Control of an Electromechanical Brake for Automotive Brake-By-Wire Systems … · 2014-01-07 · Control of an Electromechanical Brake for Automotive Brake-By-Wire Systems with an

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SAE TECHNICALPAPER SERIES 2004-01-2050

Control of an Electromechanical Brake forAutomotive Brake-By-Wire Systems with an

Adapted Motion Control Architecture

Chris Line, Chris Manzie and Malcolm GoodThe University of Melbourne

Reprinted From: Proceedings of the 2004 SAE AutomotiveDynamics, Stability & Controls Conference

(P-386)

SAE Automotive Dynamics, Stability &Controls Conference and Exhibition

May 4-6, 2004Detroit, Michigan

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ABSTRACT

A disk brake clamp force controller for electromechanical brakes (EMB) in automotive brake-by-wire systems may be obtained from a standard motion control architecture with cascaded position, speed and current control loops by replacing the outer position control loop with a force control loop. When implemented with proportional, integral and differential (PID) controllers this architecture generally performs well for standard motion control problems, but the EMB control problem is differentiated by a large operating range in which non-linear load disturbances such as friction become significant at high clamp forces of up to 30kN. This paper investigates the feasibility of a cascaded PI control architecture for an EMB with the intention of establishing a baseline standard against which the performance of future control schemes may be compared. Simulation results are presented based on an accepted EMB model.

INTRODUCTION

Borrowed from the idea of fly-by-wire and applied within the automotive industry, the concept of drive-by-wire is to replace all mechanical linkages between the driver and vehicle with electronic systems. The benefits of drive-by-wire include component reduction, weight reduction, potential for improved vehicle performance, increased cabin space, removal of the steering column, ergonomic and crash compatible mounting of controls, complete access to vehicle dynamics control, ‘plug, play and bolt’ modularity, software upgrading, and potential for better fuel economy. To realize the full benefits of drive-by-wire requires the electronic integration of the three primary vehicle control systems, throttle, steering and braking. Of these it is the latter, brake-by-wire, that is the subject of this paper.

Currently there are two implementations of brake-by-wire with disc brake calipers and these are differentiated by their mode of actuation. While one system uses electromechanical brakes the other retains current hydraulic brakes in an adapted electrohydraulic system. Because they only require some modification of an existing system, electrohydraulic brakes are considered the first approach to brake-by-wire [1]. With proportional valves, electrohydraulic brake systems have greater resolution in brake pressure levels than standard hydraulic

systems. The other characteristic that determines brake performance is the rate at which an actuator can generate and dissipate brake pressure at the disc brake caliper. Typically hydraulic systems perform well for high load applications, but an alternative is offered by electromechanical brakes that have high resolution in caliper clamp force levels as well as the potential for high brake force apply and release rates.

A number of patents exist for different electromechanical brake designs. From a survey of EMB patents held by the United States Patent and Trademark Office two categories were identified, these being electromechanical drum brakes and electromechanical disk brakes. While drum brakes can exhibit the phenomenon of self-energisation, this introduces a non-linear brake characteristic. Further, drum brakes have less heat resistance to thermal loads [2]. It is partly for these reasons that electromechanical disk brakes are being pursued more vigorously.

From patent designs of the EMB disk brake calipers [3-15] four features were identified as being common. Most EMBs have an electric motor drive, some reduction gearing that converts rotational to translational motion, a floating disc brake caliper with brake pads and some physical and communications interface with the vehicle. Running on a 42 volt direct current (DC) power supply [16] and using a safety critical time triggered communication protocol, the EMB receives brake instructions from the central vehicle dynamics controller via an in-vehicle network. These instructions command either brake torque, brake clamp force, or a particular mode of operation such as standby, off, or anti-lock braking. For the purposes of this paper it is assumed that a desired brake clamp force has been requested by the vehicle dynamics controller and the focus is on delivery of this command from the local EMB controller. It is here that the control problem for electromechanical brake actuators is introduced. A controller is required to drive the EMB and respond as best as possible to brake commands from the vehicle dynamics controller.

