i 

Dynamic Research, 1nc.r '9 

DRI-TM-85-12 

SUPPLEMENTARY REPORT 

ON 

ANTILOCK ANALYSES 

JPL NO. 9950 - (I gF 

Cm. 3 7 

Purchase Order No. 798421 

J. W. Zellner 

(NASA-CE-179355) SUPELEIENTAtiY BEPOBT ON N87-147C3 

ANTILOCK ANALYSES (Dyndmic EeEearch, IAC,) 

52 p CSCL 131 

Unclas 

G3/37 43339 

September 1985 

This report was prepared for the Jet Propulsion Laboratory, 

California Institute of Technology, sponsored by the 

National Aeronautics and Space Administration. 

355 Van Ness Avenue .Torrance, California 90501 213-212-521 1 

~ 
TABLE OF CONTENTS 

Page 

I . INTRODUCTION ...................... 1 

I1 . ANALYSIS OVERVIEW ................... 2 

A . Approach ...................... 2 

B . Full Scale Versus Simulation Comparison ...... 2 

C . Effects of Feedback Control Structure ....... 2 

E . Effects of Feedback Amplitude. Input Amplitude and 

F . System Stability Boundaries ............ 3 

G . System Optimization with Mitsubishi Modulator ... 3 

H . Effects of Modulator Dump and Reapply Rates .... 3 

I . Optimization of Toggle and Generic Modulator .... 4 

D . Effects of Toggle Design .............. 2 

Component Linearity ................ 2 

I11 . FURTHER ANALYSIS RESULTS* ............... 5 

A . Full Scale Versus Simulation Comparison ...... 5 

6 . Effects of Feedback Control Structure ....... 8 

C . Effects of Toggle Design .............. 10 

Component Linearity ................ 15 

E . System Optimization with Mitsubishi Modulator ... 15 

F . Effects of Modulator Dump and Reapply Rates .... 20 

G . Optimization of Toggle and Generic Modulator .... 26 

IV . CONCLUSIONS AND RECOMMENDATIONS ............ 27 

D . Effects of Feedback Amplitude. Input Amplitude and 

REFERENCES 47 

APPENDIX 48 

ii 
Section I 

INTRODUCTION 

. 

of antilock analysis, Ref. 1. It supports the main, overall documentation 

for the current phase described in Ref. 2. 

present the results and status of the recent analyses of toggle, modulator 

and overall system integration. 

This report provides supplementary documentation for the current phase 

Taken together, the two reports 

The two reports build on the results described in earlier documentation. 

Ref. 3 was a literature review of earlier fluidic antilock work. Ref. 4 and 5 

described a computer simulation and initial analyses of antilock dynamics. 

Ref. 6 and 7 presented the results of the preliminary analyses and conceptual 

design of the antilock system. 

recommending a specific design configuration and parameter values. 

The current reports carry this work forward, 

Specifically the objectives of the most recent analyses were to: 

0 Perform generic modulator analysis, to quantify the effects 

of dump and reapply pressure rates on antilock stability 

and performance. Analysis will include dump and reapply 

rates, and 1 umped modulator delay. 

Based on results of this and earlier toggle optimization 

analysis (with Mi tsubi shi modulator), synthesize a 

recommended preliminary antilock design and simulate its 

response and performance. 

Document the results of these analyses. 

0 

0 

The next section of this report gives an overview of the analyses, 

aimed at these objectives. 

Ref. 2, which describes the overall results, and the third section of this 

report, which gives more detailed results. 

conclusions and recommendations. 

This is keyed to the appropriate sections of 

The fourth section presents the 

1 
I Section I1 

ANALYSIS OVERVIEW 

A. APPROACH 

The analytical approach, as in earlier phases, involved a combination 

of techniques, including: 

histories; FFT's of selected full scale data collected by JPL; and gainphase analyses based on the former, and as described in Ref. 2. 

time domain and FFT analysis of simulated time 

B. FULL SCALE VERSUS SIMULATION COMPARISON 

Comparison of the dynamic response of the braked front wheel on a 

Results 

Also, the dynamic effects of high versus low mu are 

high mu surface was performed to help vailidate the simulation. 

are shown herein. 

shown for the simulation case only. 

Reference 7 compared the full scale and simulated responses of the 

Mi tsubi shi modulator. 

C. EFFECTS OF FEEDBACK CONTROL STRUCTURE 

This was analyzed in some detail in Ref. 7. Figures 5 to 7 of Ref. 2 

also verify that: 

angular jerk is not a suitable feedback. The possibility of angular velocity 

feedback i s described bel ow. 

D. EFFECTS OF TOGGLE DESIGN 

angular acceleration is an appropriate feedback; and 

This was shown and discussed in Fig. 11 in Ref. 2; further supporting 

detailed results are shown below. 

E. EFFECTS OF FEEDBACK AMPLITUDE, INPUT AMPLITUDE AND COMPONENT LINEARITY 

Describing functions of systems component responses shown bel ow are 

used to establish the linearity of the key components. 

