating range. The piecewise optimal control of gear ratio can make the actual ratio follow the desired, as it achieved the compromise between the fuel economy and drivability. 493
K. Adachi, Y. Ochi and K. Kanai. Development of CVT control system and its use for fuel-efficient operation of engine. Asian Journal of Control, Vol.8(3),2006: pp. 219-226. L. He, G. Q. Wu, Z. Q. Han and X. A Sun. An Electrohydraulic Control System for Metal V-belt CVT [J]. Society of Automotive Engineers of China, Vol. 30, NO.5, Sep. 2008. L. He, G. Q. Wu, X. J. Meng and X. A. Sun. A Novel Continuously Variable Transmission Flywheel Hybrid Electric Powertrain[C]. IEEE Vehicle Power and Propulsion Conference (VPPC), September 3-5, 2008, Harbin, China. V. D. S. Francis. Fuel consumption potential of the pushbelt CVT[C]. 5th International CTI-Symposium, Innovative Automotive Transmissions, 4th-7th December 2006, Berlin, Germany. M. Pesgens, B. Vroemen, B. Stouten, F. Veldpaus and M. Steinbuch. Control of a hydraulically actuated continuously variable transmission. Vehicle System Dynamics 44 (5),2005: pp. 387-406. W. Ryu, J. Nam, Y. Lee and H. Kim. Model based control for a pressure control type CVT. International Journal of Vehicle Design 39(3), 2005, pp. 175-188. A. F. A. Serrarens. Coordinated control of the Zero Inertia powertrain [D]. Ph.D. thesis, Technische Universiteit Eindhoven, Eindhoven, The Netherlands, 2001. J. C. Song, and C. Z. Wang. Modeling and simulation of hydraulic control system for vehicle continuously variable transmission. Industrial Electronics and Applications, 2008. ICIEA 2008. 3rd IEEE Conference on 3-5, June 2008, pp.799-803. N. Srivastava and I. Haque. A review on belt and chain continuously variable transmissions (CVT): Dynamics and control [J]. Mechanism and Machine Theory Vol.44,2009: pp.19-41. E. Spijker. Steering and control of a CVT based hybrid transmission for a passenger car [D]. Ph.D. thesis, Technische Universiteit Eindhoven, Eindhoven, The Netherlands, 1994. K. Tsukuda, T, Taniguchi, K. Tsukamoto. Toyota’s New Belt-drive Continuously Variable Transaxle for 1.3-liter FWD cars[J]. SAE paper 2006-01-1305, SAE2006. P. Vanvuchelen. Virtual engineering for design and control of continuously variable transmissions [D]. Ph.D. thesis, Katholieke Universiteit Leuven, Leuven, Belgium, 1997. J. M. A. Wade. An integrated electronic control system for a CVT based powertrain [R]. In Proc. of ISATA, vol. 1. 1984.
A Novel Pushbelt CVT Actuation System and Control Strategy ? L. He ∗ L. Li ∗ X. L. Zhang ∗ J. Song ∗ ∗
State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing, China (Tel: +10-627-97118; e-mail: [email protected]).