Control of a servo motor is a standard problem for linear motion systems. A common solution is to implement a motion control architecture with cascaded position, speed and current control loops. This architecture may be adapted to control the EMB brake clamp force by replacing the outer position control loop with a force control loop as shown in Figure 1.

2004-01-2050

Control of an Electromechanical Brake for Automotive Brake-By-Wire Systems with an Adapted Motion

Control Architecture Chris Line, Chris Manzie and Malcolm Good

The University of Melbourne

Copyright © 2004 SAE International


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Figure 1: EMB brake clamp force control architecture with cascaded force (FC), motor velocity (VC) and motor current

(CC) control loops

Although brake torque control is preferred for management of vehicle dynamics, brake clamp force is instead chosen as the control variable because robust measurements are available from a force sensor embedded in the EMB. For control of vehicle dynamics it is then possible to use the brake clamp force to estimate the brake torque.

The cascaded control architecture shown in Figure 1 requires feedback measurements of motor current, motor speed and caliper clamp force. Typically, these are available from Hall current sensors on the motor, a motor position resolver or encoder, and a load cell or strain gauge configuration on the EMB to measure the caliper clamp force. While Schwarz et al. proposed a clamp force estimation scheme that used the remaining current and position sensors [17], the issue of sensor reduction is not investigated in this paper.

Although cascaded control architectures generally perform well for standard motion control problems, the EMB control problem is differentiated by a large operating range of between 0 and 30 kN for a full brake apply. At higher clamp forces non-linearity is introduced by a load dependent component of the Coulomb friction. Further non-linearities exist due to the non-linear caliper stiffness and saturations of the power supply voltage, safe motor current limits and the maximum motor speed. Given these considerations it is not immediately obvious how well a controller with cascaded force, velocity and current loops will perform. In an attempt to address this potential shortcoming, an investigation was undertaken to assess the feasibility of a cascaded PI control architecture for an EMB.

Having an architecture with brake clamp force control rather than position control is acceptable during brake apply. During standby however, position control is required to manage the air gap between the brake pads and brake rotor. Both modes of operation are achieved by switching between outer position and force control loops across the contact point between the brake pads and disc brake rotor.

This paper is structured beginning with nomenclature and a description of the EMB simulation model that was developed and validated for the purposes of simulation and controller design. This is followed with a definition of the control problem and statement of typical performance requirements for the EMB. The design of the controller is then detailed and results presented to indicate its performance. This leads to discussion of the results and concluding remarks.

NOMENCLATURE

The following symbols are used throughout this paper. α = load dependency of Coulomb friction (Nm/N) Fcl

∗F = caliper clamp force (N)

cl = caliper clamp force set-point command (N) I = controller integral gain im

∗i = motor current (A)

mJ

= motor current set-point command (A) = system inertia lumped at motor axis (kgm2)

Kb

K = back EMF coefficient (Vs/rad)

c

K = lumped stiffness of system (N/m)

t

L = motor torque constant (Nm/A)

mN

= motor inductance (H) = gear ratio (m/rad)

P = controller proportional gain ϕm = motor position (rad)

mR = motor resistance (Ω)

CT = torque due to Coulomb friction (Nm)

ET = applied external torque (Nm)

FT = torque due to friction (Nm)

mT = motor torque (Nm)

ST = torque due to stiction (Nm)

VT = coefficient of viscous friction (Nms)

0T = constant Coulomb friction offset (Nm)

mω = motor velocity (rad/s) ∗mω = motor velocity set-point command (rad/s)

sω = Stribeck velocity (rad/s)

spx = caliper spindle position (m) MODELLING AND SIMULATION

In the first instance an EMB model was developed and validated against test data for the purposes of simulation and controller development. Previous models from Maron et al. and Schwarz et al. were used as a basis for developing the EMB model [17-19]. Using their approach the model was simplified by lumping the system inertias, stiffnesses, and damping. Their simplified brake model was modified to include the motor dynamics with back electromotive force (EMF) and voltage saturation. Also, the friction model was changed to include stiction plus Coulomb, viscous and Stribeck friction in accordance with the classical friction model stipulated by Olsson et al. [20]. A diagram outlining the shape of the friction model is shown in Figure 2.