2 
F. SYSTEM STAB I L ITY BOUNDAR I ES 

The boundaries of feasible antilock control were shown and discussed 

in Fig. 8 of Ref. 2. 

6. SYSTEM OPTIMIZATION WITH MITSUBISHI MODULATOR 

With this relatively slow automotive type modulator, the toggle design 

was adjusted across a wide range, and the resulting best achievable performance 

is shown below. 

H. EFFECTS OF MODULATOR DUMP AND REAPPLY RATES 

A "generic modulator" was analyzed with regard to the effects of its 

response on antilock stability and performance. 

sisted of mathematical expressions which gave: 

0 

The generic modulator conA linearly decreasing pressure dump mode, from some initial pressure 

value,triggered by a dump signal from the controller, 

A linear increasing pressure reapply mode triggered by a 

reapply signal from the modulator, 

A fixed time delay (simulating solenoid or other switching 

time delay) between the dump or reapply signal, and the 

initiation of the dump or reapply mode, and 

Suitable logic to prevent the pressure from exceeding the input 

pressure from the master cylinder; and to prevent the pressure 

from dropping below zero pressure. 

. 

o 

0 

The FORTRAN implemented version of these math expressions are given in the 

Appendix . 

The generic modulator models the main response features of simple, 

single rate zntilnck mc~!u!at~rs used in automotive applications. The 

dump and reapply rates and time delay were variable parameters, entered by 

the analyst. 

A range of dump and reapply rates were analyzed, to determine their 

effects on antilock stability and performance on high and low mu surfaces. 

3 
I' 

The overall results are shown in Figs. 9 and 10 of Ref. 2; more detailed 

results are presented below. 

I. OPTIMIZATION OF TOGGLE AND GENERIC MODULATOR 

Based on the results of the toggle and modulator analyses described above, 

'the more promising combinations of design parameters were used to explore a 

nominal, preliminary design.. During this process it was found that 

the modulator time delay had a relatively large effect on stability and 

performance and therefore, affected the choice of design parameters. As 

discussed below, it was decided to use a representative, "rapid" time delay 

value of 20 msec, to define the preliminary design. 

Once the preliminary design was defined and its response and performance 

simulated, a sensitivity analysis was performed. This involved independently 

perturbing each of the nominal design parameter values by an increment 

(e.g., about f 10 to 30 percent), to assess the sensitivity with respect to 

performance and stability. These results were presented in Figs. 10 and 11 

of Ref. 2 and are further discussed below. 

4 
I 

Section I11 

FURTHER ANALYSIS RESULTS 

A. FULL SCALE VERSUS SIMULATION COMPARISON 

Figure A- 1 shows full scale and simulated wheel acceleration 

frequency responses, for a pulse brake input. 

from the corresponding time histories, while the motorcycle was 

undergoing near limit braking, with a short pulse of increased brake 

pressure applied. The test surface was a dry, high mu paved surface. 

Note that the frequency response for a pulse input is not necessarily 

representative of the vehicle response during antilock cycling, 

because of nonlinear effects. A pulse input was used mainly for 

testing convenience, and to provide a comparison case, for an example 

input waveform. 

These are derived 

The results show that the simulation and full scale responses 

have very similar shapes. At a more detailed level, the simulation 

has a somewhat higher amplitude ratio, and somewhat more phase lag, 

than the full scale response. This can be attributed to the values 

used for several of the motorcycle parameters in the simulation - 

such as brake pad and tire/roadway friction coefficients and brakeline delay - which were not directly measured but rather estimated. 

Note that the tire/roadway friction was based on considering data 

such as presented in Ref. 8. Analytically, these relatively small 

inaccuracies can be accounted for by adjusting the estimated parameters to get a better match; or by shifting the gain-phase data 

appropriately in the subsequent analyses. 

be considered in a more refined, final design analysis; they were not 

included in the preliminary design analysis. 

support the validity of the vehicle simulation, for assessing anti- 

? nck dynamics. 

These refinements should 

Overall, the results 

Figure A-2 compares the simulated wheel response for a pulse 

input for the high versus low mu surfaces described in Ref. 6. 

Surprisingly, the amplitude response is essentially identical on the 

5 
.. 

40 

20 

0 

-20 

200 

IO0 

Phase 

Angle 

(deg 1 

0 

-100 

I 

I Pulse Brake I High mu 

I I I I I1111 I I I I Ill1 

IO 

Frequency (radlsec) 

Figure A-1. Comparison between Simulated and Full Scale Wheel 

Acceleration Frequency Responses 

6 

IO0 
Phase 

Angle 

(deg) 

40 

20 

0 

-20 

200 

IO0 

0 

- 100 

----- 

I 

I 

I 

\ 

I I I I 

I 10 

- 

100 

Figure A-2. Comparison between High and Low Mu Simulated Wheel Acceleration Frequency Response 

7 
two surfaces, and the main difference for the low mu surface is seen 

to be less phase lag at low frequencies, and more phase lag at 

frequencies above 2 Hz(which is typical for antilock operation). As 

seen in Fig. A-5 below, this has direct effects on antilock phasegain crossover and selection of an appropriate design compromise 

between high and low mu performance. 

