Driveline Launch Control by a Test-Based Nonparametric QFT Method

2012 Workshop on Engine and Powertrain Control, Simulation and Modeling The International Federation of Automatic Control Rueil-Malmaison, France, October 23-25, 2012

Driveline Launch Control by a Test-Based Nonparametric QFT Method Ahmed Abass ∗ A. Thomas Shenton ∗ ∗

Centre for Engineering Dynamics, University of Liverpool, Brownlow Hill, Liverpool L69 3GH, UK (e-mails: [email protected] & [email protected]).

Abstract: A novel Nonparametric (NP) Nonlinear Quantitative Feedback Theory (QFT) robust control design method is experimentally applied to the driveline launch, tracking and shuffle control problem. In the experimental setup the engine Air Bleed Valve (ABV) duty cycle (DTY) is used as an excitation input signal and the vehicle wheel speed is the controlled output. The input signal is formed as PRBS with different amplitudes and different Perturbation Periods (PPs). The NP-QFT design technique uses the discrete Hilbert transform to determine the necessary phase shift to produce the stable minimum phase (SMP) nominal plant required by the QFT approach for the non minimum phase (NMP) driveline plant. The tracking performance for the driveline with the designed controller is tested on a chassis dynamometer by several step speed demands and was found to fall within the specified response boundaries. The controlled system disturbance rejection is tested by applying a step torque to the chassis dynamometer rollers against the wheel rotation direction. The resulting speed disturbance is rejected and remains within the required limits. In contrast to previously proposed techniques the new approach does not require any parametric model and relies entirely on the non-parametric frequency response characterisation of the vehicle driveline dynamics which can be obtained quickly from experimental input output data. The NP-QFT technique is entirely systematic and does not rely on trial and error (cut and try) procedures and should significantly speed the industrial development of driveline control systems. Keywords: Backlash; Control; Driveline ; Launch; Nonlinear; Nonparametric; QFT; Shuffle, System-Identification. 1. INTRODUCTION

based control techniques are not extensively applied to the driveline control problem, and industrial practice in driveline calibration remains largely heuristic and involves extensive trial-and-error experimental track based testing and parameter tuning.

Vehicle driveline oscillations and shuffle modes must be carefully controlled to avoid excessive vehicle jerk and consequent bad driveability, especially in the most difficult low speed, high requested-torque region such as in vehicle launch. The calibration (design and tuning) of actively controlled electronic-throttle based driveline controllers currently incurs considerable expense and effort. Acceptable driveability is essential to allow customer acceptance of the new fuel-efficient emission-reducing technologies. A thorough quantitative account of vehicle driveability measures is presented by List and Schoeggl (1998), and modeling of the driveline is surveyed by Hrovat and Tobler (1991) in which parameter identification is used. Time delays in the responses of current engine technologies are also present a severe constraint on achievable levels of control. The driveline system also contains significant nonlinearities due to clutch behaviour, tyre characteristics, and backlash in gear-box, couplings and engine mounts (Lagerberg and Egadt, 2002). In addition the driveline contains structural elements with highly uncertain damping and hysteresis characteristics and nonlinear stiffnesses. The backlash accentuates oscillatory behaviour in tip-in and tip-out manoeuvres and presents a particularly severe control problem (De La Salle et al., 1999). Due to the difficulty of identifying such backlash systems, model978-3-902823-16-8/12/$20.00 © 2012 IFAC

Mo et al. (1996) present a partially NP driveline control approach consisting of the spectral identification of a third order linear discrete model from a nonlinear driveline model excited by a PRBS test signal. The associated speed-torque feedback controller is designed using a poleplacement observer scheme. The controller design process accordingly does not quantitatively address the significant time delay, nonlinearity or controller robustness. A model-based scheme is described and experimentally tested by Baumann et al. (2006). A parametric continuous time linear phenomenological model is used and its parameters are identified from experimental data. The different parameters were found to be highly dependent on the engine speed, and this dependency was attributed mainly to the system backlash. The different parameters including inertia and damping were accordingly required to be scheduled with engine speed - inconsistently the physical theory. An observer scheme was used in conjunction with a Smith predictor. The continuous observer model and controller were discretized and their parameters were scheduled in a look-up table. Robustness of the controller for the model