Figure 2: Friction model as a function of motor velocity with stiction plus Coulomb, viscous and Stribeck friction


Using the function given by Olsson et al. [20] the classical friction model is,

( ) if 0

if 0 and( ) otherwise

m m

F E m E

S E

TT

T sign T

ω ω ≠= ω =

ST<T T ( 1 )

where is the frictional torque, FT mω the motor velocity,

)( mT ω an arbitrary function, T the torque due to stiction

and is any external torque that is applied about the motor axis.

S

ET

The function T )( mω is given by,

/( ) ( )s

m sm C S C VT T T T e T

δω ωmω ω−= + − + ( 2 )

where is the torque due to Coulomb friction, T the

coefficient of viscous friction and CT V

Sω is the Stribeck velocity.

The Coulomb friction is a constant offset, T , with some load dependency,

0

α , and is given by,

0C cT T F lα= + ( 3 )

where is the EMB clamp force. clF

The Karnopp remedy [20] for zero velocity detection was employed in the friction model using a zero velocity interval 0ω± .

With the friction model, motor dynamics, and back EMF included, a simulation of the EMB model was implemented in Simulink. A block diagram of the model is shown in Figure 3.

Figure 3: Block diagram of EMB model

The input to the model is the pulse width modulation voltage across the motor and this is saturated at the maximum power supply limits of ±42V. Briefly stepping through the block diagram, the back EMF is assumed proportional to the motor velocity and is subtracted from the supply voltage. The motor current is then determined by a first order lag that models the motor impedance. The motor torque is calculated from a proportional relationship between the current and the motor torque constant. A torque balance is then considered about the motor axis, with the effects of friction included. The net torque divided by the equivalent system inertia referred to the motor axis gives the motor acceleration. The acceleration is integrated to give the motor velocity and then zero velocity

detection is employed to match that performed in the friction model. The motor velocity is integrated to give the motor position. The motor position multiplies the gear ratio to give the spindle position, that in turn determines the caliper clamp force via a non-linear stiffness characteristic. Finally, the EMB clamp force is the model output.

CONTROLLER DESIGN

DEFINITION OF THE CONTROL PROBLEM

With a cascaded control architecture the EMB control problem is subdivided into three lesser problems relating to each of the control loops. The clamp force control problem is to maintain the EMB clamp force, (N), at

the set-point value, (N), by adjusting the set-point

motor velocity demand, (rad/s). In turn, the motor velocity control problem is to maintain the motor angular velocity,

clF*

clF*mω

mω (rad/s), at the set-point value, (rad/s), by

adjusting the set-point current demand, (A). Finally, the current control problem is to maintain the motor current,

(A), at the set-point value, i (A), by adjusting the supplied motor voltage, u (V).

*mω

*i

i *

DESIGN APROACH

Normally controllers with cascaded control loops are designed beginning with the inner most control loop and then working outwards. Consequently, the motor current controller is addressed first, then the motor velocity controller, and lastly the caliper clamp force controller. Classical control theory is applied at each stage with the general approach being to linearise the system, design a controller for the linear system, and then allow feedback to handle non-linear disturbances when the controller is implemented with the actual system. To improve the controller response, integral anti-windup is incorporated as well as feed forward compensation of the back EMF and Coulomb friction.

PERFORMANCE REQUIREMENTS

The following performance specifications for each of the control loops were chosen to give an overall EMB performance that is approaching the hydraulic brake standard.

Motor current controller - The current controller is required to follow a step command between the maximum safe motor currents of ±25 A with less than 1% overshoot and a ±2% settling time under 1 millisecond.