Abstract: The CVT hydraulic actuation system almost adopt pressure sensors to feedback the pulley cylinder pressure to traction control unit (TCU), which is complex structure, high cost and poor reliability. A new electro-hydraulic actuation system that gets rid of the pressure sensors will be described in detail. It is for the clamping force control of CVT to adopt the bang-bang control and use the piecewise optimal method to control the gear ratio. Then, the rapid control prototype (RCP) of CVT is produced to evaluate the new CVT actuation system. At last, the new electro-hydraulic actuation system and its control strategy are tested on vehicle. The experimental results also confirm that the new CVT hydraulic system is stability and rapid response to actuate the CVT variator. Keywords: CVT; Electro-hydraulic Actuation System; Control Strategy; RCP. 1. INTRODUCTION Over the last few decades, environmental concerns have made it imperative for the government of most of the nations to impose stringent regulations on the fuel consumption and exhaust emissions of the vehicles in order to reduce the polluting emissions and the green-house gasses [He, 2008]. In order to fulfill these requirements, car manufacturers have been obligated to dramatically reduce vehicles gas emissions and improve the fuel consumption in relatively short times. Thus, a great deal of research has been devoted to find new technical solutions, which may improve the emission performances of nowadays IC engine vehicles. So far, vehicular drivelines with an internal combustion engine, an electronic throttle valve, and a CVT can offer much freedom in controlling the engine speed and torque, which can be used to improve fuel economy by operating the engine in fuel-optimal operating points. According to some tests of automotive company, the CVT can reduce the fuel consumption of engine 3-14% than automatic transmission reputedly, and it is possible for fuel economy to increase 5-10% of CVT driveline in the future, therefore, the CVT is regarded as a promising approach that can reduce energy consumption and exhaust emissions [Francis, 2006]. Through the number of publications concerning CVT is exceptionally large; it is seldom that introduces a full electro-hydraulic actuation system including its control strategy completely. Moreover, most of the approaches control the clamping pressure at the secondary pulley and control the CVT speed ratio by steering the oil flow into the primary pulley cylinder [Spijker, 2006, Vanvuchelen, 1997]. Wade put forward firstly the CVT thrust control concept to control both pulley pressures simultaneously
[Wade, 1984]. After that, there were lots of the researches of CVT pressure control, but in the recent years, it is seldom relatively. Thereinto, Ryu developed a model-based control algorithm for the pressure control type CVT using the steady state characteristics of the ratio control valve. In a pressure control CVT system, the desired speed ratio is obtained by controlling the primary actuator pressure [Ryu, 2005]. In order to further improve the control performance, Adachi coupled their robust controller to a feedforward controller and modeled the two-degree-offreedom CVT control system as a first-order lag system with an uncertain time constant and time delay [Adachi, 2006]. Pesgens developed a new ratio controller for a metal pushing V-belt CVT with a hydraulic clamping system whose ratio controller guaranteed that at least one of the pressure set points was always minimal with respect to its constraints, while the other was raised above the minimum level to enable shifting [Pesgens, 2005]. However, in these hydraulic actuation systems [Srivastava, 2009, Tsukuda, 2006], the pressure controllers are augmented by a ratio controller to achieve the desired ratio response accurately. Therefore, the current actuation systems adopted pressure sensors to feed the pulley cylinder pressure back to TCU, which are complex structure, high cost and poor reliability [Song, 2008]. In this paper, a full electro-hydraulic actuation system that gets rid of the pressure sensors will be described in detail, and developed a clamping force controller using Bang-Bang control principle and a gear ratio control strategy using the piecewise optimum control concept for this CVT actuation system. Then, the CVT rapid control prototype was produced to evaluate the new control strategy. At last, both this electro-hydraulic actuation system and its control strategy were tested on board.
? This work was supported in part by the State Key Laboratory of Automotive Safety and Energy of China.
978-3-902661-72-2/10/$20.00 © 2010 IFAC
489
10.3182/20100712-3-DE-2013.00151
AAC 2010 Munich, Germany, July 12-14, 2010
2. CVT HYDRAULIC ACTUATION SYSTEM
is used to make a communication between the high level control and low level drive.
As for the description of figure 1, it is easy to see that the variator of CVT transmits the power by the friction between pulley and pushbelt. Hereby, the variator need enough thrust to clamp both pulleys and pushbelt together during the operation. The hydraulic system is easy to be control, simple and low cost, in general, which was adopted to supply a pressure for the pulley of CVT variator. In Fig. 1, there is a hydraulic system sketch map to actuate the CVT pulley cylinder plunger [He, 2008].