85

10.3182/20121023-3-FR-4025.00029

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

was addressed by a Root Locus synthesis, however it was found necessary at the end of the design process to tune the controller on the vehicle, which somewhat compromised the actual controller robustness and made the final key design step less systematic. A parametric approach to driveline control in an injection controlled Diesel driveline is described by Balfour et al. (2000). This study is based on an experimentally validated driveline model. Discrete linear control models were obtained. Gain scheduling is introduced to address the likely significant system parameter variations. Pole assignment is used as the control design technique. The use of gain scheduling and tuning suggest that the process is not fully systematic. The results in-vehicle are nevertheless qualitively reported as promising. Both system identification and controller design for systems with backlash are difficult. A common approach to backlash control is based on the use of limit-cycle analysis using describing functions as in Gelb and Velde (1968); Kaya and Atherton (2001). The analytic or experimental determination of the overall system describing function however, may not be feasible, unless the problem is of special structure, or the system can be subject experimentally to a full range of sinusoidal test inputs. In the driveline problem test signals at the electronic throttle must be similar to those produced by driver input both to be representative and to prevent vehicle stall. Glielmo et al. (2006) presented an uncertain linear parametric model of a dry clutch and designed a linear QFT clutch controller. The resulting robustness of the technique was found to depend strongly on the appropriate selection of a suitable model structure for the parametric modelling.

Fig. 1. Driveline hardware setup Table 1. dSPACE board specifications Board SD1005 SD4001

Function processor board digital I/O

Specification power PC 750GX, 1GHz timing and digital I/O

of 13.87 is present when motion is transmitted from the engine to the front wheels through the driveline. An engine crankshaft 360 PPR incremental angular encoder is fixed to the crankshaft through a flexible coupling. Due to the gearing ratio reduction at wheels, for the NP system-identification it was necessary to use a high resolution 2500 PPR device for the high resoloution angular encoder encoder attached to a front wheel for the NP model capture, rather than the on-vehicle Anti-lock Braking System (ABS) wheel sensor. Subsequently the final controller may then be downsampled for lower resolution implementation in-vehicle.

In this paper, a novel NP QFT 2-degree of freedom tracking robust control method is applied to the driveline control of a gasoline engined PFI European sedan. The control is applied to the air-path to wheel speed feedback loop. The technique is experimentally validated using a 1.2m dia. chassis dynamometer. The experimental setup used in the study is described in section 2. Selection of excitation signals is discussed in section 3 and stated in section 4. Section 5 discusses the setting of stability, tracking and disturbance bounds before presenting a NP identification of the LTIE set in section 6. Section 7 presents a novel discrete Hilbert transform method to determine the stable MP nominal equivalent system required by the QFT method. The QFT open loop shaping is presented in section 8. The prefilter design is presented in section 9 and the experimental results of the controller testing are given in section 10 and finally, conclusions presented in section 11.

As shown from Fig. 1, a special purpose mechanism (Matthews et al., 2009) allows for the external fitting of the high resolution wheel speed angular encoder through a flexible coupling to the the centre of the left front wheel hub without affecting the vehicle performance. The device consists of a steel frame fitted to the front wheel suspension and bolted to an aluminium housing for the encoder as in Fig. 2. The driveline input demand signal is sent from a PC through dSPACE to the engine management system which can be switched from ECU strategy to a dSPACE programmed strategy. A dSPACE rapid prototyping flexible development system has been used for implementing the experimental controllers produced from dSPACE RealTime Interface (RTI) and MATLAB/Simulink Real-time Workshop and Control Desk software generation. The specifications of the dSPACE boards employed are given in Table 1.

