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Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering http://pid.sagepub.com/ Enhanced control performance of a piezoelectric−−hydraulic pump actuator for automotive transmission shift control G W Kim and K W Wang Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 2010 224: 161 DOI: 10.1243/09544070JAUTO1292 The online version of this article can be found at: http://pid.sagepub.com/content/224/2/161

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161

Enhanced control performance of a piezoelectric– hydraulic pump actuator for automotive transmission shift control G W Kim* and K W Wang Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, USA The manuscript was received on 12 June 2009 and was accepted after revision for publication on 6 August 2009. DOI: 10.1243/09544070JAUTO1292

Abstract: In this research, a piezoelectric–hydraulic pump (PHP) actuator is synthesized for an automatic transmission (AT) test bed to demonstrate its potentials as a controllable powerby-wire actuator. This research expands from the previous investigations by enhancing the control performance of the PHP actuator developed for AT and bringing the study to the system level. Actuation force-tracking control using an on-site force transducer is proposed and a fill volume control strategy utilizing the AT turbine acceleration information is explored. The system level evaluation of shift performance is performed to demonstrate the effectiveness of the proposed enhancements through a hardware-in-the-loop simulation environment. Keywords: automotive transmission shift control, piezoelectric–hydraulic pump actuator, force tracking control, adaptive fill volume control, hardware-in-the-loop simulation

1

INTRODUCTION

In recent years, various innovative technologies have been explored to meet the increasing expectations of consumers for cost-effective, highly efficient, and more reliable automotive transmissions [1]. In particular, new actuation systems for friction element (e.g. band brakes and clutches) control is one of the emerging trends in transmission technology for future transportation systems, since it is a primary component that can affect shift quality and efficiency [2]. Traditional electrohydraulic actuation systems for friction element control consist of many moving components, such as the engine-driven oil pump, various types of spool valve, and solenoid valves. This type of actuation and control system is inefficient since it inherently requires a large oil pump owing to the incessant exhausting flow in regulating valves. They also have numerous technical limitations for further enhancement of performance, such as heavy weight, complicated structure, *Corresponding author: Department of Mechanical Engineering, University of Michigan, 2350 Hayward Street, Ann Arbor, MI 48109-2125, USA. email: [email protected] JAUTO1292

and low reliability due to many spool valves, and low-precision controllability. In addition, because of the complexity of the current actuation systems, simple open-loop control is still widely used without taking advantages of many advanced control laws. To address the aforementioned problems, potential alternative actuation systems have been introduced recently to replace the current electrohydraulic actuation systems. A two-stage actuation system was developed by combining an electric d.c. motor and a lead zirconate titanate (PZT) stack actuator for controllable automotive brakes and clutches [3]. A high-force electromechanical linear actuator was developed to substitute a current linear actuator for dual-clutch transmissions [4]. Using this classical electric actuator (e.g. d.c. motor and linear motor) for actuating the friction elements, however, has shortcomings owing to weight (i.e. low power density) that will affect fuel economy. Another promising alternative is to utilize the piezoelectric–hydraulic pump (PHP) concept [5–8]. The primary idea of the PHP is to combine the advantages of piezoelectric transducers (high power density and large load authority) and hydraulic systems (large stroke), which is suitable for friction element actuation systems where both a large actuation force (0.7– Proc. IMechE Vol. 224 Part D: J. Automobile Engineering


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G W Kim and K W Wang

1 kN) and a large fill stroke (0.003–0.007 m) are required. Kim and Wang [9] recently explored the feasibility of synthesizing a self-contained PHP system for automotive transmissions. In that study, a prototype PHP-based actuator integrated with a band brake was considered for an illustrative friction element actuation system. It was concluded that the PHP-based actuator could be designed to satisfy the basic requirements of such applications. In addition, switching non-linear sliding-mode control with pressure feedback has been developed as an effective controller to ensure desired actuation force tracking [10–12]. While the previous studies have shown the promising potential of designing a PHP to actuate automatic transmission (AT) friction elements, a more comprehensive study is required to investigate the overall system performance of utilizing PHP for AT shift control, and eventually to realize the new power-by-wire concept. The objective of this research is therefore to enhance and investigate the control performance of the PHP actuator for AT shift control at the system level. In this paper, the standalone PHP-based actuator for friction elements (i.e. band brake) and the switching sliding-mode controller for actuation force-tracking control are first reviewed in section 2. The actuator and controller are integrated with a half-car powertrain model for power on 1 R 2 upshift event (section 3). To achieve the research goal, an actuation force-tracking controller using an on-site force transducer and an adaptive fill volume control strategy are explored and presented in section 4. Finally, the hardware-inthe-loop simulation (HILS) with a test-bed system is performed to demonstrate the effectiveness of the proposed approach (section 5).