Motor velocity controller - Establishing a performance requirement for the velocity controller is more difficult because this depends on both the caliper clamp load, which increases during an apply, and also the direction of motion. Consequently, the performance requirement has been selected as reaching 95% of the maximum motor speed of 420 rad/s (0.95 × 420 ≈ 400 rad/s) in less than 0.02 s for an apply with zero initial air gap.

EMB clamp force controller - During an apply with no initial air gap the EMB must obtain the maximum caliper clamp force of 30 kN with less than 5% overshoot and a ±2% settling time of 0.15 s. The same requirements should also be met for force commands of less than 30 kN.

CONTROLLER DESIGN

The following section describes the design of each control loop subject to the required specifications listed previously.

Motor current controller - The current controller is a feedback controller with proportional and integral (PI) gains, integral anti-windup and feed forward compensation of the back EMF and Coulomb friction. Back EMF may be considered as a disturbance and this is shown in Figure 4.

Figure 4: System showing back EMF as a disturbance

The back EMF is proportional to the motor velocity, but this is affected by the non-linear system characteristics. A feed-forward compensation term ( t mK )ω+

)t mK in the controller

is used to reject the back EMF ( ω− , and this relies on knowledge of the motor speed and torque constant.

Figure 5: Current control loop

The closed loop transfer function can be shown to be,

ImIm

II

IsRPsLIsP

sIsI

++++

=)()(

)(2*

( 4 )

where and iP iI are the proportional and integral gains for the current controller.

The proportional and integral gains were tuned for the linear system by first specifying a proportional gain and the desired overshoot and then using a search algorithm to find the corresponding integral gain. The search algorithm used a step response in the time domain that was derived via an inverse Laplace transformation.

For this system it was found that the gains could be increased to give arbitrarily better rise times. However, the system performance is limited by the ±42 V maximum power supply voltage and the current protection limits of ±25 A that are included to avoid overheating the motor. These are shown in Figure 6.

Figure 6: Current control loop with saturation of the power

supply voltage and safe motor current limits To avoid voltage saturation for a 25 A step command when the integral term in the controller is zero, the proportional gain must be 42/25 = 1.68. For a 1% overshoot requirement the corresponding integral gain was found to be 3221. Actually, the most demanding step command occurs when the system is running at −25 A and a current of +25 A is demanded, but avoiding the voltage saturation in this case was found to give an overly conservative controller. To ensure the controller demand did not exceed the ±42 V constraint a saturation function was applied to the control output.

Motor velocity controller - The motor velocity controller is a PI controller with integral anti-windup. The location of the velocity controller within the cascaded architecture is shown in Figure 7.

Figure 7: Control architecture with cascaded velocity and current loops

To arrive at a transfer function for the velocity loop the system must first be made linear. To do this the non-linear stiffness is approximated with a linear function and the technique of feed forward compensation is used to reject the back EMF and Coulomb friction disturbances. These disturbances are shown in the system diagram in Figure 8.

Figure 8: System diagram showing back EMF and Coulomb Friction as system disturbances


Accurate calculation of the Coulomb friction using a classical friction model assumes knowledge of the Coulomb friction offset and the coefficient of load dependency. These parameters must be measured prior to operation. The Coulomb friction calculation also requires real-time sensor measurements of the EMB clamp force and motor velocity.

Once a value for the Coulomb friction is available then feed forward compensation may be implemented. Given that the current loop has a high bandwidth and unity DC gain, the computed Coulomb friction may be introduced as an addition to the set point current command, scaled by the inverse of the motor torque constant Kt.