2. DRIVELINE EXPERIMENTAL SETUP The test vehicle was a 1430 kg Ford Mondeo automobile with front-wheel drive and a 1.6l, 16 valve, four-stroke, four-cylinder, in-line, double overhead cam, water cooled, multi-point fuel injected IC Zetec engine. For the datacollection, the operation of the clutch during the vehicle launch was ignored, and first transmission gear was always engaged. As the first gear ratio is 3.417, and the final drive gear ratio (differential gears) is 4.06, a total speed ratio

The test vehicle is a cable driven car, with a throttle solenoid operated air bypass valve (ABV) primarily used for control of air-fuel mixing during engine idle. The ABV has a large authority however, and for the purposes of the experimentation is made fully controllable electronically by the Control Desk and Real-time Workshop software via dSPACE and PC to emulate an electronic throttle.

86

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

0

50 100 Time [s] PP=4

50 100 Time [s]

ABV duty

0

50 100 Time [s] PP=2

ABV duty

0.8 0.6 0.4

0

50 100 Time [s] PP=6

ABV duty

0.8 0.6 0.4

0

50 100 Time [s] PP=4

0.8 0.6 0.4

0.8 0.6 0.4

ABV duty

0.8 0.6 0.4

0

50 100 Time [s] PP=2

0.8 0.6 0.4

ABV duty

50 100 Time [s]

0.8 0.6 0.4

0

PP=2 0.8 0.6 0.4

0.8 0.6 0.4

ABV duty

0

50 100 Time [s] PP=2

ABV duty

0

50 100 Time [s] PP=6

ABV duty

0.8 0.6 0.4

0

50 100 Time [s] PP=4

ABV duty

0.8 0.6 0.4

0

50 100 Time [s] PP=2

0.8 0.6 0.4

ABV duty

0.8 0.6 0.4

0

50 100 Time [s] PP=6

ABV duty

50 100 Time [s]

0.8 0.6 0.4

0

PP=6 0.8 0.6 0.4

ABV duty

0

50 100 Time [s] PP=6

ABV duty

0

50 100 Time [s] PP=4

ABV duty

0

50 100 Time [s] PP=2

ABV duty

0.8 0.6 0.4

0

50 100 Time [s] PP=6

0.8 0.6 0.4

ABV duty

0.8 0.6 0.4

0

50 100 Time [s] PP=4

ABV duty

ABV duty

0.8 0.6 0.4

0

PP=4 0.8 0.6 0.4

ABV duty

ABV duty ABV duty ABV duty

0.8 0.6 0.4

ABV duty

Fig. 2. Wheel angular encoder installation

0.8 0.6 0.4

ABV duty

PP=2 0.8 0.6 0.4

0.8 0.6 0.4

0

50 100 Time [s] PP=4

0

50 100 Time [s] PP=6

0

50 100 Time [s] PP=2

0

50 100 Time [s] PP=4

0

50 100 Time [s] PP=6

0

50 100 Time [s]

Fig. 4. Input data set for ABV duty ranges 0.4 to 0.45 in subplots 1,2,3 & 0.4 to 0.5 in subplots 4,5,6 & 0.4 to 0.55 in subplots 7,8,9 & 0.4 to 0.6 in subplots 10,11,12 & 0.4 to 0.65 in subplots 13,14,15 & 0.4 to 0.7 in subplots 16,17,18 & 0.4 to 0.75 in subplots 19,20,21 & 0.4 to 0.8 in subplots 22,23,24