B. EFFECTS OF FEEDBACK CONTROL STRUCTURE 

As described in Ref. 2, phase-gain analysis can be used to 

determine the feasibility of various potential feedback variables. 

Those results examined angular acceleration feedback (which is feasible), and angular jerk feedback (which is not suitable). 

speed feedback was also considered on a very preliminary basis, and 

an initial gain-phase plot example is shown in Fig. A-3. 

a gain-phase curve which may be compatible with toggle type feedback 

control. In the region of toggle effectiveness (-90 to -180 degrees 

phase lag), the wheel speed gain-phase data seem to give stable 

intersections for a limited range of toggle widths. 

of the intersection appears to be near orthogonal and this is desirable, 

as discussed in Ref. 2. For toggle halfwidths( i;e,trigger values) 

of 2 to 4 ft/sec antilock limit cycles in the region of 2.5 to 3.5 

Hz appear possible. 

control - which seems to be a new result, and could potentially have 

significant impact on design simplification - may be feasible, at least 

on a first look basis. 

Wheel 

The data for wheel angular speed response to dump commands shows 

The angularity 

So, using a wheel speed sensor for antilock 

Several words of caution need to be mentioned in considering this 

possibility. First, the suggested toggle trigger values are quite 

small, perhaps similar to the noise level present in some existing 

electromagnetic or fluidic speed sensors. 

low mu vehicle response has not been addressed here. 

fundmental ly, though not immediately apparent from the gain-phase 

analysis, the low frequency-high gain nature of the wheel speed 

response must be accounted for. That is, the average value of wheel 

Second, the effect of the 

Third, and 

8 
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c 

- 

A \. - - 

i I 

w0 

3, 

b--- \ 

QI 

c - .- 

x 

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nc 

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z?! 

0 

T 

1 I I I I 

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d 

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(u 

9 
speed will be decreasing as the vehicle decelerates, and this must 

be distinguished from higher frequency wheel locking motion. From a 

design standpoint, this might be achievable by providing a washout 

(or AC coupling) filter. 

response, so that it wouldn't affect the triggering action. 

ditional analysis would be needed to verify this. 

This could attenuate the low frequency 

AdAssuming a suitably filtered wheel speed sensor did have potential for antilock usage, there are several potential design approaches. 

One would be to develop a fluidic speed sensor, and washout filter, 

based on analog principles. Another approach would be to develop a 

wheel acceleration sensor with a midfrequency lag. This could 

potentially provide the necessary response shape, when viewed as a 

speed sensor. 

developed under the current effort may be such a lagged acceleration 

sensor. 

Note that, coincidentally,the fluidic transducer 

In any case additional analysis of this area is indicated; 

and it is conceivable that such could lead to simplified antilock 

des i gns . 

C. EFFECTS OF TOGGLE DESIGN 

The shape of a toggle can be described by its width (ie., difference between dump and reapply trigger levels), and its bias (le., 

value of its midpoint, relative to zero). 

parameters on system response was analyzed. 

The effects of these 

Past textbook analyses of toggles, such as those cited in Ref. 2, 

have indicated that the effect of increasing width is to increase 

the phase lag of the toggle. 

and is only a function of the input amplitude. These theoretical 

characteristics are verified numerically, with the simulation model , 

in Fig. A-4. This shows the toggle describing function for 2 toggle 

half widths (ie., zero, that is, a contactor switch; and 90 per cent 

of the input amplitude. The gain and phase valuse are in very close 

agreement with theoretical values, as would be expected. Of course, 

when the width of the toggle exceeds 100 per cent of the input 

amplitude, the device no longer triggers (ie., the gain is zero); 

so that the cases in Fig. A-4 span-most of the useful design range. 

10 

The gain is unaffected by the width, 
Gain 

db 

100 

0- 

-100- 

Phase 

Angle 

(deg) 

- 

Xo/A =O. 

---- --. 0.9 

--.-- --- 

’ I I I I IIIII I I I I I111 

20 

0 

-20 

Xo/A = 0.. 0.9 - 

.- 

Figure A-4. Effect of Toggle Relative Width, Xo/A, on ToggleSinusoidal Frequency Response 
The cross plotted gain-phase characteristics for several pertinent toggle widths (ie., 0.5, 1.0 and 2.09) are shown in Fig A-5. 

Also shown for comparison are the gain-phase data for the motorcycle/ 

Mitsubishi modulator part of an antilock system,,on low and high mu 

surfaces, for wheel acceleration feedback. Recalling that toggles 

only operate across a 90 degree phase range, it becomes clear that 

only a limited range of toggle widths will intersect the vehicle 

curves,which is a necessary condition for limit cycling. 

particular case, lesser or greater toggle widths would tend to result 

in no(or little) braking or lockup, respectively. A toggle half 

width of about 1.Og (width of 2.09) would seem to represent a good 

compromise between braking and antilock stability, low and high mu, 

with the Mitsubishi modulator. 

