ABS Prof. R.G. Longoria Spring 2002 v. 1
ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
Anti-lock Braking Systems • These systems monitor operating conditions and modify the applied braking torque by modulating the brake pressure. • The systems try to keep tire operating within a desired range of “skid”, and by preventing wheel lock-up during braking they can help retain steerability and stability • Anti-lock braking systems are closed loop control systems within the braking system. ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
Desired Range of Slip or Skid Wong (1993)
Bosch (1999)
Trying to control slip in a ‘desirable range’ is complicated by changing road conditions.
ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
Background • Concept dates back to early 1900s, and first patent went to Bosch in 1936. • Concept is now well established.
Figures from Gillespie (1992)
ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
Some ABS Requirements Adapted from Bosch (1999) • Maintain steering response at all times, regardless of road conditions • Adapt to and exploit available friction to maximum effect, but put emphasis on stability and steering rather than stopping distance, independent of how driver applies pedal force • Effective over large speed range (walking speed) • Control yaw effect in split-µ conditions • Self-diagnostics ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
ABS Closed-Loop Concept Controlled Variables: wheel-speed and data measured from wheel (3)
Controller: wheelspeed sensors and ABS unit (4)
Manipulated Variable: brake pressure (1-3)
Reference input: pressure applied to brake pedal (2)
Disturbance: roadsurface conditions, brake condition, vehicle load and tire characteristics
Controlled system: vehicle with wheel brakes, wheels and friction between tires and road surface Bosch (1999)
ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
Ideal Braking Concept Ref. Bosch Idealized concept: nondriven wheel, 1/4 mass of vehicle, stable and unstable regions.
Applied braking torque builds up linearly over time. Road surface torque lags slightly, and reaches maximum (saturates). Note that the torque differential can provide a measure of wheel acceleration. The opposing response is a good indicator of conditions at tire.
ME 379M/397 Vehicle System Dynamics and Control
200
ms
Department of Mechanical Engineering The University of Texas at Austin
Control Issues • Wheel-speed sensors must be used to find – wheel peripheral deceleration/acceleration – brake slip – reference speed and vehicle deceleration
• It is not practical to use wheel acceleration or deceleration or the slip as the controlled variable. • How can this information be used? ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
Estimation of Reference Speed • Since vehicle speed can not be measured directly, the ECU must estimate an appropriate value. • The Bosch ABS system, for example, uses information from “diagonal” wheels, and bases an estimate on information obtained during non-ABS usage. • Under moderate braking, the ECU will estimate reference speed based on the diagonal wheel that is turning the fastest. • During panic stops, a ramp-shaped extrapolation of the speed collected at the start of the cycle is used to calculate the reference speed. ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
Some Example Ways for Predicting Lock-up
Wong (1993)
•
Anti-locking may be initiated when the product of angular acceleration of the tire and its rolling radius exceeds a predetermined value (e.g., 1 to 1.6 g).
•
Passenger car ABS may have a track-and-hold circuit that stores any wheel acceleration values of 1.6 g and higher. If the measured angular speed drops 5% during a predetermined time (e.g., 140 ms), and if the vehicle acceleration as measured by an accelerometer is not higher than, say, 0.5 g, then the tire is considered to be at the point of locking, and the brake is released when angular speed decreases by 15% of stored value.
•
If the vehicle deceleration is greater than 0.5 g, locking is predicted and brake is released when angular speed decreases by 15% of stored value.
ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
Some Example Ways for Reapplying Pressure Wong (1993) • As soon as none of the conditions discussed for ‘decreasing’ pressure at the brake are met, reapply the brake. • Use some hysteresis; that is, wait a fixed amount of time before reapplying pressure. • In some systems, the brake is reapplied as soon as the product of the angular acceleration of the tire and the rolling radius exceeds a predetermined value. Some typical values are 2.2 to 3 g, and sometimes the ‘build-up’ rate may depend on actual value of acceleration. ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
Two-Position or On-Off Controllers In a two-position control system, the actuating element can take on only two positions, and often this is either on or off. This is a very common and inexpensive way to control systems. For example, a level controller can be built this way, as shown below. A simple two-position controller could follow the basic rule,
M1 m(t ) = M 2
e(t ) > 0 e(t ) < 0
Ogata (1978)
Ogata (1978) ME 379M/397 Vehicle System Dynamics and Control
While the controller is in a given position, the system may behave linearly, however on-off controllers are classified as nonlinear because they are not amenable to classical linear control design methods. Department of Mechanical Engineering The University of Texas at Austin
On-Off Controller Issues Sometimes, an on-off controller may have some hysteresis, and the range that the error signal must go through before actuating either way is called the differential gap. This hysteresis may be unintentional (caused by friction or gap in the mechanism), or it may be intended. One reason to purposefully include hysteresis in an on-off controller is to ‘slow down’ the switching between the two-states. Switching too often can lead to reduced life in the control actuating element. A differential gap, however, will cause the output to have some oscillations, the amplitude of which can be reduced by decreasing the gap. ME 379M/397 Vehicle System Dynamics and Control
Ogata (1978)
Typical oscillations, as induced by on-off control of tank level. Department of Mechanical Engineering The University of Texas at Austin
Bang-Bang Control The ‘bang-bang’ principle of control says that a system being operated under limited power can be moved from one state to another in the shorted time possible by at all time utilizing all available power. This was hypothesized and proven experimentally and theoretically long ago. Not all bang-bang implementation guarantee time-optimal control, of course, but for certain systems this is the case. For, With the input,
Y b G (s) = = U an s n + an −1s n −1 + " + a0
−uo ≤ u ≤ uo
It can be proved that bang-bang gives time-optimal control, and you can reach a desired state in at most n-1 switches. ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
Example Operation Heavy Vehicle with Pneumatic Brakes (Wong, 1993)
This figure shows results for a heavy vehicle braking on wet pavement. The cycle of reducing and restoring pressure can be repeated from 5 to 16 times per second. The ABS operation is usually deactivated once the vehicle slows to about 2 or 3 mph.
ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
Wheel-speed Sensors The wheel-speed sensor's pole pin with its external winding is located directly above the sensor ring, which is a type of pulse rotor joined directly to the wheel hub (the wheel-speed sensor is also installed in the differential in some applications). The pole pin is connected to a permanent magnet producing an electrical field that extends outward to the sensor ring.
May generate 90 to 100 pulsed per wheel revolution.
Bosch (1999)
As the ring turns, the pole pin is exposed to an alternating progression of teeth and gaps. This results in the magnetic field changing continuously so that a voltage is generated in the sensor's winding, the frequency of which provides a precise index of the current wheel speed.
ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
Pressure Modulator The hydraulic pressure modulator contains an accumulator, return pump, and solenoid valve.
ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
Brake-Pressure Modulation Bosch (1999) Hold pressure Pressure buildup
Reduce pressure
•Pressure decrease at appropriate wheel •Pressure hold •Pressure increase ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
Typical ABS Control Cycle Not your ‘basic’ on-off control! •This figure shows cycling on a high traction surface. •Monitoring ‘peripheral acceleration’. •The reference speed is used to determine the slip switching threshold. •Pressure is dropped as long as peripheral acceleration is below threshold. •Increases in acceleration will lead to pressure build-up, but there are ‘gaps’ where system waits.