Fig. 3. Driveline experimental setup The throttle valve is closed to 8deg when the engine control is switched to ABV through a selectable input buffer interface. A dSPACE expansion box is used with boards DS4001 and DS1005 in the experimental setup as shown in Fig. 3. Board DS4001 is a timing and digital I/O board. This board receives the engine speed and the wheel speed encoders signals as digital signals. The data is then exchanged with the DS1005 board, which is a digital I/O processor board. Processor boards provide the computing power for real-time controller and also function as interfaces to the I/O boards and the host Personal Computer (PC) (dSPACE GmbH., 2010) through a Local Area Network (LAN) cable. The DS4001 sends two signals, a Pulse Width Modulated (PWM) signal to control the ABV and an 8-Bit spark-word command signal to control the spark. Those signals go through a buffer interface. The buffer interface acts to protect the dSPACE and the ECU from any erroneous signals. It has two modes of operation: normal ECU, and bypass, whereby the operator replaces the command logic signals in the ECU with their own. Both modes of operation utilise the powerstages within the ECU to drive the coil of the ABV.

was chosen throughout to ensure stable engine running. An upper ABV limit is chosen as 0.85 because the ABV response to the driving signal becomes very nonlinear after this point but it is found that control can be adequately achieved within these limits. 4. THE LTIE I/O DATA SET Input and output data is collected for a time period of over 200s from the driveline experimental setup as in section 2. All signals are sampled on-line each at 0.001s. The input signals (ABV duty) are formed as PRBS with different amplitude ranges (0.4 to 0.8) and three Perturbation Periods (PPs) (2s, 4s, and 6s) for each range. Fig. 4 shows the elements of the input data set used in the study in which the ABV duty is changed from 0.4 to 0.8. Fig. 5 show the output data set of the relevant wheel speed responses in RPM. Both figures display the first 100s of collected data. Varying the normalised ABV duty from 0.4 to 0.8 randomly by PRBS causes wheel speed responses up to 200 RPM.

3. SELECTION OF EXCITATION SIGNAL The ABV opening controls the air that passes into the engine inlet manifold in the experimental setup. The throttle valve opening was fixed at 8deg during the tests and all identification and control actions were done by ABV duty instead. All data is collected during engagement of the vehicle transmission gearbox in first gear where the backlash and clutch nonlinear effects are usually at their maximum.

5. SETTING OF STABILITY, TRACKING AND DISTURBANCE BOUNDS The QFT tracking boundaries are chosen according to the required time domain specification of the controlled system. In the driveline speed control problem, the upper and lower limits for tracking boundaries have been chosen to achieve a settling time of 20s, an overshoot of 16%, and a speed disturbance rejection within 14s as in Fig. 6. The upper and lower tracking bounds used in the design for the experimental validations are

For this work, the ABV duty signal is normalised, so 1.0 represents a full opened valve and 0.0 represents a fully closed valve. Because the vehicle engine stalls when the normalised ABV duty goes under 0.35, a lower limit of 0.4

87

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

Tracking control ratio TR(s)=Y(s)/R(s)

0

0

50 100 Time [s]

200 0

0

50 100 Time [s]

50 100 Time [s]

100 0

0

50 100 Time [s]

200 0

0

50 100 Time [s]

400

50 100 Time [s]

100 0

0

50 100 Time [s]

200 0

0

50 100 Time [s]

200 0

0

50 100 Time [s]

|TR |, |TR | [dB]

L U

200

200

400

100

1

50

0.8

0

50 100 Time [s]

0

0

50 100 Time [s]

Tracking control ratio T (s)=Y(s)/R(s) R

δ

R1

−10

δR2

0

50 100 Time [s]

−20

δ

R3

δR4

0

δR6

Fig. 5. Wheel speed response output data set

upper bounds lower bounds −12 dB magnitude difference

0.6

0.4

0.2 upper bounds lower bounds

0 0

10 20 Time [s]



YR (s) R(s)



uncertain plant templates boundaries nominal plant

5.5rad/s 0

1

4rad/s

5rad/s 3rad/s

0.8

−50 2rad/s

0.6

0.4

−100

1rad/s 0.5rad/s

−150

0.2

0

5

Time [s]

10

−200

15

Fig. 6. Time domain specifications   YR (s) 0.2s2 + 0.4s + 0.1 TU (s) = = , R(s) U s2 + 0.4s + 0.1 TL (s) =

Frequency [rad/s]