2

CONTROLLABLE PIEZOELECTRIC– HYDRAULUC PUMP ACTUATOR

A new PHP-based actuator that can satisfy the aforementioned performance requirements has been designed and developed on the basis of the shift control-oriented hydraulic circuit illustrated in Fig. 1 [9, 10], which consists of a PZT stack transducer, a gas accumulator, and a double-acting hydraulic cylinder. The PZT transducer will be oscillating because of the input voltage with a high frequency and its alternating motion will be transformed into a large inchworm motion of the hydraulic cylinder through two one-way valves (reed valves). The gas accumulator is primarily used to provide pumping. Additionally, it provides various essential

Fig. 1

Schematic diagram of the PHP actuator [9, 10]

functions, which include cavitation prevention, and preloading to the PZT stack transducer. Since bidirectional control actions are not required for AT shift control, the normally closed-type on–off solenoid valve is utilized for releasing the actuation pressure. The stand-alone prototype PHP actuator is illustrated in Fig. 2. This prototype can achieve a flowrate of 19 cm3/s for a driving frequency of about 200 Hz under an accumulator pressure of 0.4 MPa, which is sufficient to satisfy the required fill time of nominal AT operations for the band brake testbed system used in this study. A maximum deadhead pressure of 0.55 MPa can be generated, which is also sufficient to complete the engagement of the band brake. This actuator can become the building block of a distributed power-by-wire system; i.e. the conventional electrohydraulic control system can be substituted by an electronic control system driving a compact PHP actuator. Hence, traditional components such as the oil pump, regulating valve, control valves, and fluid lines can be eliminated, reducing cost and complexity. The additional advantages are the elimination of an incessant exhausting flowrate and more flexibility in installation, as opposed to the conventional approach. However, because of the large capacitance of the PZT stack transducer (30 mF), an efficient driver that can fully compensate for the capacitive load is required in this application. In this research, a two-level driver using advanced driving topology is utilized, as shown in Fig. 2. This driver switches a capacitive load between low level (0 V) and high level (120 V) by the input signal of the transistor–transistor logic (TTL) pulse (i.e. 0 V to 5 V). Compared with conventional linear power amplifiers, this driver can provide sufficient current to produce the pulse voltage with extremely fast rise or fall response time (less than 24 ns) and can operate at high frequencies (above 200 Hz).

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Enhanced control performance of a piezoelectric–hydraulic pump actuator

163

Fig. 2 Prototype PHP actuator and driving circuitry

Therefore, it is more efficient and more compact, which is essential for automotive applications. Two separate control laws have been synthesized to command the piezoelectric stack so that the actuation force can track a certain desired force profile (pressure) [12]. During the fill stage (x ( xs), based on the concept of minimum time control resulting from the shortest fill time requirement, open-loop bang–bang control is applied until the end of the fill according to Vi ~Vi ðfmax Þ

for x¡xs ðfill stageÞ

ð1Þ

where Vi(f ) is the control input voltage pulse (i.e. 120 V with frequency f ) and xs is the fill stroke of cylinder piston. For the shortest fill time, the maximum frequency fmax is applied during the fill stage (e.g. 200 Hz). In order to develop the non-linear tracking control law during the actuation stage (x . xs), a sliding-mode controller is designed according to Vi ~

Vi ðfc Þ if u~z1 0

if u~{1

for xwxs ðactuation stageÞ

where fc is the control frequency (e.g. 30 Hz) and u represents discontinuous control input for the actuation stage, which can be instantaneously switched by following the feedback control law derived from the non-linear sliding-mode control theory according to ð3Þ

where s is the reduced-order sliding surface defined JAUTO1292

s~e~Fd {Fa

ð4Þ

with Fd the desired actuation force trajectory and Fa the actuation force. The details of the sliding-mode matching condition have been described in reference [12]. The implementation of this control law requires an intermediate step, since the customized driver has to be driven by the TTL pulse. Accordingly, the control input (i.e. control input voltage pulse with frequency f ) will be converted into the equivalent control voltage Ve, which in turn becomes an input to the TTL pulse generator. The final control pulse input voltage is eventually applied to the PZT stack transducer through the two-level driver, which will be same as the original control input determined by the control law (i.e. equations (1) and (2)).