For the linearised system the closed loop transfer can be shown to be,

* 2 2

( ) ( )( ) ( )

m t v v

m v t v c

s K P s I

t vs Js T K P s K N K Iωω

+=

+ + + + ( 5 )

where and are the proportional and integral gains for the velocity controller. The DC gain of this transfer function is less than unity:

vP vI

* 2

(0)1

(0)m t v

m c t v

K IK N K I

ω= <

ω + ( 6 )

The resulting steady-state error may be reduced by setting the integral gain large. Specifying a steady-state error requirement of less than 1%, the integral gain is calculated to be . 8.457vI =

The proportional gain may now be selected to give the desired rise time and overshoot. However, the performance of the EMB is limited by the ±42 V voltage saturation. During a typical apply the motor can reach a maximum velocity of approximately 410 rad/s. Depending on the set-point motor velocity the motor speed error can instantaneously reach values in the order of 100-200 rad/s. To avoid the ±42 V saturation the proportional gain must be Pv = 42/200 = 0.21.

EMB clamp force controller – The EMB clamp force controller is a PI controller with integral anti-windup. This controller determines the commanded motor velocity, but since the EMB response is limited by the maximum motor speed the controller should avoid excessive demands. The limitation of the maximum motor velocity is used to determine the proportional gain.

Neglecting external forces, the maximum theoretical motor speed is reached when the back EMF fully cancels the applied voltage across the motor. Using as the back EMF coefficient, and setting the back EMF equal to the maximum applied voltage of 42 V we find

1.0=tK

max 420=ω rad/s.

During simulations of a brake apply a maximum motor speed of 410 rad/s was observed. This is close to the theoretical limit, but reduced somewhat due to external forces such as friction and load. The maximum speed is similar to a saturation, but instead of having a sharp cut-off value the acceleration is reduced as the maximum speed approaches. The PI force controller should avoid the effective speed saturation and not demand unattainable motor speeds. For a more conservative controller the maximum set-point motor velocity command is limited to 85% of the observed maximum speed

rad/s. To avoid demanding a motor speed of more than 348.5 rad/s with a force error signal of 30 kN at the beginning of a full apply, the proportional gain must be 348.5/30000 = 0.0116. A small integral gain of 10

5.34885.0410* ±=×=ω

-3 is chosen to help eliminate the steady state error.

Having now designed a controller for each of the control loops, the details are summarized in Table 1.

Control loop Controller Gains Variations EMB motor current (A)

PI

P = 1.68 I = 3221

Anti-windup Back EMF compensation

EMB motor velocity(rad/s)

PI P = 0.21 I = 8.457

Anti-windup Coulomb friction compensation

EMB clamp force (N)

PI P = 0.1 I = 0.001

Anti-windup

Table 1: Specification of the EMB clamp force controller with cascaded force, velocity and current control loops

It was found that using the gains shown in Table 1, the performance requirements for each control loop were satisfied.

RESULTS AND DISCUSSION

The performance of an EMB is in part determined by how quickly the unit can respond to a brake apply and how well it can track fine modulations about a particular caliper clamp load. These characteristics are important to provide both a rapid brake response during a critical brake maneuver and also allow implementation of anti-lock braking. Hence, a series of tests were simulated to determine the EMB step and frequency responses. Before presenting the results however, the validation of the model is first addressed.

In an attempt to validate the model, the simulation output for a 30 kN full brake apply is compared with experimental data from an actual EMB provided by an industry partner. The results are shown in Figure 9.


Figure 9: EMB response to full brake apply simulated for the newly designed controller and measured with a former gain

scheduled controller

In Figure 9 it may be observed that the response predicted by the present EMB model is somewhat faster than the experimental result. In part this may be attributed to the model containing ideal sensors and a controller with continuous rather than discrete operation.

Importantly, the predicted response has a maximum slope that agrees with the measured result. This indicates that the simulation is accurately modelling the physical limitations of the actuator. Similar observations were made for other comparisons between simulation and actual EMB responses.

Management of the separation between the EMB brake pads and brake rotor is incorporated within the controller by switching the outer control loop between position and clamp force control across the contact point between the pads and rotor. Continuous operation between the regions of position and force control may be observed in Figure 9 where the clearance is represented on the force plot using an imaginary negative force.