1.2

0 30

0

10

Fig. 8. Tracking boundaries down to −12 dB

Imaginary

System response yd(t) to unit step disturbance

System response yr(t) to unit step input

0.8

δR7

−40

50 100 Time [s]

−60

1

δ

R5

−30

−50

1.2

Frequency [rad/s]

0

200 0

0

10

Fig. 7. Tracking and disturbance rejection boundary widths

100 0

0.6

50 100 Time [s]

100 0

0

10 Frequency [rad/s] Disturbance control ratio TD(s)=Y(s)/D(s)

0.4

100 50

upper bounds lower bounds

−60

|TD| [dB]

400

0

Wh. S. [RPM]

Wh. S. [RPM]

Wh. S. [RPM]

400

0

50

−40

L

100

200

0

200

100

150

50 100 Time [s]

−20

U

50 100 Time [s]

100

50 100 Time [s]

0

|TR |, |TR | [dB]

0

50 100 Time [s]

0

Wh. S. [RPM]

0

200

0

50

150

Wh. S. [RPM]

100

50

100

50

Wh. S. [RPM]

50 100 Time [s]

100

150

50 100 Time [s]

100

Wh. S. [RPM]

0

50 100 Time [s]

0

150

Wh. S. [RPM]

50

0

Wh. S. [RPM]

100

150

50

150

Wh. S. [RPM]

50 100 Time [s]

100

60

Wh. S. [RPM]

0

50 100 Time [s]

80

Wh. S. [RPM]

400

50

150

0

100

Wh. S. [RPM]

200

100

60

Wh. S. [RPM]

Wh. S. [RPM]

200

50 100 Time [s]

Wh. S. [RPM]

Wh. S. [RPM]

150

0

80

Wh. S. [RPM]

Wh. S. [RPM]

150

Wh. S. [RPM]

60

100

Wh. S. [RPM]

80

Wh. S. [RPM]

100

Wh. S. [RPM]

Wh. S. [RPM]

0

−50

0

50

Real

100

150

200

Fig. 9. Nyquist plot of driveline uncertainty templates [RPM]

(1)

The FRF representation of each I/O data element of the experimental data set of section 4 is represented by a point in the complex plane at each frequency element of Ωi as in Fig. 9. The outer boundary of all the points at an individual frequency represents the plant uncertainty template at the frequency. The aribtrary discrete frequency QFT nominal plant FRF is chosen for this study as the locus of the centre of gravity of each template. The templates are mapped to the Nichols chart for the loop shaping described in section 8.

= L

0.06s4 + 0.5s3 + 1.4s2 + 0.9s + 0.2 (2) + 6.6s5 + 17.1s4 + 18.4s3 + 9.5s2 + 2.3s + 0.2 and the disturbance rejection bound   s2 + 0.6s YD (s) = 2 (3) TD (s) = D(s) U s + 1.1s + 0.3 0.5s6

7. DETERMINATION OF THE SMP QFT NOMINAL SYSTEM

6. NP IDENTIFICATION OF LTIE SET Due to the existence of time delay between the excitation and the plant response, the plant is expected to be NMP. As in the QFT methodology developed by Horowitz and Sidi (1978) for NMP feedback systems with plant uncertainty, an all-pass function A(s) multiplied with an equivalent MP plant Lm (s) can be used to represent the NMP plant. The QFT design boundaries in the Nichols chart should then be shifted to the right by the phase of the all-pass function A(s) before shaping a loop locus

For this work the LTIE of the driveline plant is modelled as a set of frequency response functions (FRFs). These are obtained directly from the experimental data using local frequency smoothing estimation (Ljung, 2003). The grid of frequencies Ωi = {0.5, 1, 2, 3, 4, 5, 5.5} rad/s (as employed in Fig. 8) is chosen to cover the system bandwidth down to −12 dB according to the guidelines given in Houpis et al. (2006).