CVT Stepper Motor
Secondary Solenoid
Clutch Solenoid
Oil Temp . Sensor
Speed Sensor
CAN Low-level Drive
Step Switches
PRND Switches
CVT Control Strategy of TCU
Steering Wheel Switches
Shifter Interlock Relay
Gear Shifter
Fig. 2. CVT components relation block diagram. 3.1 CVT control principle
Fig. 1. CVT hydraulic actuation system. According to the Fig. 1, it can be seen that the principle of CVT hydraulic system is: the outlet of gear pump connects directly to the secondary pulley cylinder whose pressure is steered by the secondary valve in the first oil circuit that is between secondary pulley cylinder and gear pump. The secondary valve is an overflow valve, whose spool position is adjusted by the synthetic force among pitot pressure of engine speed, the force of return spring, the outlet pressure of secondary solenoid valve and so on. The secondary solenoid valve is digital high speed on-off valve, whose inlet connects to the first oil circuit and whose outlet pressure is adjusted by the PWM duty cycle. For preventing the first oil circuit pressure is larger than the rating pressure, moreover, the first oil circuit connects to clutch oil circuit by the secondary exhaust valve which is equivalent to bypass outlet of first oil circuit. The primary pulley cylinder connects directly to the outlet of primary valve whose inlet connects directly to the first oil circuit, whose pressure is steered by a synthetic force among the pitot pressure of primary pulley speed, the force of return spring and the stepper motor that is controlled by target position and desired speed. 3. CVT CONTROL STRATEGY Before the description of CVT control, it is important that make a clear of the frame of CVT electrical hardware. Fig. 2 is a full aggregation of CVT control hardware. From the Fig. 2, it can be known that the whole CVT control system is subdivided into two parts, high level control system and low level drive system. The high level control supplies mostly the control strategy of CVT, that is to say, is equivalent to the cerebrum. And the low level system take mainly charge of driving these electrical components, e.g., Stepper motor and solenoids. CAN buses 490
As a rule, about the CVT control principle, it is chosen to use pressure control instead of flow control, whose reasons is presented by Serrarens [Serrarens, 2008]. Due to the special structure of variator, it can be seen that the slip between pulley and pushbelt is not beyond the rating security slip ratio, if either of two pulleys clamping force is enough to prevent this slip. In general, the secondary pulley is selected as the control objective to supply enough clamping force to guarantee that the slip of variator is limited within rating value. When the secondary pulley clamping force is in the range of set-point, it is considered that the operating state of variator is safe. Now the primary pulley clamping force is controlled to let the gear ratio of variator change the target one. That is to say, the secondary pulley cylinder pressure is used to provide enough clamping force to transmit the torque of engine, and the primary pulley cylinder pressure is controlled to adjust the gear ratio of variator. 3.2 Clamping force control strategy The clamping force control of variator is directly relative to the safety, endurable performance, life of CVT variator, which is important for CVT control. In reality, the control method of the secondary pulley cylinder pressure often adopts the accurate feedback pressure control usually. It is easy to deduce the clamping force Fs of secondary pulley for the actually transmitted torque, which is denoted by Tp cos β Fs = (1) 2µRp Where, Tp is the input torque of primary pulley, generally, this value is equivalent to the engine torque Te , Nm; β is the half sheave angle of pulley, rad; µ is the friction coefficient between the pulley and pushbelt, Rp is the deformed belt pitch radius, m. In practice, a safety margin is applied. For this purpose, in determining the minimum clamping force, the actual torque is increased with 30% of the maximal primary torque Tp,max . The minimum clamping force then is determined from |Tp | + 0.3Tp,max cos β F30% = (2) 2µRp
AAC 2010 Munich, Germany, July 12-14, 2010