In Figure 9 it can be seen that the EMB and controller give satisfactory performance for a full brake apply of 30 kN. However, the same performance requirements should be met for all step commands within the range of operation. To test this a series of step responses were conducted. The results are shown in Figure 10.

Figure 10: EMB response to force step commands of 1, 2, 3, 4,

5, 10, 15, 20, 25 and 30kN

In Figure 10 it may be observed that the EMB controller satisfied the performance requirements for a series of step commands. However, upon closer examination it is seen that the controller responds slower to clamp force commands less than 5 kN. The reason for this is that the controller gains were conservatively chosen to avoid the system saturations for the maximum demand. However, for small force commands the reduced error signal results in less effort being commanded via the proportional control. This can be a problem when responding to small clamp force commands or even more so when tracking modulations about a large clamp force. In these cases the error signal and proportional gain may not be sufficiently high to overcome the Coulomb friction. Instead, we find the response is delayed until the integral control ramps up the command and friction is overcome. A solution to this problem may be offered either by friction compensation or gain scheduling based on the clamp force error signal. With this scheduling approach higher gains may be used to obtain a better response for small error signals in the clamp force command.

As well as responding to step commands it was mentioned earlier that the EMB should be able to track modulations about a particular clamp force. To assess this performance objective a series of tests were conducted to observe the response to sinusoidal modulations about a given clamp force. The results from these tests are presented in Figures 11 and 12.


Figure 11: EMB response to force commands of 5, 10, 15, 20,

25 and 30 kN with 50 rad/s (7.95 Hz) sine wave, amplitude 10% of the step value

In Figure 11 it may observed how the controller tracks a sinusoidal modulation about a desired clamp force. In this case the modulation was arbitrarily selected as a 50 rad/s sine wave with an amplitude that is 10% of the step value. While this gives the response to a single input frequency, it is useful to know the full frequency response. This is determined by repeating the tracking test across a range of frequencies. The result of this is shown in Figure 12.

Figure 12: EMB frequency response to a 10% sinusoidal input at the given clamp forces

In Figure 12 it may be observed that for a 10% sinusoidal modulation about a given EMB clamp force the frequency response drops off at around 20 Hz. Non-linearity of the system may also be observed with the bandwidth decreasing at higher clamp loads.

It should be noted that the frequency response in Figure 12 was achieved using both the back EMF and friction compensation detailed in the controller design. Initially there was no compensation included in the controller, but

this was later added for improved disturbance rejection. To assess its effectiveness, the EMB response was compared with and without compensation. The results are shown in Figures 13, 14 and 15.

Figure 13: EMB response to a step force command of 10kN with and without back EMF compensation.

Figure 13 compares the EMB response to a 10kN step force command with and without back EMF compensation. It may be observed that the response with compensation marginally leads and suffers slightly less overshoot than the case without. However, the improvement with back EMF compensation appears minor and has been included in the controller mainly to demonstrate the best achievable results with feed forward compensation of the system nonlinearity.

In order to test the impact of Coulomb friction compensation on the frequency response, a slowly varying frequency chirp signal was input into the model about a steady state clamp force. The fundamental harmonic of the model output was then used to estimate a linear transfer function of the EMB system. The accuracy of the linear approximation was determined using the standard technique of coherence evaluation. In this approach, power spectral densities of the input and output, PXX and PYY respectively, are used along with the cross spectral density, PXY, to calculate the coherence, CXY, according to the following relationship

[ ]2

0,1XYXY

XX YY

PC

P P= ∈ ( 7 )

Coherence values close to 1 indicate that there is good linear correlation between the input and output, and hence the transfer function estimate is a good approximation of the system behavior. The coherence is plotted in Figure 14 for each of the corresponding bode plots.