In this 

With respect to the vehicle response, several factors are apparent in Fig. A-5. For a given toggle,'the high mu limit cycling is 

generally at a higher frequency than low mu, and this has been observed in various past full scale prototypes. Also, on high mu, the 

system operates at lower gain margins than on low mu(ie., a smaller 

change in gain can destabilize it). 

shows that on low mu, the limit cycle amplitude will tend to be 

greater, and this is also observable in extant full scale antilocks. 

On the other hand, Fig. A-5 

The general effects of toggle bias are shown in Fig. A-6. This 

shows that bias affects the dwell time of both the dump and reapply 

modes. Since the latter have essentially ramp-like time histories, 

bias can be used to either truncate the ramp, or once the ramp has 

reached its final value, hold the final value (ie.,either zero 

pressure, or maximum applied pressure). 

the center point of the limit cycle, in the expected way. 

negative bias, which is the case for acceleration feedback, a more 

negative value results in a shorter dump mode and a longer reapply 

mode, that is more braking of the wheel, for equal dump and reapply 

positive, the system will become either unstable or have no braking, 

although no clear boundaries were uncovered. 

The bias also tends to affect 

For a 

nunrcaau plcaaule rates. Obviously, if the tcggle is too negative or too 

- 

12 
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0 

m 

13 
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c 

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X 

In 

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rr) 

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X 

cu 

0 

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X 

rc) 

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14 
E. EFFECTS OF FEEDBACK AMPLITUDE, INPUT AMPLITUDE, AND COMPONENT 

L IN EARITY 

The amplitude of the feedback signal - which may have various 

frequency components in it, as well as harmonics and noise - directly 

affects only the toggle element of the antilock, since the toggle 

has only a discrete, on/off output. Fig. A-7 shows the effect of . 

increasing wheel acceleration feedback amplitude on the toggle frequency response. This has the expected effect on gain (the phase was 

unchanged and is not shown). 

present in the wheel acceleration signal, can reduce the effective 

gain of the toggle. This again underlines the fundamental nonlinear 

nature of the toggle. Another amplitude effect which could potentially affect antilock operation - but which doesn't - is input 

amplitude (that is the command pressure from the master cylinder). 

Figure A-8 shows the frequency response of the Mitsubishi modulator 

plus vehicle, for different brake lever forces, below and above values 

corresponding to lockup on a low mu surface. Some differences are 

seen at frequencies below 2 Hz, but this is below the frequency of 

antilock operation. At higher frequencies , there is essentially 

no difference due to input force level. 

lator and vehicle elements are essentially linear. 

So, for example, large harmonics 

i 

This suggests that the moduThis is verified in Fig. A-9, which shows the modulator, 

vehicle, and combined response to periodic square wave inputs 

(eg., as generated by a toggle). 

equal to the sum of the individual responses, demonstrating linearity. 

The combined response is virtually 

E. SYSTEM OPTIMIZATION WITH MITSUBISHI MODULATOR 

A wide range of toggle designs were tried in combination with the 

Mitsubishi modulator, and wheel acceleration feedback. 

in Fig. A-5 above, it was found that a stable l'imit cycle was readily 

obtainable. 

were quite low. 

able high mu deceleration was as shown in Fig. A-10, namely 0.179 

which is far below values of 0.6 - 0.79 attainable by conventional 

(non antilock) front wheel braking, as shown in, for example, Ref.9. 

As suggested 

On the other hand, corresponding stopping decelerations 

After considerable tuning efforts, the best achiev15 
0 

-20 

121 = 1.0 

-40 

-60 

I 

Fi~~re A-7. Effects of Feedback Signal Amplitude on Toggle Frequency 

Response 

10 

Frequency (rad/sec) 

I00 

16 
! 

r 

Step brake,with 

frequency sweep of 

modulator command 

Low mu 

60 

40 

20 

0 

200 

100 

Phase 

Angle 

(deg 1 

0 

- io0 

I 

Hand Lever 

Force (I b) 

9. IO 

Hand Leve-r 

Force ( I b 1 

IO 

Frequency ( rad /set) 

I00 

Figure A-8. Effects of Input Force Level on Modulator/Vehicle Frequency Response 

17 
60 

40 

Amplitude 

Ratio 

(d8) 

Phase 

Angle 

(deg) 

20 

0 

200 

too 

0 

-100 

I 

Vehicle + 

Modulator , I frequency sweep 

Low mu 

Modulator, I L:ELI 

\ I 

\ I 

\I 

\I 

\I 

\I 

- \I 

\I 

\I 

\I 

\' I 

h I I I I I11II 

10 

Frequency ( rad /sec 1 

IO0 

Figure A-9. Frequency Responses of Vehicle, Modulator, and Their Series 

Combination, Demonstrating Superposition 

18 
. '1 

F82 15- 

0 

3.3 Hz 

I I 1 I 1 

LREL I 

0 . - -- 

0 JFigure A-10. Closed Loop Response of Optimized System, Based on Mitsubishi 

Modulator, High Mu Surface 

19 
I 

! 

