Abstract—In this paper we present a novel claming force control method for electric parking brake systems without using force sensors. The control method consists of three steps for a simple control structure. First, we show how to approximately detect the initial contact point between brake pads and a brake disk with the angular velocity of motor. Second, the clamping force is estimated with the function of angular displacement from the maximum angular velocity. Third, since the motor continues to rotate about several tens milliseconds even after power-off we propose a novel on-off control method to decrease the inertia effect of DC motor. The proposed control method is validated by experiments. It enables low cost manufacturing of electric parking brake systems due to its simple control structure. Keywords-electric parking brake, clamping force, estimation, DC motor, inertia effect

I. INTRODUCTION ECENTLY, electric parking brake (EPB) system that generates clamping force for parking by controlling a

DC motor has been introduced to improve safety and convenience for drivers. At the press of a button on the dashboard a driver can easily apply or release the parking brake. The EPB systems provide some advantages. They allow for a larger interior space than conventional parking brake systems. And drivers with physical difficulties can activate the parking brake easily just by pushing the button. The EPB systems also support dynamic braking and anti-lock braking system (ABS) as well as the conventional parking brake function [1], [2]. Because of these advantages, the production of vehicles equipped with EPB systems is increasing.

Force sensors have been used to measure clamping force in EPB or electric mechanical brake (EMB) systems, which are brake-by-wire systems. However, it is difficult to install the force sensor due to the limited mounting space and the cost of the sensor [3]. Therefore, a clamping force estimation method

Manuscript received February 15, 2009. This work was supported in part

by the Minster of Knowledge and Economy, Republic of Korea under Grant 10014728.

M. Jang, Y. O. Lee, W. Lee, C. W. Lee are with Dept. of Electrical Engineering, Hanyang University, Seoul 133-791, KOREA (e-mail: Skyler.Jang06@gmail.com, e-mail: foryou5252@hotmail.com, e-mail: hillfolk219@gmail.com, and chungwoo.lee@gmail.com)

C. C. Chung is with Div. of Electrical and Biomedical Engineering, Hanyang University, Seoul 133-791, KOREA (+82-2-2220-1724; fax:+82-2-2291-5307; e-mail: cchung@hanyang.ac.kr)

Y. Son is with Central R&D Center, MANDO Corporation, Kyonggi-Do 446-901, KOREA (e-mail: ysson@mando.com)

without using the sensor was proposed for EMB systems [4]. In [4], the motor rotor position and the motor current were used for clamping force estimation. The characteristic curves of the relation between motor angle/ motor current and clamping force of an EMB caliper were used to estimate the clamping force. The clearance between the brake pads and the brake disk needed to be adjusted when the brake is released. And the stiffness quotient was evaluated to detect the contact point between the brake pads and the disk independent of the clamping force setting signal.

In this paper, we propose a novel clamping force control method independent of the clearance between the brake pads and the brake disk unlike the conventional method [4]. This control method consists of three steps: (1) detecting of the contact point between the brake pads and the brake disk, (2) clamping force estimation, (3) a novel on-off control method considering inertia effects. First, the proposed control method does not need the clearance management since we can approximately detect the initial contact point between brake pads and the brake disk with the angular velocity of motor. To detect the contact point, we derive the relationship between the angular velocity of motor and the contact point. From this relationship, we will show the contact happens when the angular velocity of motor reaches near its maximum. Second, we will show that the clamping force can be estimated with a function of the angular displacement of the motor from the maximum angular velocity. The function is approximated as a second order polynomial. Third, a novel on-off control method considering the inertia effects is employed for low-cost control. Since the motor continues to rotate about several tens milliseconds even after power-off, we propose a novel clamping force prediction method to decrease the inertia effect of DC motor. The control method brings the smaller error between the target clamping force and the final clamping force than the simple on-off control method. The proposed control method is validated by experimental results. From the experimental results we observed that the proposed method meets the clamping force specifications.

This paper is organized as follows: In Section II, the structure and specifications of EPB system are introduced. Also detecting method of the contact point and the estimation method of the clamping force are introduced. In Section III, the inertia effect is analyzed to decrease the error between the target clamping force and the final clamping force. In Section IV, the experiments are executed to validate the proposed estimation method. The conclusions are given in Section V.

Novel Clamping Force Control for Electric Parking Brake Systems Minseok Jang, Young O. Lee, Student Member, IEEE, Wongoo Lee,

Choong W. Lee, Student Member, IEEE, Chung C. Chung†, Member, IEEE, and Youngsub Son

R

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Fig. 1. Structure of EPB system.

II. CLAMPING FORCE ESTIMATION

A. Structure and specifications of EPB system In this paper, we study a stretch type EPB system depicted

in Fig. 1. It includes a controller, parking cables, a DC motor, a gear box, an assembly of screw, a nut, a controller, a motor driver, and a current sensor. The parking cables of EPB system are connected to the brake pads. There are two operating modes: applying and releasing force mode. In the applying force mode, the clamping force is increased by pulling the parking cables using the DC motor until it reaches the target force [13]. In the releasing force mode, the clamping force is decreased by releasing the parking cables reversely. In order to measure the angular displacement of motor, the current sensor is used by using current ripples as [5], [6]. In Table I, specifications of EPB systems are listed [7].