3

ð2Þ

u~sgn ðsÞ

by a tracking error and is given by

AUTOMOTIVE POWERTRAIN MODEL

A half-car powertrain system for power on 1 R 2 upshift is used as a test bed for illustration in this study. It consists of three main components: an engine, a torque converter with a planetary gear set and a differential (frequently referred to as transaxle), and a driveline. A schematic diagram of this powertrain model is illustrated in Fig. 3. The impeller (pump) of the torque converter is directly connected to the engine and the turbine of the torque converter is connected to the input shaft of the AT. The planetary gear set used in this model is the combination of two compound planetary gears (frequently referred to as the two-simple type). A drum Proc. IMechE Vol. 224 Part D: J. Automobile Engineering


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Fig. 3

Simplified inertia elements of the half-car powertrain system for power-on 1 R 2 upshift

of the band brake (oncoming friction element) is connected to a second sun gear (S2) and an off-going friction element – namely one-way clutch (OWC) – is also connected to a first ring gear (R1) through a second carrier (C2). The output rotational speed is finally reduced by the transfer drive gear with the final gear ratio (FGR). The governing equations of motion can be expressed as the following torque balance equations. For the engine and impeller (pump) IE v_ E ~TE {TI

ð5Þ

IV v_ OUT ~TOUT {TLOAD 3.1

ð11Þ

Engine and torque converter

A static engine model based on an experimental torque map is adopted. The engine torque is calculated from the steady-state torque map of a 2.0 l doubleoverhead-camshaft gasoline engine, as shown in Fig. 4(a). It can be characterized as a function of throttle opening hth and rotational speed vE (r/m) of the engine as given by TE ~f ðvE , hth Þ

for the turbine (input) shaft IT v_ T ~TT {TF

ð6Þ

for the sun gear of the first planetary gear set (S1) ISI v_ SI ~TF {TSI

ð7Þ

for the ring gear of the first planetary gear set (R1)

A steady-state performance curve is also adopted for the torque converter model, as shown in Fig. 4(b). This curve can also be characterized by the torque ratio Rt and the torque capacity factor Cf as a function of speed ratio r as given by TI ~Cf ðr Þv2E , TT ~Rt ðr ÞTI

ð8Þ

where

for the sun gear of the second planetary gear set (S2)

r~

IR1 v_ R1 ~TS2 zTR2 {TOWC {TR1

IS2 v_ S2 ~{TS2 {TB

ð9Þ

ð10Þ

vT vE

Rt ðr Þ~

for the ring gear of the second planetary gear set (R2) IR2 v_ R2 ~TS1 zTR1 {TR2 { TOUT Y

ð12Þ

(

ð13Þ

t1 zt2 rzt3 r 2 zt4 r 3 , rv0:85 0:99,

r¢0:85 ð14Þ

3.2

Planetary gear sets

The torque relationships of the planetary gear sets are

and, for the output shaft Proc. IMechE Vol. 224 Part D: J. Automobile Engineering


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Fig. 4

Steady-state engine torque map and torque converter performance curves: (a) engine; (b) torque converter

TR1 ~r1 TS1 , TR2 ~r2 TS2

ð15Þ

where r1, and r2 are the gear ratios (i.e. r1 5 ZR1/ZS1, and r2 5 ZR2/ZS2). The kinematic relationship in the planetary gear sets can be defined as Y ð1zr1 Þv_ OUT ~v_ S1 zr1 v_ R1

ð16Þ

ð1zr2 Þv_ R1 ~v_ S2 zYr2 v_ OUT

ð17Þ

where Y is the FGR.

3.3

mined by the direction of the second sun gear speed as TBC ~sgn ðvS2 Þ TB

For the purpose of real-time simulation, a simple algebraic model of the band brake is used [13]. The relationship between the generated braking torque capacity TB and applied net actuation force Fa on the band is Rd e m(v)a {1 Fa TB ~ Rd 1{e {m(v)a Fa

sgn ðxÞ~

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1 {1

ðxw0Þ ðxv0Þ

and vS2 is the angular velocity of the second sun gear. When the one-way clutch is overrunning, the reaction torque of the one-way clutch becomes zero since the one-way clutch is designed to transmit the torque only in one direction, according to TOWC ~ 3.4

TOWC

if vR1 ~0

0

if vR1 w0

ð20Þ

Power-on 1 R 2 upshift model

Since the ring gear of the second planetary gear set (R2) is connected to the output shaft, equations (10)

for energizing engagement

ð18Þ

for de-energizing engagement

where a is the contact angle, Rd is the radius of the drum, and m(v) is the friction coefficient, which is assumed to be the function of the slip speed and independent of temperature. When the brake is slipping, the actual band brake torque TBC is deter-

ð19Þ

where

Friction elements: band brake and one-way clutch

(

165

and (11) can be modified and yield the equation IEQV v_ OUT ~Y ðTS1 zTR1 {TR2 Þ{TLOAD

ð21Þ

where IEQV 5 IV + Y2IR2. Internal torques of planetary



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gear sets (i.e. TS1, TR1, TS2, and TR2) can be related using kinematic constraints. Equation (15) can be first expressed by TR1 {TR2 ~r1 TS1 {r2 TS2

