Extremwertsimulation eines Reglers für blockierungsfreies Bremsen auf dem Hybriden Präzisionsanalogrechner RA 770

Complete English translation of the original German-language document (15 pages).

AEG DATENVERARBEITUNG — Analog Computers and Hybrid Systems

Armin Coinaud, Peter Maier

Simulation of an Electronic Brake Controller for Lockup-Free Braking on the Hybrid Precision Analog Computer RA 770

Armin Coinaud is employed at the company TELEX, Heidelberg. Peter Maier is employed at the company AEG-TELEFUNKEN, Konstanz.

	Section	Page
1.	Introduction	1
2.	Operating Principle of the Brake Controller	2
3.1.	Simulation of the Braking Process	4
3.2.	Structure of the Simulation	4
3.3.	Input of the Controller	6
3.4.	Simulated Portion of the Controller	8
4.	Sequence of the Simulation Run	7
	Literature	11

1. INTRODUCTION

On the roads of the Federal Republic of Germany, there has been a marked increase in road traffic over recent years, with correspondingly greater numbers of accidents. The trend toward higher vehicle speeds combined with greater traffic density increases the risk of collision at every moment. This risk can be reduced substantially through improvements in the quality of braking systems.

The Bosch company has already developed, in collaboration with the Teldix company, an electronic anti-lock brake controller (ABS). This device regulates the braking process in such a way that the wheels never lock completely.

If a wheel locks while braking, three undesirable effects arise:

The vehicle cannot be steered.
The braking distance becomes longer.
The vehicle may skid.

2. OPERATING PRINCIPLE OF THE BRAKE CONTROLLER

The brake controller makes use of a hydraulic actuating element (modulator) to control the brake pressure at each individual wheel. The modulator is capable of both increasing and decreasing the brake pressure. This makes it possible at each instant to set the brake force — and thus the braking deceleration — to the highest practicable value.

In a conventional braking process, the driver applies the brake pedal with a force that remains roughly constant throughout. The modulator then ensures that at each wheel, the brake pressure never exceeds the value at which the wheel would lock.

The controller operates with a great degree of “overshooting” — at each instant the controller is at the limit between braking and locking, and continuously readjusts itself to the current conditions. This can also be called adaptive control.

3. SIMULATION OF THE BRAKING PROCESS

For the long-term development of the electronic brake controller, the use of the hybrid precision analog computer RA 770 is found to be advantageous, since it allows both the analysis of the controller equations and the optimization of the controller parameters. No less important is the ability to perform realtime simulation, which is the principal tool for demonstrating the function of the controller.

In the preliminary simulation runs, the controller circuit is reproduced completely, meaning:

a) as a complete, self-contained electronic braking controller,

b) the electronic braking controller of the Teldix company,

c) a driver element and a load distribution amplifier as a simulator of the dynamic braking process of each individual wheel, and

d) the display unit and the loading simulator of the RA 770 hybrid computer for displaying and evaluating the results.

During the simulation, several physical quantities of the controller are provided in part by analog quantities and in part by digital quantities. As a result, the interface between analog and digital portions represents an essential part of the simulation.

The purpose of the analog computer simulation is to perform comprehensive, carefully planned, and thorough tests of the controller, as well as optimization toward the goal of digitizing the analog computer.

3.2. Structure of the Simulation

At the current first phase of the controller development, the simulation on the RA 770 analog computer is carried out such that the controller equations are set up on the analog machine as circuits that are then simulated. There are no digital components at this stage. The simulation includes several essential portions of the controller:

a) A complete, self-contained circuit diagram of the electronic brake controller,

b) The hydraulic braking force generator for each wheel,

c) The driver element and the load distribution circuit,

d) A circuit element for the tire-road adhesion characteristics for each wheel, and

e) A display unit including the data presentation and the documentation of the simulation results.

The description covers the following essential characteristics of the controller:

The logical switching between the various control phases (valve control, vehicle deceleration, slip detection).

[Page 6: Photograph]

Figure 1 — Hybrid Precision Analog Computer RA 770 with Digital Unit (Photo: AEG-TELEFUNKEN)

3.3. Input of the Controller

The following description first covers only the initial phase of the controller development, and from that point focuses on the analog computer circuit for simulating the braking process, particularly the electronic braking controller. No digital components are used at this stage.

The simulation on the analog machine is set up as a block-schematic diagram. The inputs to the controller consist of the following quantities:

a) A complete self-contained circuit of the electronic braking controller,

b) The hydraulic braking force generator as a simulator of the dynamic braking process for each wheel,

c) The driver element and the load distribution circuit,

d) A circuit element for tire-road adhesion characteristics, and

e) The display and data acquisition unit.

The accuracy of the mechanical quantities is very great. At the same time there is a high degree of flexibility in the analog computer since modifications can be made easily by setting potentiometers and changing connections without major effort.

[Page 8: Block Diagram]

Figure 2 — Schematic block diagram of the electronic brake controller circuit and the vehicle dynamics model on the analog computer

Caption labels visible in the diagram:

Einflüsse des Fahrwegs — Influences of the road surface
Dynamisches Verhalten des Fahrzeugs und auf dem Analogrechner simulierte Schaltkreise — Dynamic behavior of the vehicle and circuits simulated on the analog computer

3.4. Simulated Portion of the Controller

At the simulated portion of the controller on the RA 770 analog computer, it is apparent that the accuracy of the controller is very high. The controller equations are reproduced on the analog computer as electronic circuits that are then simulated. In this way, a comprehensive analysis and optimization of the controller becomes possible.

The analog computer simulates the following:

The vehicle velocity v_F and the target velocity based on control criteria,
The dynamic braking process for each wheel,
The tire-road adhesion characteristics as a function of vehicle velocity and braking force,
The electronic braking controller and its switching logic, and
The display and data acquisition unit for evaluating the simulation results.