88

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

−60 −80

5.5rad/s 0.5rad/s 1rad/s 2rad/s 4rad/s 5.5rad/s 3rad/s 0.5rad/s 5rad/s 1rad/s 2rad/s 1rad/s 3rad/s 4rad/s 5rad/s

−100 0

0

Frequency [rad/s]

0 −5

−10

2rad/s

−20 3rad/s

−10 −30

−15 −20 −25

phase shift

4rad/s 5.5rad/s

−40 0

10

−250

−150 −100 Phase [degree]

Frequency [rad/s]

Fig. 10. All-pass phase shift locus

Mag. [dB]

In this paper, the nominal plant may be conventionally chosen as the centre of area of each frequency template as in Figure 11. The resulting locus is found NMP. The corresponding all pass function the discrete Hilbert transform is used to determine the locus of stable MP (SMP) plant with equivalent gain and the all pass system found from the difference in phase of of the original NMP plant and transformed SMP plant. ∠Po∗ (jω)−∠Po (jω))

−50

0

Fig. 11. Open loop shaping of the MP NP Lmo (jω) in the Nichols chart

of Lm (s). This parametric approach cannot be applied in the NP model simply because the unstable zeros are not known as a parametric value.

A(jω) = e

−200

5rad/s

10 5 0 −5

0 −2.8dB 0.5rad/s

−4.8dB

Mag. [dB]

−150 −100 −50 0 Phase [degree] −10 −12 −14 −16 −18

−18.2dB

Mag. [dB]

The equivalent MP plant is constructed as in Fig. 10. The SMP nominal loop transmission locus can thus be used in the QFT design instead of the original NMP version. The shaped locus may then be converted back through multiplication by the all-pass phase shift component A(jω) giving Lo (jω) = A(jω)Lmo (jω) (5)

−20 −25

−22dB 4rad/s

−30

−30.55dB

Mag. [dB]

−100 0 Phase [degree]

−18.18dB

−20 3rad/s −25

−24.65dB −200

−100 0 Phase [degree]

−24.2dB

−25 −30 −35

5rad/s −34.7dB −200 0 Phase [degree]

200

−22.5dB

−25 −30 −35

1rad/s

−15

−300 −200 −100 0 100 Phase [degree]

which may then be used to obtain the QFT controller as Lo (jω) G(jω) = (6) Po (jω)

−11dB

−10

−200 −100 0 100 Phase [degree]

(4)

−6.7dB

−5

−15 −200

50

−13.3dB 2rad/s

Mag. [dB]

Phase shift [degree]

10

Mag. [dB]

−140

nominal plant Hilbert plant

Mag. [dB]

−120

disturbance stability tracking templates Lmo

0.5rad/s

10

Magnitude [dB]

Phase [degree]

−40

5.5rad/s

−38.5dB

template M circls

−200 −100 0 100 Phase [degree]

8. QFT OPEN LOOP SHAPING Fig. 12. Prefilter F (jω) design in the Nichols chart

Shaping the locus of the MP equivalent plant Lmo in the Nichols chart requires that each template should be above the tracking boundary and outside the stability boundary and disturbance rejection boundaries. Keeping the template as close as possible, but above it, is required Lo to keep the magnitude of 1+L to a minimum. Fig. 11 o shows how these templates are shaped in the Nichols chart and the resulting locus of Lmo (jω).

to position the system tracking response within the tracking specifications as in Fig. 8. The values of the maximum and minimum magnitude M circles in the Nichols chart for each template are determined as shown in Fig. 12. The values of Mmax , Mmin for the closed loop loci are obtained from Lmax (jω) 1 + Lmax (jω) Lmin (jω) and Mmin (jω) = 1 + Lmin (jω) However, the QFT design also requires that F (jω)Lo (jω) ≤ |TR (jω)| |TRL (jω)| ≤ U 1 + Lo (jω) Mmax (jω) =