ð22Þ

Substituting equations (7) to (9) into equations (21) and (22), the governing equations can be shown to be r1 IS1 v_ S1 {ð1zr2 ÞIS2 v_ S2 {IR1 v_ R1 ~r1 TF zðr2 z1ÞTB zTOWC

ð23Þ

represented by StateflowH [14]. Once the turbine acceleration v ˙ T is calculated from the known torques TT, TBC, and TLOAD, the unknown torques can be sequentially determined. According to the different transition condition, the AT dynamics will switch from one phase or gear to another (e.g. vS2 5 0 is the condition to switch from the inertia phase to the second gear). Finally, the output states of interest – namely vT, vOUT and vS2 – can be calculated by numerically integrating their angular accelerations. 4

CONTROL PERFORMANCE ENHANCEMENTS

4.1 IEQV v_ OUT zY ðIS1 v_ S1 zIS2 v_ S2 zIR1 v_ R1 Þ ~Y ðTF {TB {TOWC Þ{TLOAD

ð24Þ

During the 1 R 2 shift, the forward clutch is engaged to transmit turbine torque (i.e. constrained). Thus, the forward clutch torque TF can be replaced by TT 2 Irv ˙ T and v ˙ S1 can be replaced by v ˙ T. Equations (23) and (24) can be further modified to r1 ðIS1 zIT Þv_ T {ð1zr2 ÞIS2 v_ S2 {IR1 v_ R1 ~r1 TT zðr2 z1ÞTB zTOWC IEQV v_ OUT zY fðIS1 zIT Þv_ T zIS2 v_ S2 zIR1 v_ R1 g ~Y ðTT {TB {TOWC Þ{TLOAD ð25Þ Equations (16), (17), and (25) are the final governing equations for the power-on 1 R 2 upshift model. The 1 R 2 shift event can be divided into several phases according to the velocity sign of the sun gear and ring gear of the planetary gear sets. In the first gear and torque phase, the input turbine torque is transmitted through the one-way clutch. When the 1 R 2 shift starts according to the shift schedule, the oncoming band brake starts to engage (i.e. the torque phase including fill). At that instant, the output torque is inevitably dropping since some of the turbine torque is rerouted through oncoming friction element (i.e. the band brake). As a result, the torque transmitted by the OWC becomes decreasing until the point when it starts free-wheeling (i.e. the onset of the inertia phase). During the inertia phase, the output torque is suddenly increasing owing to the gear ratio change and deceleration of engine speed (also referred to as the speed phase). Details for each phase are derived and summarized in Appendix 2. Based on the derived power on 1 R 2 upshift model for each phase, the overall shift events can be

Actuation force feedback

The actuation force calculated from the measured actuation pressure was utilized for the feedback force-tracking control of the PHP actuator in references [11] and [12]. In that case, the pressure signal was inherently contaminated by fine pressure riffles caused by the pulse-driven operation of the PHP actuator. Accordingly, a pressure feedback control system requires the use of a low-pass filter with a cut-off frequency (e.g. 10 Hz), which in turn causes an undesirable delay in sliding surface switching. In addition, the force value computed from the pressure signals can also deviate from the actual actuation force due to the effect of friction in the hydraulic cylinder. In this study, the actual actuation force measurement without filtering is utilized to improve the performance of the controller. To measure the actual actuation force, an on-site force transducer is customized by using a pressure-resistive elastomerbased load sensor (which is cost-effective, compact, and suitable for automotive applications [15]). Figure 5 illustrates the prototype on-site force transducer, which consists of a d.c. power supply (3–5 V), a converting circuit, and the pressure-resistive elastomer-based load sensor. The relationship between the actuation force (in newtons) (y axis) and output voltage (in volts) (x axis) can be fitted by the equation y~ax{b

ð26Þ

where a is the slope of the solid line (equal to 496) and b is the y intercept (equal to 93). The prototype on-site force transducer shows good sensitivity that is sufficient for the force-tracking control purpose. 4.2

Fill volume control strategy

The fill control scheme described in equation (1) is performed by applying the maximum control input



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Fig. 5

Pressure-resistive elastomer-based on-site force transducer and its sensitivity curve

voltage until the end of the fill. For the fill stroke xs of 0.003 m, a control pulse of 200 Hz is scheduled for 0.3 s based on the experimental data for the flowrate of the PHP actuator. However, this open-loop fill control scheme is not robust against the variation in fill volume that can be caused by the inaccuracy in the flowrate and the tolerance stack-up of components. Hence, a more robust fill control strategy by detecting the end of fill is required to improve the tracking performance at the transition stage (i.e. fill R actuation stage). The output torque would be a good feedback signal in order to detect the end of fill since the output torque starts to drop immediately after stroking and transmitting the turbine torque through the oncoming friction element (i.e. the torque phase start). However, reliable and costeffective output torque transducers are not available in current ATs. In this research, it is proposed to use the turbine angular acceleration of the AT to detect the end of fill based on the useful relationship between the output torque and the turbine acceleration. The output torque equation during the torque phase can be expressed by (see Appendix 2) TOUT ~