To steer the clamping force accurately, it is important for CVT system to get the precise value of pulley cylinder pressure through the pressure sensors, which will be more complex, the cost will be higher and the reliability will be worse, after the pressure sensors were put into the hydraulic system. Considering the pump is driven directly by the engine crank, the pressure of hydraulic system is lower only within the range of low speed of engine. If utilizing properly all available power to provide the maximum clamping force, on this condition, it also can be enough thrust to prevent the slip of variator during the operation. At the same time, the pressure change of this hydraulic system is in direct proportion to the demand increment of pulley clamping force, that is to say, along with engine output power increasing, engine speed is higher, the pressure of hydraulic system is also higher, which can suffice the increment of clamping force demand with the output torque increasing. Thus, the hydraulic system pressure control is divided into two states: one is low pressure serve state (LPSS), where the hydraulic system only provides the lowest pressure on current condition as soon as possible, but the LPSS pressure is larger than the basic demand pressure to prevent the variator slip; the other is high pressure serve state (HPSS), where the hydraulic system provides the highest pressure potentially to confirm the requirement of clamping force in the emergency. According to the above analysis, the hydraulic system is usually in the LPSS. The LPSS of hydraulic system will be changed into the HPSS utilizing properly all available power, when the emergency occurs, e.g., the low engine speed and the kickdown acceleration. The control operation is very similar with the Bang-Bang control that has been an intuitive assumption for some time that if a control system is being operated from a limited source of power then the system can be moved from one state to another in the shortest time by at all times utilizing properly all available power. Under the condition of neglecting the clutch system, according to CVT hydraulic system principle of the figure 1, it is easy to obtain the state equation of actuation system: x˙ t = A(t)x(t) + B(t)u(t)
(3)
T
u(t) = [ u1 u2 u3 ]
(4) T
x(t) = [ x1 x2 x3 x4 x5 x6 x7 x8 x9 ] 0 0 0 At Ase Kso 0 ms ms 0 0 Vum 0 0 0 K sm B(t) = 0 0 mra 0 0 0 Kt 0 0 Arr 0 0 0 0 0 0 · ¸ A1 A2 A(t) = A3 A4
(5)
0 K s m s A1 (t) = −Kqs 0 0
1 0 Ds As ms ms 0 0 1 0
0 0
0 0 0 0 D
0 0 Kra ra 0 mra mra 0 0 Kss 0 ms 0 0 0 0 0 0
0
0 0 0 0 A2 (t) = 0 0 0 0 0 0 0 1 0 0 0 Krs 0 1 0 0 A3 (t) = mr 0 0 0 0 0 0 0 −Krd Ksn Ksc 0 0 0 0 0 0 Kr Dr 0 0 A4 (t) = mr mra K 0 Kcr 0 qr 0 0 Krd Krn Krc −Krd Krc
(8)
(9)
(10)
(11)
Where x1 is the secondary valve spool position, x˙ 1 = x2 ; x3 is the secondary cylinder pressure;x4 is the primary assistant spool position; x˙ 4 = x5 ; x6 is the primary spool position; x˙ 6 = x7 ; x8 is the primary cylinder pressure; x9 is the gear ratio of variator; ms , Ks , Ds is the mass, stiff and damp of secondary spool respectively, only changing the suffix into r9 and ra, these will be the primary spool and its assistant spool; Kt is the pitot tube pressure coefficient; As e and Arr is the pitot actuation area of secondary spool and primary spool respectively; Kso is the secondary pressure coefficient; Vum is the gear pump parameter; Ksm is the stepper motor coefficient; Kss is the gear ratio actuation coefficient to secondary spool; Kqs is the secondary valve flow pressure coefficient; Krs is the stiff of primary valve between main spool and assistant spool; Asc and Arc is the secondary and primary cylinder piston area; Krd , Ksn and Krn are all the gear ratio rate coefficient relative with cylinder pressure; Krc is the gear ratio coefficient. Due to the Bang-bang control principle, yields Performance index: Ztf min J = dt (12) u
0
Control constraints: |ui (t)| ≤ 1, (6)
i = 1, 2, 3
Hamilton function: H[x, u, λ] = 1 + xT AT λ + uT B T λ
(13) (14)
For the minimum of Hamilton function, the optimal control: u∗i (t) = −sgn[B T λ(t)]i , i = 1, 2, 3 (15) (7)
491
Where the sgn is a sign function. According to canonical equations:
AAC 2010 Munich, Germany, July 12-14, 2010
∂H = x˙ = Ax + Bu ∂λ ∂H λ˙ = = −AT λ ∂x
(16) (17)
PI controller to get the desired position of stepper motor. And then the new real gear ratio is produced by CVT driveline. Go around and around, the new ratio backs to compare with new desired ratio. /CZ2QYGT4GIKQP
Yields: T
λ(t) = e−A t λ0
(18)
Where λ0 = λ(0) is the initial value of adjoint vector. Substituting Eq. (18) into Eq. (15), resulting in: T
u∗i (t) = −sgn(B T eA t λ0 )
(19)
Te /Nm 150 125
75
The gear ratio control is important for CVT performance. As for the above mentioned, the pressure of primary cylinder is for the gear ratio control. Whenever the secondary cylinder is in any clamping forces state, there is always a primary clamping force corresponding to the secondary clamping force in the any gear ratio. For any gear ratio, only need to adjust the primary clamping force correspondingly. As we all know, during the travel, the vehicle speed changes very slow compared with the engine speed, CVT gear ratio and throttle position. That is to say, it can be assumption for the vehicle speed to be a constant when the gear ratio was adjusted to let engine speed adapt to the current vehicle speed under the condition of current throttle position. Therefore, the intent of gear ratio adjustment is to let engine operate on the optimal operation points, at the same time, this optimal engine speed also is fit for the current vehicle speed and throttle position. So the optimal gear ratio i0 can be defined: nd imax > imax n DN n nd d imin ≤ ≤ imax itarget = (20) n n DN DN n d imin ≤ imin nDN