TABLE I SPECIFICATIONS OF EPB SYSTEM

Target force 80 – 100 [kgf]

Settling time Less than 1 [s]

Permitted error bound ±10[%] of target force

B. Detecting the contact point The clearance between the brake pads and the brake disk is

different whenever the brake is released. To overcome this problem, the conventional method requires clearance management [4]. Three experimental results for different clearances are plotted in Fig. 2.

0 20 40 60 80 100 1200

20

40

60

80

100

120

angular displacement [rev]

forc

e [k

gf]

Clamping force vs. angular displacementRelease for long timeRelease for mid timeRelease for short time

Fig. 2. Clamping force versus angular displacement for different clearances.

In Fig. 2, we see that the final clamping forces are different even for the same angular displacement due to different clearances. To resolve this problem, we studied the relationship between the angular velocity of motor and the contact time.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-0.5

0

0.5

1

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2

2.5

3

3.5

4

4.5

5

time [s]

mag

nitu

de[n

ot to

sca

le]

Comparison between 3 signals' outputAngular velocityMotor currentClamping force

The initial contact point

Fig. 3. The clamping force, the angular velocity and the current in applying force mode Fig. 3 shows the motor current, the angular velocity, and the

clamping force in applying force mode. The results show that the three signals have correlations. The angular velocity decreases and the motor current increases when the clamping force increases. Thus we will derive the relationship between the angular velocity and the clamping force from now on. The dynamics of the DC motor may be represented by (1) - (3) [8].

( ) ( ) ( ) / ( )a m m emfv t Ri t Ldi t dt v t= + + (1)( ) ( )emf bv t K tω= (2)

( )m m mT K i t= (3)

where R is the resistance, L is the inductance, and Kb is the back emf constant of the motor. The torque developed by the motor is Tm and the motor torque constant is Km. The motor current is im(t), the applied input voltage is va(t) and the back emf is vemf(t). The torque relation in EPB system is given by

m a i fT T T T= + + (4) where Ta is the applying torque of EPB system, Ti is the inertia torque, and Tf is the friction torque. Then Ta is proportional to the clamping force, f(θeff), which is defined by

( )a t effT fγ θ= (5)

where max( ) : ( ) ( ).eff t t tθ θ θ= − tγ is a constant determined by the screw gain and gear ratio. Details on the modeling are referred to [9]. The clamping force, f(θeff), is a function of the angular displacement from the contact point. This function will be derived in Section Ⅱ. C. And Ti is proportional to the

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angular acceleration, ( )tω , as defined by (6)

( )i tT J tω= (6) where Jt is the total inertia constant. In (4), Tf is a sum of the viscous friction, Tv, and coulomb friction, Tc as follows (7).

f c vT T T= + (7)

The coulomb friction dominates the viscous friction torque in the EPB system so that we have Tc >>Tv. Thus (7) can be approximated such as Tf ≅ Tc [4]. Then we can rewrite Tc as a function of f(θeff) with two constants μ and α defined by [10], [11]

( )f c effT T fμ θ α≅ = + . (8) Equation (4) can be rewritten as (9).

( ) ( ) ( )m t eff t effT f J t fγ θ ω μ θ α= + + + (9) In (1), L can be disregarded because the response of the armature circuit is much faster than the mechanical response. And (10) can be derived by rearranging (1), (2), (3), and (9).

( ) ( ) / ( ) ( ) /( )

( ( ) ) /( )a b t eff b m

t b m

t v t K R f K K

RJ t R K K

ω γ μ θ

ω α

= − +

− + (10)

Let ta be the time of the contact point between the brake pads and the brake disk. Then (10) can be rewritten by

( ),

( )( ) ( ) ( ),

m a b ma

t

m b m ta eff a

t t t t

K v K K t Rt t

RJt

K K Kv t t f t t

RJ RJ J J

ω α

ωγ μαω θ

− −⎧ ≤⎪⎪= ⎨ +⎪ − − − >⎪⎩

(11)

In (11), va(t) is a constant, whose magnitude is va , for t>0 because the controller uses a on-off control for low-cost control in this paper. In t ≤ ta case, (12) is a solution of the differential equation for ω(t).

( ) ( )( / )1( )

b m tK K RJ tm a

b m

K v R et

K K

αω

−− −= (12)

In (12), if the input voltage, va(t), is large enough such as Kmva(t) - Rα > 0, the angular velocity, ω(t), will increase at least until the contact point as depicted in Fig. 4. In t > ta case, a solution of the differential equation for ω(t) is (13).