IV v_ T zTLOAD ~f ðv_ T Þ Y ð1zr1 Þ

ð27Þ

It is self-evident that the output torque is an explicit function of the turbine angular acceleration. Like the output torque sensors, hardware-based direct measurement of angular acceleration, however, is not applicable. A natural alternative is to differentiate directly the turbine angular velocity (rotational speed) measured from the only available pick-up sensor (pulse encoder) in the current AT. The backward-difference operator can be used to differentiate the velocity quantity according to JAUTO1292

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aðkÞ~v_ ðkÞ~

vðkÞ{vðk{1Þ Ts

ð28Þ

where Ts is the sampling (interrupt) time. However, during the differentiation process, measurement errors will inevitably cause significant noise in the signal. The measurement error e(k) is defined by ~ ðk Þ e ðkÞ~vðkÞ{v

ð29Þ

˜ (k) where v(k) is the primary angular velocity and v represents the measured angular velocity. To facilitate useful acceleration signals, several post-filtering techniques, such as finite impulse response and infinite impulse response low-pass filters, can be used to restore the corrupted measured velocity signal. However, although most conventional filtering solutions including digital filters have shown stable and reliable performance, they will still lead to slight phase delay, which will be problematic especially in an AT application since the interested interval of torque phase is relatively short (e.g. 100– 200 ms). Indeed, the estimation of angular acceleration without phase delay has been recognized as one of the most challenging tasks in the realization of many industrial applications [16, 17]. Accordingly, more advanced filtering techniques, such as predictive digital filters (or phase advancing), have been studied to resolve the delay problem [16]. Recently, a cascaded neural-network-based predictive filter has been introduced [18]. Compared with conventional methods, the new acceleration estimation scheme has the advantage of implicit adaptability and is applicable for smoothly changing velocity signal, which is suitable for an AT application. Figure 6 shows the structure of a neural-network-based filter Proc. IMechE Vol. 224 Part D: J. Automobile Engineering


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Fig. 6

Structure of the neural-network-based filter for turbine acceleration estimation

with time delay neural network, which is proposed for the application in this research. xi is the input pattern and n is the number of input nodes (equal to 6). zs represents the output at the sth hidden neuron and h is the number of neurons at the hidden layer (equal to 5). It can be observed that the tapped delay line is feeding not only to the current samples but also to the delayed samples. Thus, this neuralnetwork-based filter can be described as a nonlinear function of the stored sample data as a^ðkÞ~f ½~ aðk Þ, ~ aðk{1Þ, , ~ aðk{N Þ

ð30Þ

where N is the order of the neural-network-based estimator, which is generally determined by empirical tuning (N 5 5, in this case). The set of delayed data is the noisy acceleration samples and will be input to the neural networks, which are the online training data. The set of delayed noisy data will be eventually averaged by the appropriate weights. In this research, the adaptive weighting of coefficients (i.e. Wsj and Wis) is performed by using optimization algorithms, such as the error backpropagation algorithm [19]. The r.m.s. error is considered as the cost function to be minimized and is given by vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u X m 2 u1 n X ðk Þ ðk Þ E~t aj {yj n k~1 j~1

ð31Þ

To illustrate the feasibility of this proposed approach, a sample estimation result using measured turbine speed data is shown in Fig. 7. The turbine angular velocity (or rotational speed) of a five-speed AT for a commercial vehicle is first recorded with a sampling rate of 0.02 s. The backward-difference

Fig. 7 Turbine acceleration estimation result using the neural-network-based filter

operator is also used to differentiate the angular velocity with a sampling time of 0.01 s. The threshold point indicating the end of fill can be detected by comparing two consecutive sampled acceleration such as jaðkÞ{aðk{1Þjwar

ð32Þ

where ar is the critical difference depending on the filtered acceleration quality. If the difference between the two sampled acceleration is greater than



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the predetermined constant ar, this point can be represented as an actual end of fill point (i.e. the torque phase starting point). As seen, the turbine acceleration signal derived using this advanced filtering method is no longer noisy and is useable to detect the end of fill.