Figure 14: EMB frequency response to a sinusoidal input of amplitudes 10% and 1% about a 10kN brake apply with and

without friction compensation

In Figure 14 it may be observed that the EMB response without friction compensation is attenuated for small modulations at high frequency and this is attributed to the effect of stiction. It is also seen that the friction compensation is more beneficial for finer clamp force modulations, and although there is little improvement in the response to a sinusoidal force modulation with amplitude of 10% about a 10kN apply, a significant improvement is observed for the smaller 1% modulation. This occurs because at finer levels of force modulation the friction becomes more significant when compared with the magnitude of the force error that drives the controller response.

The coherence plots indicate this is a reasonable representation of the overall system frequency response, especially for frequencies under 10Hz. This is due to the controller being able to overcome ‘slow’ disturbances such as stiction through integral action. The drop in coherence for the 1% modulation scenario at approximately 10 Hz indicates this is the fastest rate at which the existing integral action can be successfully applied in this context.

Figure 15 demonstrates the resulting output with and without friction compensation at 8 Hz, which is close to the corner frequency observed in the gain plots of Figure 14.

Figure 15: EMB response to a sinusoidal input at 50 rad/s (7.95 Hz) about a 10kN brake apply with and without friction

compensation

Figure 15 compares the EMB response to a sinusoidal force command with and without friction compensation, and as before, the friction compensation appears to be more beneficial for finer modulations. In particular, it is


seen that the uncompensated system suffers stiction to a greater extent for smaller amplitudes of modulation. Importantly, this disturbance is partly overcome when friction compensation is included in the controller to command more effort from the EMB actuator.

Satisfactory disturbance rejection and control robustness are important issues for an EMB in a safety-critical brake system. It is necessary for the controller to handle parameter uncertainties such as variations in friction levels with wear and also characteristic stiffness with temperature and wear of the brake pads. This is a topic for future work on robust control.

As a secondary outcome of modeling an EMB and designing a controller it was realized that EMB design is a difficult optimization problem. The mechanical unit must provide high and reliable performance over many operating cycles during its lifetime. Further, the unit must endure high loads, high temperatures up to 800°C at the brake pads, and an environment that can be both dirty and rough. All this must be achieved with an actuator that is compact and constrained in size by the limited available space. To assist with the design task it would certainly be helpful to understand what parameters were most influential in limiting the performance of an electromechanical brake. A high performance motor and appropriate gear ratio are important. It is also desirable for the motor and gearing to be compact and efficient with low friction. Ultimately however, it was observed that the EMBs performance is limited by the maximum power supply voltage, maximum motor speed and the limits on the safe motor current.

CONCLUSION

Automobile brakes are a critical vehicle system and consequently the performance demands are high. Prior to this work it was unclear how well a cascaded EMB clamp force controller would handle the large operating range in which non-linear load disturbances such as friction become more significant at high clamp forces of up to 30kN. In this paper the design of a cascaded EMB controller is presented and its capacity to supply and track brake caliper clamp force commands is observed from its response to step and sinusoidal inputs. It was found that provided the controller gains were selected to avoid saturations of the maximum motor speed, maximum power supply voltage, and limits on the safe motor current then the conventional motion control architecture with an outer force loop provided a satisfactory response to clamp force commands over a wide range of operation. However, it is suggested that for operation about low clamp forces, where the selected controller gains were more conservative than necessary, the performance may be further improved with the inclusion of gain scheduling. Additionally it was found that the ability to perform fine modulations about a steady clamp force level is significantly improved if feed forward compensation of the load dependent friction force is implemented based on an accurate friction model.

The important results of this paper include: • the design of an EMB controller. • the validation of an EMB model simulation. • characterization of the step and frequency

responses for the EMB. • an assessment of the effectiveness of back EMF

and Coulomb friction compensation.

Future research directions include implementing the controller on an EMB and updating the model to include uncertainties before addressing the problem of robust control.

ACKNOWLEDGMENTS

The authors would like to acknowledge and thank their industry partner, Pacifica Group Technologies for providing both data and assistance. We would also like to acknowledge that this work was supported by the Research Centre for Advanced By-Wire Technologies (RABiT).