The advantage of the analog computer over a digital computer for this task is the greater flexibility — modifications can be implemented by simple potentiometer adjustments and patch-panel changes, and this can be done much more quickly than making changes to a digital program. Furthermore, the analog computer provides a real-time simulation that allows direct testing of the actual electronic braking controller hardware.

4. SEQUENCE OF THE SIMULATION RUN

The following block diagram (Figure 3) shows, at the level of the overview diagram, the simulation procedure for the controller and the interconnection structures. The controller inputs are applied from the left side of the diagram.

[Page 10: Block Diagram]

Figure 3 — Block diagram of the analog computer circuit for one wheel

The block diagram contains the following functional elements:

Sollwert-Vorgabe (Setpoint specification)
Reifenverhalten (Tire behavior)
Bremsanlage (Braking system)
Hydraulik (Hydraulics)
Regel-Algorithmus (Control algorithm)
Bewertung des Bremssignals (Evaluation of the braking signal)
Ansteuerung der Bremsanlage (Activation of the braking system)
Dynamik des Fahrzeugs (Vehicle dynamics)
V_FZ (Vehicle velocity)

Variable Designations

Symbol	Meaning
p_VZ	Pressure in the master brake cylinder
p_RB	Pressure in the rear brake circuit
μ_GN	Dynamic coefficient of friction of the tire, dependent on road surface conditions; derived from the braking force
μ_GN = μ (p_BA, p_Reifenart)	Coefficient of friction as a function of brake pressure and tire type
V_FA	Initial vehicle velocity or target velocity at the start of braking
V_R = V_FZ · (1 − λ)	Peripheral wheel velocity, a function of vehicle velocity and slip
λ = 1 − (V_R / V_FZ)	Braking slip
c_p	Brake coefficient, expressing the ratio of braking force between maximum and optimum slip; used as a measure for the Teldix-Brake safety; for the target velocity, slip, tire type, and vehicle speed
W_Dyn	Dynamic moment of inertia of the braking process
M_F	Mass of the vehicle

In the sub-routine “Phase,” the following analog quantities are converted: the setpoint V_FA and the “setpoint” V_FZ quantities. Using these quantities, the slip control is activated and the synchronous brake simulation begins. The result may then be read off the analog computer display.

The braking force coefficient μ_GN is a function of the tire behavior and depends on the dynamic load of the brakes and the tire-road conditions. The dynamic slip coefficient K_Dyn (Figure 4, left curve) takes on a maximum value and then decreases. From the display unit (Figure 4, left), one can observe the braking force coefficient as a function of slip.

The dynamic simulation shows that the largest braking moment occurs at a value of slip of approximately 20 percent. The braking process runs as follows: at the start of braking, the coefficient of friction rises to a maximum with increasing slip. The maximum coefficient of friction corresponds to the optimum slip value λ_opt. Above this slip value, the braking force decreases; the tire then tends toward lockup. The electronic brake controller is designed to keep the slip near the optimum value.

[Page 12: Graph]

Figure 4 — Braking force coefficient as a function of braking slip

Curve I: Braking force coefficient without control
Curve II: Braking force coefficient with control
Axis labels: horizontal = λ (slip, %), vertical = μ_GN (braking force coefficient)

As shown by Figure 4, the qualitative behavior of the vehicle dynamics at a preliminary simulated velocity of 100 km/h on an optimal adhesion surface (Bremsschlupf λ_opt), the controller holds the braking force coefficient near its maximum value. The tire slip is monitored and the vehicle deceleration and braking distance are optimized accordingly.

The control brings a significant improvement — the braking distance is substantially reduced and the vehicle remains steerable throughout the braking event. At an initial velocity of 100 km/h with optimum control the braking distance is reduced by approximately 10% compared to uncontrolled braking.

The vehicle velocity and braking distance as functions of time are shown in Figure 5. Additional simulation runs provide, among other results, characteristic data for the braking performance as a function of initial velocity and surface conditions.

[Page 13: Graph]

Figure 5 — Vehicle velocity and braking distance as a function of time

The graph shows vehicle velocity (V_F) and braking distance as a function of time for an initial velocity of 100 km/h with and without braking regulation.

Footnote: The RA 770 can also be coupled via an interface to a digital computer.

[Page 14: Two Graphs]

Figure 6a — Vehicle velocity vs. braking — braking at initial velocity of 100 km/h on different surfaces — with and without braking control

Figure 6b — Vehicle velocity vs. braking — braking at initial velocity of 100 km/h with and without braking control — different surface conditions

Caption for both figures: “Variation of vehicle velocity as a function of braking at an initial velocity of 100 km/h with and without electronic braking control”

LITERATURE

[1] Electronic Brake Controller for Hydraulically Actuated Vehicles, TDI 1088, TELEFUNKEN Technical Communications, July 1968, p. 2–14 and ATZ 1969, No. 11, p. 1, 2

[2] H. Leiber, G. Lampert — The Electronic Brake Controller. TELEFUNKEN Technical Communications, July 1969, p. 2–18 and ATZ 1969, No. 11

[3] H. Glos, G. Kaufmann, K. Kaufmann — Der Präzisions-Analogrechner RA 5000. TELEFUNKEN-Zeitung Jg. 44, Heft 1, 2, 125–131

[4] R. Schwarz — Experiences with the Hybrid Precision Analog Computer RA 770. TELEFUNKEN-Zeitung Jg. 44 (1971), p. 19–49

[5] R. Nibs — Simulation of an Electronic Brake Controller with the TELEFUNKEN Precision Analog Computer. ATZ 1969, p. 329 (Part II) and No. 11 (Part II)