5

HARDWARE-IN-THE-LOOP SIMULATION

Building upon the simulation model developed in section 3, the HILS is performed to demonstrate the effectiveness of new actuation concept and controller. When combined with the real-time simulation model and the physical PHP actuator hardware, the online HILS environment is constructed without an AT spin test facility, as shown in Fig. 8. The dSPACEH (model, 1103 board) is used as a rapid control prototyping tool for implementing the realtime control task. The process for the HILS is summarized as follows. 1. The simulation model and the controller are coded in MATLAB/SimulinkH. The turbine speed signal vT and engine rotational speed signals vOUT vT, which are available sensing signals in the current AT, are also adopted to determine the shift schedule and the adaptive fill control strategy. 2. The real-time workshop (RTW) module converts the Simulink models into an executable C code and downloads it into the built-in digital signal processor (DSP).

Fig. 8 JAUTO1292

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3. The digital output (i.e. equivalent control input) determined by the microprocessor is converted into an analogue output voltage through the built-in digital-to-analogue converter (DAC). The control input drives the PHP actuator through the two-level driver, which in turn generates the actuation force. The dSPACE system converts analogue inputs (i.e. from pressure or force transducer) into digital inputs using the built-in analogue-todigital converter (ADC) with 16 bit output resolution. A Dormand–Prince fifth-order integrator with a fixed step size of 100 ms and interrupt time of 1000 ms is used for real-time numerical integration. Figure 9 shows the overall experimental set-up for HILS, which includes a host personal computer connected to the dSPACE system, the PHP actuator, and two-level driver. To represent the entire stroke of the band brake, a plate spring is introduced at the front of the piston. Since the actual band brake will be slightly deformed at the beginning of actuation, owing to the band elongation and the compression of friction pads, the plate spring will allow a small deflection (about 0.5 mm) given the stroking action of the piston. The piston will be nearly stopped after stroking, emulating the fully compressed phase of the band brake. The customized force transducer described in section 4 is attached on the plate spring to measure the actual actuation force. A typical example of actuation force tracking control responses is illustrated in Fig. 10. The PHP actuator is actuated under an accumulator pressure of 0.4 MPa. A fill control input of 120 V with 200 Hz

HILS structure Proc. IMechE Vol. 224 Part D: J. Automobile Engineering


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Fig. 9 Photographs of HILS set-up

Fig. 10

Actuation force-tracking control results with respect to different throttle openings h of (a) 15u and (b) 10u (accumulator pressure, 0.4 MPa; Vi 5 120 V; fc 5 60 Hz). In the middle plots, the curves are as follows: ????, desired; ––, controlled

(i.e. equivalent control input of 10 V) is initially scheduled as 0.3 s for the fill stroke (xs 5 0.003 m), and the control frequency fc is then set to be 60 Hz

(i.e. equivalent control input of 3 V) from the end of fill to generate a flowrate sufficient to satisfy the sliding-mode condition. The desired force trajectory



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Fig. 11

Fill volume control results for (a) offline simulation and (b) HILS (accumulator pressure, 0.4 MPa; Vi 5 120 V; fc 5 60 Hz). In the middle plots, the curves are as follows: ????, desired; –, controlled; - - - -, uncontrolled)

of these illustrative examples is determined by the actuation pressure profile (maximum 0.6 MPa) and the diameter of band brake servocylinder (diameter, 0.038 m), which are currently used for commercial midsize passenger cars of Ford. As shown, the controller can successfully track the desired trajectory in the case of throttle openings 15u and 10u respectively. Owing to the correct fill, good tracking performance can be achieved although the openloop fill control scheme is applied at the transition stage (i.e. around 3.4 s). However, the performance of this simple open-loop fill control scheme is not robust against the variation in fill volume. To represent the overfill scenario due to fill uncertainties, the fill stroke is intentionally set to 0.0028 m. As seen in the offline simulation results (i.e. no hardware in the loop; Fig. 10(a)), without adaptive fill volume control (the fill control time duration is fixed at 0.3 s), undesired spikes in the force and torque signals are created because of over-fill. JAUTO1292

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To examine the effectiveness of proposed fill volume control, both offline simulation and HILS are performed and typical examples are illustrated in Fig. 11. By detecting the end of fill from the turbine acceleration, the original fixed fill time interval of 0.3 s is adaptively adjusted to 0.245 s when the controller is exercised. Consequently, the overfill spike in the actuation force and the output torque is significantly reduced, owing to the successful prevention scheme for the overfill.