REFERENCES

[1] W.-D. Jonner, H. Winner, L. Dreilich, and E. Schunck, "Electrohydraulic brake system - The first approach to brake-by-wire technology," SAE Technical Paper, vol. 960991, 1996.

[2] E. Gohring and E.-C. v. Glasner, "Performance comparison of drum and disc brakes for heavy duty commerical vehicles," SAE Technical Paper, vol. 902206, 1990.

[3] A. G. Taig, "Electrically actuated disc brake," in United States Patent 4850457. United States of America: Allied-Signal Inc., 1989.

[4] Y. Fujita, T. Aral, and M. Ogura, "Motor disc brake system," in United States Patent 5107967. Japan: Honda Giken Kogyo Kabushiki, 1992.

[5] S. S. Shaw and D. E. Schenk, "Electric disc brake," in United States Patent 5219048. United States of America: General Motors Corporation, 1993.

[6] G. Halasy-Wimmer, K. Bill, J. Balz, L. Kunze, and S. Schmitt, "Electromechanically actuated disc brake system," in United States Patent 5829557. United States of America: ITT Automotive Europe GmbH, 1998.

[7] A. W. Kingston, R. L. Ferger, T. Weigert, S. Oliveri, L. Tribe, and H. L. Linkner, "Electric actuation mechanism suitable for a disc brake assembly," in United States Patent 5931268. United States of America: Kelsey-Hayes Company, 1999.


[8] K. Bill, J. Balz, and V. Dusil, "Electromechanical disc brake," in United States Patent 6158558. United States of America: Continental Teaves AG & Co. OHG, 2000.

[9] K. L. Holding, "Electrically-operated dics brake assemblies for vehicles," in United States Patent 6145634. United Kingdom: Lucas Industries public limited company, 2000.

[10] J. Dietrich, B. Gombert, and M. Grebenstein, "Electromechanical brake with self-energization," in United States Patent 6318513. United States of America: Deutsches Zentrum fur Luft- und Raumfahrt e.V., 2001.

[11] K. Takahashi and K. Kawase, "Electric braking device," in United States Patent US 6279691 B1. Japan: Akebono Brake Industry Co., Ltd., 2001.

[12] T. Usui and Y. Ohtani, "Electric disc brake," in United States Patent US 6491140 B2. Japan: Tokico, 2002.

[13] F. Keller, "Electromagnetic wheel brake device," in United States Patent US 6536561 B1. United States of America: Robert Bosch GmbH, 2003.

[14] A. H. E. A. Olschewski, H. J. Kapaan, C. Druet, T. W. Fucks, M. Antensteiner, A. C. Rinsma, J. Gurka, and A. J. C. D. Vries, "Actuator having a central support, and brake calliper comprising such actuator," in United States Patent US 6554109 B1. Netherlands: SKF Engineering and Research Centre B.V., 2003.

[15] D. B. Drennen, E. R. Siler, G. C. Fulks, and D. E. Poole, "Caliper with internal motor," in United States Patent US 6626270 B2. United States of America: Delphi Technologies, Inc., 2003.

[16] M. Smith, "42 Volts - enabling a technological revolution," in Auto Briefing, Special Eddition May 2001 ed: Knibb, Gormezano and Partners, 2001.

[17] R. Schwarz, R. Isermann, J. Bohm, J. Nell, and P. Rieth, "Clamping force estimation for a brake-by-wire actuator," SAE Technical Paper, vol. 1999-01-0482, 1999.

[18] C. Maron, T. Dieckmann, S. Hauck, and H. Prinzler, "Electromechanical brake system: Actuator control development system," SAE Technical Paper, vol. 970814, 1997.

[19] R. Schwarz, R. Isermann, J. Bohm, J. Nell, and P. Rieth, "Modeling and control of an electormechanical disk brake," SAE Technical Paper, vol. 980600, 1998.

[20] H. Olsson, K. J. Åström, C. C. d. Wit, M. Gäfvert, and P. Lischinsky, "Friction models and friction compensation," European Journal of Control, 1998.


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