50
α
nd
Engine Map
PI Control Stepper motor
io =
nDN
nd nDN
id Desired -
+
Ratio
ia CVT Driveline
VS
Fig. 3. Gear ratio control course. Fig. 3 describes the control course of gear ratio, which includes three parts: Firstly, get the optimal ratio using equation (16); secondly, based on vehicle conditions, calculate desired gear ratio; at last, after getting the error between actual gear ratio and desired gear ratio, use the 492
F
B
A
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2000
3000
4000
5000
ne /rpm
Fig. 4. Gear ratio optimal control path to engine. During the desired gear ratio calculation, the piecewise optimum control was adopted. If the kickdown was triggered, the powertrain adopts the maximum power control. See red triangle track in the figure 4. If the throttle position change rate exceeded the set-point, the powertrain uses sport mode control. See magenta rhombus track in the Fig. 4. At last, adopt the optimal fuel economy control, that is to say, the desired ratio is the optimal ratio. See blue circle track in the figure 4. Through the piecewise optimal control of gear ratio, consequently, vehicle obtained compromise characters between fuel economy and drivability. 4. TEST ON BOARD To validate the forementioned CVT control strategy, the CVT RCP was produced. The CVT RCP and new control strategy were installed into a car, which is tested in ECE cycle on road. The results of road test are shown from Fig. 5 to 7. Figure 5 depicts the result to compare between actual engine speed and desired engine speed. It is easy to see for this test that the actual engine speed could track the desired speed preferably. In the park condition, nevertheless, it is obvious there is being speed difference between the actual speed and desired speed, which is due to being some loads in idle, e.g. air conditioner. At the same time, the engine speed increased abruptly during the course of shifting on park condition, since the clutch had been clamped a little before the start, for quickly starting. Engine speed [1000rpm]
Where nDR is the primary pulley speed, nDN is the secondary pulley speed, imin , imax are the minimum and maximum values of gear ratio of CVT.
G
T
C
100
3.3 Gear ratio control strategy
E
D
2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0
Actual engine Speed Desired engine Speed
50
100 Time [s]
150
200
Fig. 5. Actual & desired engine speeds compare.
Engine speed deflection ratio
AAC 2010 Munich, Germany, July 12-14, 2010
ACKNOWLEDGEMENTS
0.3
The research was supported by the Tongji-Continental Powertrain Technology Laboratory that was subsidized by Continental Company. Wendelin Kluegl contributes to this project, who is a chief technology officer of powertrain in Regensburg Germany. These supports are gratefully acknowledged.
0.2 0.1 0 -0.1 -0.2
0
50
100
Time [s]
150
200
REFERENCES
Fig. 6. Actual & desired engine speed deflection. Fig. 6 shows the result of engine speed deflection rate between the actual nd the desired. It can be seen that the deflection rate is larger when park and starting, where the largest exceeded 30%. During the start, the clutch didn’t engage completely, and the control strategy didn’t permit the gear ratio to change, hence the actual engine speed could not track the desired. Usually, the deflection rate is very small and is under the 5%. And then, the average ratio is about 6.28%. So it can be concluded that the new CVT control can let engine track the desired speed better.
Gear ratio
2.5 Actual gear ratio Desired gear ratio
2
1.5 1 0.5 0
50
100
Time [s]
150
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Fig. 7. Actual & desired gear ratio compare. In Fig. 7, there is a result to compare actual gear ratio and desired gear ratio, which show the actual can follow the desired properly. Since the desired gear ratio change along with throttle position and vehicle speed, but the clutch do not lockup and the gear ratio of variator can not change, the actual gear ratio couldnt track the desired during starting. During the others conditions, the actual ratio was consistent with the desired. Therefore the piecewise optimum algorithm could apply into CVT gear ratio control. 5. CONCLUSION Through the verification on car, the new CVT hydraulic system for no pressure sensor could actuate the variator of CVT, and it is stability and rapid response. At the same time, the new system is lower cost than others CVT hydraulic actuation system using pressure sensors. For bang-bang control algorithm, it is very fit for the clamping force control of the new CVT hydraulic actuation system to limit the slip ratio of variator within the rating range. The piecewise optimal control of gear ratio can make the actual ratio follow the desired, as it achieved the compromise between the fuel economy and drivability. 493
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