A series cjf exploratory cases were run to see whether varying 

the dump and reapply rates, or solenoid time delay would help this 

situation. These were unsuccessful and also began to exceed the 

validity assumptions of the math model of the modulator mechanics. 

It was concluded, and later verified, that the effective time 

delay of this particular automotive modulator is too slow for use 

on a motorcycle front wheel brake. 

was analyzed, having variable dump and reapply rates, and time delay, 

recognizing that a new modulator would be needed for the current 

application. 

As a result, a "generic" modulator 

E. EFFECTS OF MODULATOR DUMP AND REAPPLY RATES 

i 

I 

, 

After developing a generic modulator model , open loop frequency 

response runs were made with various dump and reapply rates, and the 

results are shown in Figs. A-11, A-14 and A-15. 

were selected to span a range above and below those found in past 

motorcycle antilocks, such as in Ref. 

Fig. A-11 shows a pronounced effect of dump rate on antilock dynamics. 

High dump rates give higher amplitude, higher frequency limit cycles, 

for a given toggle, on high mu. Reapply rate seems to have little 

systematic effect. Subsequent analyses, discussed in Ref. 2, 

suggested that low mu results are quite different or even converse 

from these. Soythat should be kept in mind in viewing these data. 

The pressure rates 

9. The gain-phase plot of 

The effects on roughness and deceleration performance on high mu 

are shown in Figs. A-12 to A-15. Generally speaking, increasing both 

the dump and reapply rates, as in Figs. A-12 and A-13, increased the 

roughness and deceleration level. 

was mapped as a function of pressure rates, as in Figs. A-14 and A-15, 

it appeared that the more sensitive way to increase deceleration on 

high mu was to increase reapply rate. 

not necessarily true throughout the parameter space, as shown in Fig. 

11 of Ref. 2. 

When the open loop deceleration 

Later, it was found that this is 

It was also clear from these last data that the deceleration levels 

are higher at lower frequencies; yet are still not close to the target 

level of about 0.69. 

to reduce the net time delay of the vehicle brake system, from lOOms 

In order to increase deceleration, it was decided 

20 
CI, 

u) 

0 

0 

rz) 

0 

0 - 

0 

v) 

0 

3 

D 

I 

21 
I I CASE 15 I 

50 - 

= - 2500 psi/sec 

= 1400 psi/sec 

50 -* 

- 

ax =-0.17g 

1 

U' 

WI 

PI 

100 1 

300 

0 

30 7 

8 I 1 

0 I 2 3 4 

Time (sed 

Figure A-12. Antilock Closed Loop Time History for Slow Dump and Reapply 

Rates, High Mu 

33 
i 

I I ,CASE 17 I 

= - 7500 psi/sec 

= 2800 psi/sec 

LREL 

U' 

- 

ax =-.O.ZIg 

loo 1 

50 1 

PI 

I 

6o01 

300 

0 

30 1 

0 I 2 

Time (sed 

-igure A-13. Antilock Closed Loop Time History 

Rates, High Mu 

.3 4 

for Rapid Dump and Reapply 

23 
I 

I40C 

105C 

p reapply 

(psi /sec) 

70C 

35c 

Open Loop lH2I 

QY639' 

2500 5000 7500 1oOoo 

Pdump (psilsec) 

Figure A-14. Effects of Modulator Dump and Reapply Rates on Vehicle Average Deceleration, for 2 Hz Open Loop Command into Modulator, 

High Mu 

24 
1400 

1050 

0 

Pr.apply 

(psi/sec) 

7oc 

.03 

.02 

0 (.OMS) 0 (.OI 55) 0 (.Ol55) 

I I I I 

2500 5000 7500 10000 

bdump (psi/sec) 

Figure A-15. Effects of Modulator Dump and Reapply Rates on Vehicle Average Deceleration, for 5 Hz Open Loop Command into Modulator, 

High Mu 25 
(in the above data) to loins, which is an estimate of the minimum 

practical limit. 

analyses was fixed at lOms, which is probably a typical value for an 

anti 1 ock solenoid. 

Note that the generic modulator delay for all the 

A large variety of pressure rates and toggle shapes were assessed, 

with the faster brake system response, in order to find higher performance 1 eve1 s . 0. OPTIMIZATION OF TOGGLE AND GENERIC MODULATOR 

An extensive, though not exhaustive search for higher performance - 

accompl ished by varying toggle and modulator parameters - resulted in 

a nominal design configuration, defined as follows: 

0 Feedback: Wheel angular acceleration 

0 Dump rate: -3600 psi/sec 

(assumed to have no sensor dynamics) 

0 Reapply rate: 2000 psi/sec 

0 Toggle width: 3.09 

0 Toggle bias: -1.59 

0 Modulator to- caliper delay: 20 msec 

This gave low mu stops of -0.239 at 13 Hz, and high mu stops of -0.549 

at Hz. Subjectively, these were felt to be reasonable performance levels 

for an initial design; these are not intended to imply minimum acceptable 

levels, or maximum attainable levels. 

wheel brake performance levels seen in previous tests (e.g., Ref 9). 