hold
‘Maintain pressure’ ME 379M/397 Vehicle System Dynamics and Control
Bosch (1999)
Department of Mechanical Engineering The University of Texas at Austin
Modeling the ABS System • • • • •
Vehicle dynamics and base brake system Wheel speed sensors Hydraulic modulator and valves Control Module (all logic, diagnostics) Other: pedal travel and switch, accelerometers, accumulator and electric priming
ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
ABS Block Diagram Td −
Tt
−
+ +
wheel
T
Gw
DRAFT
Loads
ωw
Tire & vehicle
Tb
Gb ABS and brake actuation
ECU 1
Sensor
vx
Vehicle speed estimation
sr or λr
ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
MathWorks ABS Simulation ABS Braking Model
100
0.2
1 s
TB.s+1 Desired relative slip
Bang-bang controll er
Kf
Brake pressure
Hydraul ic Lag
1/I
brake torque
Force & torque
tire torque
ctrl -Kmu-slip friction curve
Weight
-1/m
slp
Explain
Wheel Speed 1/Rr
Rr
Ff
1 s
Mux
yout
Vehicle speed (angular)
1 s
STOP 1 s
Vehicle speed
Stopping distance
1.0 - u(1)/(u(2) + (u(2)==0)*eps)
ωw Developed by Larry Mi chaels ωv The MathWorks, Inc Open function: ‘runabs’ PreLoadFcn = ‘absdata’ (in a Simulink model, you set this using set_param( ) on MATLAB command line. Relative Sli p
Double cl ick to run model and pl ot the results
ME 379M/397 Vehicle System Dynamics and Control
1−
Department of Mechanical Engineering The University of Texas at Austin
ABS Simulation Results Vehicle speed and wheel speed
Speed(rad/sec)
80
60
Vehicle speed (ωv)
mu-slip curve 1
40
0.9 0.8
20
Wheel speed (ωw)
0.7 0.6
0 0
5
10
15
Time(secs) Slip Normalized Relative Slip
1
µ
0.5 0.4 0.3
0.8
0.2 0.1
0.6
0 0.4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
slip
0.2
0 0
5
10
15
Note: should also show stopping distance plot!
Time(secs)
ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
ABS Simulation Results Vehicle speed and wheel speed
Lower µ surface
Speed(rad/sec)
80
Vehicle speed (ωv)
60
mu-slip curve 1
40
0.9
Wheel speed (ωw)
0.8
20
0.7 0.6
0 0
5
10
15
20
25
Time(secs) Slip
µ
1
Normalized Relative Slip
0.5
0.8
0.4 0.3 0.2 0.1
0.6 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
slip
0.4
0.2
0 0
5
10
15
20
Time(secs) ME 379M/397 Vehicle System Dynamics and Control
25
Department of Mechanical Engineering The University of Texas at Austin
ABS Simulation Results Stopping Distance
Use the simulation model to examine 3 different cases, with the last one the lower m case with no ABS. This demonstrates the basic advantage of ABS.
1400 No ABS lower mu 1200 Lower mu with ABS
1000
800 c e s, e mi T
Higher mu with ABS
600
400
200
0
0
5
10
15
20
25
Distance, m
ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
Other Examples Ulsoy and Peng (1997)
• Many articles in the literature • Linear ABS controller (example 8.4) – – – –
using linearized model of basic braking model (no actuator) integral (error in slip) plus state feedback (both states, proportional) poor performance, even for linearized system not practical to assume you will know µ-slip curve, and there will be many other uncertainties in parameters
• Nonlinear controller (example 8.5) – rule-based, or look-up table to give torque change needed to achieve desired result – very hard to tune, calibrate, etc – difficult to give any guarantee on performance or stability ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
Driven vs. Non-Driven Wheels There is a significant difference in applying ABS on non-driven versus driven wheels. The deceleration/acceleration rates for the nondriven wheel are generally a good indication that you may be inducing wheel lock. The engine will act on the driven wheels , resulting in extra moment of inertia coupled into the wheels, and they will react as if they are ‘heavier’. This means that the ‘peripheral’ deceleration rates may not exhibit the same sensitivity to entering the unstable region, an event that precedes lockup. Use bond graph to explain inertia coupling in driven wheel ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
Summary • • • •
How can you model this in a simple way? In the end, how good are model predictions? Will you always have to test and tune? There exist very good solutions, there are many open questions, and what goes into production is usually proprietary. • How well can you quantify reliable operation?
ME 379M/397 Vehicle System Dynamics and Control
Department of Mechanical Engineering The University of Texas at Austin