6

CONCLUDING REMARKS

In this research, an actuation force-tracking controller using an on-site force transducer and an adaptive fill volume control strategy are developed to utilize PHP actuators effectively for automotive transmission shift control at the system level. The effectiveness of the proposed approach is successProc. IMechE Vol. 224 Part D: J. Automobile Engineering


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fully validated by evaluating the shift performance of a test-bed system in an HILS environment. With these research efforts and results, it has been shown that the PHP actuator can be utilized to form a potential power-by-wire actuation system for automotive transmission shift control. ACKNOWLEDGEMENT This work is supported by the Ford Motor Company University Research Program. F Authors 2010 REFERENCES 1 Sun, Z. and Hebbale, K. Challenges and opportunities in automotive transmission control. In Proceedings of the American Control Conference, 2005, pp. 3284–3289 (IEEE, New York). 2 Turner, A. J. and Ramsay, K. Review and development of electomechanical actuators for improved transmission control and efficiency. SAE technical paper 2004-01-1322, 2004. 3 Neelakantan, V. A., Washington, G. N., and Bucknor, N. K. Two-stage actuation system using DC motors and piezoelectric actuators for controllable industrial and automotive brakes and clutches. In Smart structures and materials 2005, industrial and commercial applications of smart structures technologies, Proceedings of SPIE, vol. 5762, 2005, pp. 275–286 (SPIE, Bellingham, Washington). 4 Turner, A. J., Ramsay, K., Clark, R. E., and Howe, D. Development of high force electromechanical linear actuator for shift-by-wire automated manual transmissions. SAE technical paper 2006-01-0360, 2006. 5 Sirohi, J. and Chopra, I. Design and development of a high pumping frequency piezoelectric–hydraulic hybrid actuator. J. Intell. Mater. Systems Structs, 2003, 14, 135–147. 6 Lee, D. G., Or, S. W., and Carman, G. P. Design of a piezoelectric–hydraulic pump with active valves. J. Intell. Mater. Systems Structs, 2004, 15, 107–115. 7 Tieck, R. M., Carman, G. P., Lin, Y., and O’Neill, C. Characterization of a piezohydrualic actuator. In Smart structures and materials 2005: smart structures and integrated systems, Proceedings of SPIE, vol. 5764, 2005, pp. 671–679 (SPIE, Bellingham, Washington). 8 Chapman, E. G., Herdic, S. L., Keller, C. A., and Lynch, C. S. Development of miniaturized piezohydraulic pumps. In Smart structures and materials 2005: industrial and commercial applications of smart structures technologies, Proceedings of SPIE, vol. 5762, 2005, pp. 299–310 (SPIE, Bellingham, Washington).

9 Kim, G.-W. and Wang, K. W. Piezoelectric–hydraulic pump based band brake actuation system for automotive transmission control. In Active and passive smart structures and integrated systems 2007, Proceedings of SPIE, vol. 6525, 2007, pp. 65251E.1–65251E.10 (SPIE, Bellingham, Washington). 10 Kim, G.-W. and Wang, K. W. Nonlinear force feedback control of piezoelectric–hydraulic pump actuator for automatic transmission shift control. In Industrial and Commercial Applications of Smart structures technologies 2008, Proceedings of SPIE, vol. 6930, 2008, pp. 69300A.1–69300A.8 (SPIE, Bellingham, Washington). 11 Kim, G.-W. and Wang, K. W. Power-by-wire piezoelectric–hydraulic pump actuator for automotive transmission shift control. SAE technical paper 2009-01-0950, 2009. 12 Kim, G.-W. and Wang, K. W. Switching sliding mode force tracking control of piezoelectric–hydraulic pump based friction element actuation systems for automotive transmissions. Smart Mater. Structs, 2009, 18(8), 085004. 13 Fujii, Y., Tobler, W. E., Clausing, E. M., Megli, T. W., and Haghgooie, M. Application of dynamic band brake model for enhanced drivetrain simulation. Proc. IMechE, Part D: J. Automobile Engineering, 2002, 216(11), 873–881. DOI: 10.1243/095440 702321031423. 14 StateflowH V6.5 user’s guide, 2006 (The Mathworks, Natick, Massachusetts). 15 Flexiforce sensor, information available at www. tekscan.com. 16 Ovaska, S. J. Angular acceleration measurement: a review. IEEE Trans. Instrum. Measmt, 1998, 47(5), 1211–1217. 17 Liu, G., Zhang, Q., Xiong, J., Xie, X., and Peng, S. An investigation of calculation method of wheel angular acceleration in anti-lock braking system. In Proceedings of the 2008 IEEE International Conference on Information and automation, 2008, pp. 840–843 (IEEE, New York). 18 Gao, X. Z. and Ovaska, S. J. Acceleration signal estimation using neural networks. Measmt Sci. Technol., 2001, 12, 1611–1619. 19 Passino, K. M. Intelligent control: biomimicry for optimization, adaptation, and decision-making in computer control and automation, 2004 (Springer, London).