They do not include the effects of aerodynamic drag or rear tire rolling 

resistance, which could account for some of the difference. 

They are somewhat less than single 

In order to assess the degree of optimization, and also to quantify 

the design sensitivity (e.g., oversensitivity to small variations is 

not desirable), the toggle and modulator parameters were varied about 

their nominal values as follows: for the modulator, 

Dump Reapply Rate (psi/s) 

Rate -- 1500 2000( Nom. ) 2500 

(PWS 1 

-3100 X 

-3600( Nom. ) xx X 

-4100 X 

26 
1. 

! 

I 

I 

and for the toggle, 

Bias Width( g) 

-1.0 X 

-1.5 X X X 

-2.0 X 

a --- 2.5 3.0 3.5 

For the modulator variations, the nominal toggle was used, and vice versa 

for the toggle variations. Both high and low mu surfaces were simulated. 

The results of the sensitivity analyses have a1 ready been presented 

in Figs. 10 and 11 of Ref. 2. The corresponding detailed time histories 

are collected in Figs A-16 to A-33. 

CONCLUSIONS AND RECOMMENDATIONS 

. Considering the results of the antilock analyses accomplished to 

date, leads to 

0 

0 

0 

the following conclusions and recommendations: 

Comparisons with full scale test data show the vehicle 

and modulator elements of the simulation to be quite 

accurate. 

acheivabl e, a1 so. 

Wheel angular acceleration feedback provides a feasible single loop feedback design. 

Wheel angular jerk feedback is not desirable as a primary feedback control varibale, in part because it 

results in excessive sensitivity to smal 1 variations 

in vehicle and systems parameters. 

Wheel angular speed feedback may potentially provide 

a feasible control structure, if its low frequency 

characteristics are accounted for. 

1 agged wheel acceleration feedback could provide such 

a system. This would be a high priority area for further 

analyses, and could potentially lead to simplified antilock sensors, fluidic or otherwise. 

Refinement of such accuracy is readily 

EquSvalently, a 

For single loop antilock control, design compromises 

amoung high versus low mu, and deceleration versus 

27 
! 

I 

? 

roughness, appear to be fundamental. 

The combined effects of toggle and modulator design 

parameter values on antilock performance are complex 

and dependent on the shape of the local parameter space. 

They can be quantified by means of computer simulation 

and maps of deceleration and wheel speed roughness. In 

general, percentage changes in toggle parameters have 

re1 atively larger effects than similar percentage changes 

in modulator parameters. 

Net time delay between the modulator and caliper seems 

to be a key design parameter affecting performance and 

stabil ity, and should be analyzed more completely to 

more precisely define fluidic and other antilock design 

requirements. 

A set of controller and modulator characteristics was 

found that gave a reasonable balance amoung performance, 

stability, and stability margin on both high and low mu 

surfaces. 

One way to potentially achieve higher performance and 

stability levels on both high and low mu surfaces could 

involve use of mu dependent, adaptive controller or 

modulator, as may be found on some existing electromechanical antilock systems. 

to provide on all mechanical antilocks, but may be achievable with fluidic systems. 

0 

0 

0 

0 

Such a feature is difficult 

28 
LREL 

I 

0 

IO0 

50 

0 

100 

50 

0 

500 

0 

-500 

600 

CASE 41 I I +dump = -3600 psilsec 1 I -* -3.0~ PIItJPPlY = 2000psi/sec I 

1 

300 

0 I 2 

Time (sed 

3 4 

Figure A-16. Step Brake Time History for Preliminary Antilock Design, 

High Mu Surface 

29 
CASE 45 t 

= - 3600 psi/sec 

= I500 psi/sec A 

I 

LREL 

0 

100 

50 

0 

500 

0 

-500 

600 

300 

0 

30 

I5 

0 

0 

__ 1 I I 

I 2 3 

Time (sec) 

4 

Figure A-17. Time History Showing the Effect of Reduced Reapply Rate, 

High Mu 

30 
I CASE 47 

I- I -3.59 -.bg prropply = 2500 psi/sec I 

LREL 

0 'I 

0- 

too - 

-500 4 

"Ol 

30 - 

I5 - 

0- I I i 1 

0 I 2 3 4 

Time (sec) 

~ 

Figure A-18. Time History Showing the Effect of Increased Reapply Rate, 

High Mu 

31 
LREL 

U' 

"I 

I CASE49 

I dB +dump =- 3100 psi/sec I 

I 

0 

0' 

500 1 

-500 

300 

6oo~ 30 0 1 

0 

I 

Figure A-19. Time 

High 

I. 2 

Time (sed 

History Showing the Effect 

Mu 

3 

of Reduced Dump 

4 

Rate, 

32 
LREL ' ] 

0 

U' 

Wt 

: 

CASE 51 

Pdump = - 4100 psi/sec 

OJ 

I00 1 

30 f 

I5 - 

J 

I I i 

4 0- 

0 I 2 3 

Time (sec) 

Figure A-20. Time History Showing the Effect of Increased Dump Rate, 

High Mu 

33 
! 