The next step is to then obtain the locus of the QFT controller G(jω) as Ao (jω)Lmo (jω) G(jω) = (7) Po (jω) In the presented design, the controller is found to be 0.03s4 + 0.3s3 + 2s2 + 4.6s + 2 G(s) = (8) 0.4s4 + 5.5s3 + 552.2s2 + 1500s

(9)

(10)

Because Mmax and Mmin are not necessarily within the range between |TRU (jω)| and |TRL (jω)|, a forward path compensator is needed to achieve this. The upper and lower limits of the prefilter frequency domain specifications are then determined as

9. QFT PREFILTER DESIGN Following the usual QFT methodology, the prefilter F (s), which is a feed-forward path compensator, is synthesized

89

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

20 10

220 demand response

0 −10 −20

180

TR (jω) U

−30

T (jω)

Wheel speed [RPM]

Magnitude [dB]

200

R

L

M

(jω)

max

−40

Mmin(jω) F

(jω)

F

(jω)

max

−50

min

F(jω) −60

0

10

160 140 120

Frequency [rad/s]

100 80

Fig. 13. Prefilter F (jω) frequency domain boundaries

60

20 log10 |FU (jω)| = Controller effort

20 log10 |FL (jω)| = 20 log10 |TRL (jω)| − 20 log10 |Mmin (jω)| (12)

where

250

300

0.6 0.4 messured filterd

0.2 0

100

150

200 Time [s]

250

300

(13)

The prefilter is designed to be inside those boundaries as shown in Fig. 13 The successful shaping of Lmo (jω) together with the required uncertainty tolerance on the unfiltered tracking dynamics allows a guarantee of the required performance robustness. The prefilter for the driveline controller is accordingly determined as

Fig. 14. Controller tracking performance testing

190 180 170 160 Wheel speed [RPM]

0.2s2 + 1.1s + 1 F (s) = 0.1s2 + s + 1

200 Time [s]

0.8

20 log10 |FU (jω)| ≥ 20 log10 |F (jω)| ≥ 20 log10 |FL (jω)|

150

1

20 log10 |TRU (jω)| − 20 log10 |Mmax (jω)|(11) and

100

(14)

150 140 130 120 110

10. CONTROLLER TESTING

100 demand response

90 80

The tracking performance of the final controller design was tested by several step demands of wheel speed. Steps from 90 RPM to 180 RPM, 80 RPM to 160 RPM and 80 RPM to 200 RPM were tested. A typical resulting response is shown in Fig. 14. The tracking performance is always within the desired boundaries. These step input responses including that in the more detailed plot in Fig. 15 represent the possible vehicle driver demands during engagement of the fist gear in vehicle launch.

0

10

20

30 Time [s]

40

50

Fig. 15. Controlled system step response 180

Wheel speed [RPM]

170

The controlled system disturbance rejection is tested by applying a step torque of 450 Nm to the chassis dynamometer rollers against the wheel rotation direction. During these steps the wheel speed demand was set to the reference value of 150 RPM. The disturbance signal was sent as a voltage to the chassis dynamometer DC motor and the applied torque was measured by a load cell fixed 534.95 mm from the roller axis.

160 150 140 130 120 50

60

70

80 Time [s]

90

100

110

60

70

80 Time [s]

90

100

110

Disturbance [Nm]

600 400 200 0

As can be seen from Fig. 16, the controller demonstrated significant robustness to change in load disturbance. Both loading and unloading show similar time response results where the wheel speed returns to ±5 RPM of the nominal wheel speed in around 9s. The experimental testing shows that the response is always inside the pre-specified time domain closed loop response boundaries of Fig. 6.