APPENDIX 1 Notation e I r T Ts

tracking error inertia moment (kg m2) gear ratio torque (N m) sampling time (s)



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u Vi(f )

switching control input control input voltage with the pulse frequency f number of gear teeth

Z

C~Y ð1zr1 ÞðIS1 zIT Þz

173

Yr2 2 IEQV IS2 z 1zr 1 Y ð1zr1 Þ

Also Y v v ˙ v(k)

r2 ð1zr2 Þ TOWC ~ r1 ðIS1 zIT Þz IS2 v_ T {r1 TT 1zr1

final gear ratio angular velocity (rad/s) angular acceleration (rad/s2) sampled angular velocity

The transient output torque TOUT of interest can be determined from equations (11) and (33) to give

Subscripts B C1, C2 E F I LOAD OUT OWC R1, R2 S1, S2 T V

band brake carriers of planetary gear engine forward clutch impeller (pump) load output shaft one-way clutch ring gears sun gears turbine vehicle

TOUT ~

v_ OUT ~

1 ðv_ T zr1 v_ R1 Þ Y ð1zr1 Þ

ð37Þ

v_ R1 ~ðADzBE Þ{1 fðYA{r1 E ÞTT

(a) First gear and torque phase

{½ð1zr2 ÞEzYATBC {ATLOAD g

In first gear and torque phase, because of the OWC, the first ring gear is constrained (i.e. v ˙ R1 5 0). Once the oncoming band brake starts to engage, the braking torque is governed by equation (19) (i.e. TB 5 TBC) and the second sun gear is not constrained (vS2 ? 0, i.e. ˙ OUT can be expressed by slip). Then, v ˙ S2 and v v_ T v_ S2 ~{Yr2 v_ OUT , v_ OUT ~ Y ð1zr1 Þ

ð38Þ

Then, v ˙ T can be derived as v_ T ~ðADzBE Þ{1 fðYBzr1 DÞTT z½ð1zr2 ÞD{YBTBC {BTLOAD g

ð39Þ

where ð33Þ

Also, eliminating v ˙ S2 and v ˙ OUT in the governing equations (i.e. equations (16), (17), and (25)) yields the equation (which is an explicit function of three known torques)

ð1zr2 Þ IS2 A~r1 ðIS1 zIT Þz r21zr 1

ð1zr1 zr2 Þ B~ ð1zr2 Þ1zr IS2 zIR1 1

Yr2 EQV E~Y ðIS1 zIT Þ{ 1zr IS2 z Y ð1zr 2 1Þ I

v_ T ~C {1 ½Y ð1zr1 ÞTT zYr2 TBC {TLOAD

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ð36Þ

The transition condition from the torque phase into the inertia phase is TOWC 5 0 and both the oncoming and offgoing friction elements are slipping (i.e. ˙ R1 and v ˙ OUT can be defined vR1 ? 1, vS2 ? 0). Then, v by

Power on 1 R 2 upshift equations

~f ðTT , TBC , TLOAD Þ

IV v_ T zTLOAD Y ð1zr1 Þ

(b) Inertia (speed) phase

APPENDIX 2

where

ð35Þ

{ð1zr2 ÞTBC

ð34Þ D~

Y ð1zr1 zr2 Þ r1 IEQV IS2 zYIR1 z 1zr1 Y ð1zr1 Þ



174


and TOUT can be derived as TOUT ~

the equation

IV r1 IV v_ T z v_ R1 zTLOAD Y ð1zr1 Þ Y ð1zr1 Þ

ð40Þ

v_ T ~D{1

h

Y ð1zr1 zr2 Þ TT {TLOAD 1zr2

i

ð42Þ

where D~

(c) Second gear The transition condition from the inertia phase into second gear is vS2 5 0 because the rotational speed of the second sun gear connected with the drum of band brake will become zero. Then, v ˙ OUT can be expressed as v_ OUT ~

1zr2 v_ T Y ð1zr1 zr2 Þ

r2 ð1zr1 zr2 Þ ð1zr2 Þ IEQV ðIS1 zIT Þz 1zr2 Y ð1zr1 zr2 Þ z

Yr2 2 IR1 ð1zr2 Þð1zr1 zr2 Þ

h i r1 1 TB ~ 1zr r1 ðIS1 zIT Þ{ 1zrr12zr2 IR1 v_ T { 1zr TT 2 2 ð43Þ

ð41Þ

Substituting this constraint (˙ vS2 5 0) into governing equations and rearranging v ˙ R1 in terms of v ˙ T yields

TOUT ~

1zr2 IV v_ T zTLOAD Y ð1zr1 zr2 Þ



ð44Þ

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Engineering Engineers, Part D: Journal of Automobile ...

Engineering Engineers, Part D: Journal of Automobile ...

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