I 

LREL 

0 

IO0 

U' 

01 

50 

0 

I00 

50 

0 

500 

0 

-500 

600 

300 

0 

30 

I5 

0 

0 

CASE 53 

eni 1 i)dump = -3600 psi/sec 

-2.5g -5gy Prrap PI = 1500 psi/sec . 

1 1 1 1 

1 2 

Time (sed 

3 4 

Figure A-21. Time History Showing the Effect of Less Negative Toggle 

Bias, High Mu 

34 
I CASE55 I 

-t: Pdump = - 3600 psi/sec -3.50 -.5g Prropply = 2500 psilsec 

I 

I 

LREL 

0 

U' 

WI 

IO0 

50 

0 

too 

50 

0 

500 

0 , 

-500 

600 

PI 300 

0 

0 

I I 1 

I 2 

Time (sec) 

3 4 

Figure A-22. Time History Showing the Effect of More Negative Toggle 

Bias, High Mu 

35 
1 CASE 57 I 

100 - 

50 - 

0 

100 - 

50 - 

0. 

I 

I 

i 

I 

LREL 

0 

U' 

WI 

;I 

PI 

500 

0 

-500 

600 

300 

0 

U I 

Time (sec) 

Figure A-23. Time History Showing the Effect of Narrower Toggle Width, 

High Mu 
LREL 

U’ 

I 

0 

IO0 

50 

0 

100 

50 

0 

500 

0 

-500 

600 

PI 300 

0 

30 

0 

I CASE 59 I I 

0 

7/1 I ~ f;dump =- 4100 psi/sec 

-3.250 -25 g Prrappl y = 2000 psi/sec 

i I I 1 

0 

Figure A-24. 

.I 2 3 

Time (sed 

Time History Showing the Effect of Wider Toggle Width, 

High Mu 

37 

4 
LREL 

0 

100 - 

U' 

WI 

i 

I 

.' 

CASE 44 I 

Pdump = - 3600 psilsec -t: -3.Og PW3DPlY = 2000 psi/sec 

0 

50 

'O01 

300 

0 I

301 

0 i 1 

0 I i 3 4 

Time (sed 

I5t/ , 

Figure A-25. Step Brake Time History for Preliminary Antilock Design, 

Low Mu 

38 
I CASE46 I 

= I 500 psi/sec I I-' I -2.50 3 0 Preaml Y 

I 

LREL 

0 

U' 

WI 

I 

I 

Figure A-26. Time History Showing the Effect of Reduced Reapply Rate, 

Low Mu 

39 
! 

I 

LREL 

U' 

I CASE 48 I 

4-i I - 

bdurnp =-3600 psi/sec 

-3a -30 Prropply = 2500 psi/sec 

I 

0 

0 

0' 

500 

0 

-500 

600 

PI 300 

Time (sed 

Figure A-27. Time History Showing the Effect of Increased Reapply Rate, 

Low Mu 

40 
I 

i 

I 

LREL 

! 

0 

I00 

50 

0 

I00 

50 

0 

500 1 

CASE 50 

-2.750 -.25g Praapplr - 2000 psi/sec 

Time (sec) 

Figure A-28. Time History Showing the Effect of Reduced Dump Rate, 

Low Mu 

41 
I I CASE 52 I 

50 - 

! 

! 

! 

LREL 

u' 

'. WI 

i 

7 

= - 4100 psi/sec 

= 2000 psi/sec 

I 

0 

500 

-500 OI 

Figure A-29. Time History Showing the Effect of Increased Dump Rate, 

Low Mu 

42 
I I CASE 54 I 

, 

a 

t 

LREL 

bdum) = - 3600 psi/sec 

-2.59 39 Prrapplr = I500 psiIsec 0 

100 

50 

0 

100 

50 

0 

500 

0 

-500 

600 

300 

0 

30 

I5 

I 

- I I 1 

I 2 

Time (sed 

3 4 

Figure A-30. Time History Showing the Effect of Less Negative Toggle 

Bias, Low Mu I 

43 
I CASE 56 

Pdump = - 3600 psi/sec 

LREL 

U' 

, 

I 

0 

OJ 

0- 

500 1 

-500 4 

Figure A-31. Time History Showing the Effect of More Negative Toggle 

Bias, Low Mu 

44 
LREL 

U' 

I CASE 58 I 

I 

0 

IO0 

50 

0 

100 

50 

0 

500 

-500 

600 

0 I 2 

Time (sec) 

3 4 

Figure A-32. Time History Showing the Effect of Narrower Toggle Width, 

Low Mu 

45 
'I 

LREL 

U' 

0 

IO0 

50 

0 

too 

50 

0 

500 

0 

-500 

600 

PI 300 

0 

I I I 1 

0 I .2 

Time (sed 

3 4 

Figure A-33. Time History Showing the Effect of Wider Toggle Width, 

Low Mu 

46 
REFERENCES 

* 

i 

i 

1. "Generic Modulator Analysis and Preliminary Antilock Design," 

Contract RE 182/351, between Jet Propulsion Laboratory and 

Dynamic Research, Inc. , January 1985. 