50

Controller effort

1 0.8 0.6

0.2 50

11. CONCLUSION

messured filterd

0.4 60

70

80 Time [s]

90

100

110

Fig. 16. Disturbance rejection response in the controlled system

The conclusion of this paper can be itemised as:

90

2012 IFAC E-CoSM (E-CoSM'12) Rueil-Malmaison, France, October 23-25, 2012

I. Horowitz and M. Sidi. Optimum synthesis of nonminimum phase feedback systems with plant uncertainty. International Journal of Control, 27,3:361–386, 1978. C.H. Houpis, S.J Rasmussen, and M. Garcia-Sanz. Quantitative Feedback Theory, 2nd edition. CRC Press, Taylor &d Francis,Florida., 2006. D. Hrovat and W.E. Tobler. Bond graph modeling of automotive power trains. Journal of the Franklin Institute, 328,5/6:623–662, 1991. I. Kaya and D.P. Atherton. Parameter estimation from relay autotuning with asymmetric limit cycle data. ELSEVIER, Journal OF Process Control, 11:429–439, 2001. A. Lagerberg and B.S. Egadt. Estimation of backlash with application to automotive powertrains. 2002. H.O. List and P. Schoeggl. Vehicle dynamics and control synthesis for four-wheel steering passenger cars. ASE, International Congress and Exposition, Detroit, Michigan, 1998. L. Ljung. Linear system identification as curve fitting. Springer Lecture Notes on Control and Identification, 286:203–215, 2003. C. Matthews, Paul B. Dickinson, and A. Thomas Shenton. Chassis dynamometer torque control: A robust control methodology. SAE International Journal of Passenger Cars, 2:263–270, 2009. C.Y. Mo, A.J. Beaumount, and N.N. Powell. Active control of driveability. pages 215–221, 1996.

• A novel NP QFT controller design technique is described and experimentally applied to the driveline launch speed control problem • The vehicle is kept in first gear with clutch engaged. • The ABV duty cycle is used as the excitation signal in the used experimental set. The set of test input signals is formed from PRBS signals with different amplitudes and different PPs. • Vehicle wheel speed which was the controlled output variable was measured by a high resolution angular encoder attached bt a special purpose mechanism for data capture during the modelling phase. • The NP LTIE model set for the driveline required by the QFT method is obtained directly as a set of FRFs from experimentally obtained input-output (IO) data. • The corresponding QFT plant templates of the IO FRFs were then calculated from the IO data by using a local smoothing technique. • A novel technique using the discrete Hilbert transform is applied to determining the necessary phase shift to obtain the nominal stable MP plant required of the QFT design. • The tracking performance for the driveline with the controller was tested by several step speed demands. The tracking performance was found to satisfy the chosen time domain response specifications. • The controlled system disturbance rejection was tested by applying a step torque to the chassis dynamometer rollers against the direction of wheel rotation. The resulting speed disturbance is rejected so that the tracking response remains within the chosen time domain response boundaries. • The experimental validation of the NP QFT control design method demonstrates its capability to systematically and quickly design effective driveline controllers able to maintain the vehicle wheel speed response within the desired boundaries, without the need for parametric model development or time consuming trial-and-error procedures. REFERENCES G. Balfour, P. Dupraz, M. Ramsbottom, and P. Scotson. Diesel fuel injection control for optimum driveability. SAE 2000 World Congress, Detroit, MI, USA, 2000-010265, 2000. J. Baumann, D.D. Torkzadeh, A. Ramstein, U. Kiencke, and T. Schlegl. Model-based predictive anti-jerk control. ELSEVIER, Control Engineering Practice, 14:259–266, 2006. S. De La Salle, M. Jansz, and D. Light. Design of a feedback control system for damping of vehicle shuffle. EAEC European Automotive Congress, Barcelona, Spain, 1999. dSPACE GmbH. Embedded Success dSPACE Catalog. dSPACE GmbH.,33102 Paderborn, Germany, 2010. A. Gelb and W.E.V. Velde. Multiple-Input Describing Functions and Nonlinear System Design. McGraw-Hill book Company, New Yourk St. Louis, 1968. L. Glielmo, P. Gutman, L. Iannelli, and F. Vasca. Smooth engagement of an automotive dry clutch. 4th IFACSymposium on Mechatronic Systems, Heidelberg, Germany, F1:632–637, 2006.

91