2. Zellner, J. W., and Chiang, D. P., 

Antilock Brake Design," presented at the 10th Experimental Safety 

Vehicle Conference, Oxford, England, July, 1985. 

A Feedback Control Method for 

3. "Critical Review of Report DOT-HS-802-288, Towards a Low Cost 

Highly Re1 iable Anti-Lock Brake System for Small Motorcycles," 

Dynamic Research, Inc. Technical Memorandum 82-7, Sept., 1982. 

4. "Documentation for Digital Simulation of Motorcycle Braking," 

Dynamic Research, Inc. Technical Memorandum 83-2, March, 1983. 

5. "Preliminary Analysis of Motorcycle Antilock Dynamics,'' Dynamic 

Research , Inc. Techni cal Memorandum 83-4, Apri 1 , 1983. 

6. "Analysis and Preliminary Design of a Motorcycle Antilock Brake 

System," Dynamic Research, Inc. Technical Memorandum 83-5, May, 1983. 

7. Zellner, J., "An Analytical Approach to Antilock Brake System 

Design," SAE Paper No. 840249, presented at the SAE Congress and 

Exposition, Detroit, MI, Feb. 1984. 

Test Report on Motorcycle with Antiskid Brake System, Japan 

Automobile Manufacturers Association, Inc. , Motorcycle Brake 

Working Group, Jan., 1978. 

8. 

9. Zellner, J., and White, M., Advanced Motorcycle Brake Systems, 

Fi nal Report , DOT-HS-806-095, Nov. 1981. 

47 
, 

i 

! 

! 

APPEND I X 

GENERIC MODULATOR SUBROUTINE LISTING 

This appendix presents the listing of the FORTRAN source code for 

the subroutine 'MOD.' This provides for linear pressure dump and reapply 

rates,irigerred by the appropriate signal from the toggle. 

for upper and lower limits on pressure (namely, applied pressure and zero 

pressure). As shown, the listing is self documenting, and is meant to 

replace the corresponding subroutine describing the Mitsubishi modulator 

in the digital simulation program, 'CYCLE2.I 

It also provides 
SUBROUTINE MOD (P1) 

LOGICAL LREL,LBL,LVALR,LVALB,LFLAG 

LOGICAL LSVALR (30) ,LSVALB (301 

INTEGER KK 

C 

C 

C ROUTINE WILL DETERMINE THE MODULATED PRESSURE 

C TO THE WHEEL CYLINDER IF ANTI-LOCK IS NEEDED 

C 

C INWT/OUTPUT COMWNS: 

C 

COMMON/CTRL/LREL,LB~IREL~IBL 

COMMON/ALBVAR/PD (2) 

COMMON/DELVAR/TDl,XT,IDZ 

COPmON/VAR/V (14) 

EQUIVALENCE (PSI 1, W (13) 1 

C 

C 

C LSVALR=STORAGE LOGIC VARIABLE OF RELEASE VALVE 

C LSVALB=STORAGE LOGIC VARIABLE OF BUILD VALVE 

C LVALR=DELAYED LOGIC VARIABLE OF RELEASE VALVE 

C LVALB=DELAYED LOGIC VARIABLE OF BUILD VALVE 

C 

c----------------------------------------------------- 

C 

C 

C 

C 

C 

C 

C 

C 

2110 

C 

C 

c 

C 

C 

C 

CHECK MODULATOR STATE 

IREL = 0 

IBL = 0 

IF (LREL) IREL=l 

IF(LBL1 IBL = 1 

DRAY OF CONTROLLER COMMANDS TO VALVES 

TDZ-0.01 

KK-INT (30.- (TDZ/XT) 1 

LSVALf? (30) =LREL 

LSVALB (30) =LBL 

DO 2110 I=l,Z9 

LSVALR ( I) =LSVALR ( I+ 1) 

LSVALB(1) =LSWALB (I+l) 

CONTINUE 

LVALR=LSVALR (KK) 

LVALB=LSVALB (KK) 

DETERMINE RELEAS OR BUILT RATE 

PDI = 0.0 

IF(LVALR1 PDI = PD(1) 

IFtLVALB) PDI = PD(2) 

IF( (.NOT.LVALR) .AND. (.NOT.LVALB)) GO TO 2900 

49 
B 

‘D 

i 

i 

1 

C 

C 

C 

C 

2900 

2999 

500 

C 

CALCULATE MODULATED PRESSURE 

PSIl = PSIl + (PDI*XT) 

IF(PSI1 o6T. P1) PSIl Pi 

IF(PSI1 .LT. 00) PSIl = 0. 

GO TO 2999 

PSIl = P1 

WRITE(6,500) KK,IREL,IBL,PDI,Pl,PSIl 

FORMAT(lX,312,3Fl2.4) 

RETURN 

END 

50