( / )( )

( )

( ) ( )

( ) ( ) 1

b m t a

b ma

t

K K RJ t ta

K Kt t

RJt m aeff

b m b m

t t e

R K v Rf e

K K K K

ω ω

γ μ αθ

− −−

− −

=

⎧ ⎫⎧ ⎫+ − ⎪ ⎪− − −⎨ ⎬⎨ ⎬⎩ ⎭⎪ ⎪⎩ ⎭

(13)

Fig. 4. Comparison between θ(ta) and θ(tmax) It is possible to detect the point, tmax, when the motor’s angular velocity is the maximum using current ripples [6]. However, it is not possible to detect the point, ta, when the parking cable force begins increasing without using a force sensor. Thus in this paper we use θ(tmax) instead of θ(ta) for clamping force estimation. It is essential to investigate the influence on the force control from this position difference, Δθ= θ(tmax) - θ(ta).

0 0.05 0.1 0.15 0.2 0.250

0.5

1

1.5

2

2.5

3

3.5

ta [s]

Δθ

[rev

]

Comparision Δθ vs. ta

Fig. 5. Comparision of Δθ=θ(tmax) - θ(ta) vs. different at

Fig. 5 is the simulation results with the parameters used in [7]. In Fig. 5, Δθ is plotted as a function of the time of contact point, ta. Here, ta=0 is the case the clearance is zero. For ta>0.2, Δθ is nearly zero. In other words, we see that maxat t≅ for a large clearance. Further, the worst case of Δθ is less than 3.3[rev]. The possible clamping force error due to the maximum Δθ for each target force is listed in Table II. In the operating target force range, these errors are acceptable based on the specification in Table I.

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TABLE II THE FORCE ERROR DUE TO θΔ AT EACH TARGET FORCE [UNIT: KGF]

Target force Force error

80 2.7

90 3.8

100 4.2

C. The clamping force vs. the angular displacement

0 10 20 30 40 50 60 70 80 900

20

40

60

80

100

120

140

angular displacement [rev]

forc

e [k

gf]

angular displacement vs. force1st2nd3rd4th5thestimated force

Fig. 6. Comparison between the approximated function, f(θeff), and the absolute clamping force measured by the force sensor.

We showed that the parking cables begin applying the

clamping force near the time of the maximum angular velocity of the motor in Section II. B. In this section, we will validate that the clamping force can be estimated from the angular displacement of the motor after the maximum angular velocity. Fig. 6 shows the experimental results about correlation between the clamping force and the angular displacement, which is counted after the maximum velocity point, tmax, for different clearances. The clamping force is measured by the force sensor.

Unlike Fig. 2, Fig. 6 shows that f(θeff)’s agree within a bound which is tolerable. We calculated an approximated function of f(n) as

2

1 2 3( ) ; / 2f n a n a n a n θ π= + + = (14) where n is the rotational number of the motor after the maximum velocity point. The rotational number is counted using the current ripples. This method estimates the angular displacement and angular velocity of the motor by detecting periodical oscillations of the armature current caused by rotor slots. The method has higher resolution than cheap digital position sensor like an encoder. Moreover, the method has less computational effort than model based estimation methods than state observer [5], [6]. In order to get coefficients, ai’s of (14), the weighed least square estimation method (15) is used [12].

1ˆ ( ) ( 1,2,3)T Tia W WY i−= Φ Φ Φ = (15)

where ˆia ’s are coefficients, TΦ is the input matrix, W is a diagonal matrix with the weights in the diagonal, and Y is the output matrix. We used the higher weighting factor for the larger clamping force. In Fig. 6 the measured clamping forces by the force sensor and the estimated clamping force using (14) are plotted. The estimated clamping forces are plotted by the green dotted lines. The maximum estimation error is less than 3.5[kgf].

III. ANALYSIS OF THE INERTIA EFFECT First we tried a simple on-off control for the EPB system.

The simple on-off control means that it cuts off the input signal when the clamping force reaches the target force. Such a simple switch off control makes the motor continue to rotate further due to its momentum even without power. Although this simple on-off control meets the specifications, there is a large error. If the prediction how much the inertia effect makes the motor rotate is possible, the error can be reduced. We propose a novel prediction method analyzing the inertia effect and validate it with experiments.

When the power is off, the input voltage, va, becomes zero, (10) may be rearranged as follows

( ) ( ) ( ) ( )b m t eff tK K t R f RJ t Rω γ μ θ ω α= − + − − (16)

In (16), we linearize f(θeff) such as

f(θeff)=klθ at the desired clamping force. The linearized spring constant, kl is obtained from the clamping force function (14).

1 2( ) ( ) / 2desired

l desired eff desiredk f a aθ

θ θ θ θ= ∂ ∂ = + (17)

Taking the Laplace transform of (16) and rearranging its result gives

2

1( ) ( )( / ) ( ) /f

t b m t t l t

s tJ s s K K RJ s k Jαθ ω

γ μ− ⎛ ⎞⎛ ⎞

= − ⎜ ⎟⎜ ⎟ + + +⎝ ⎠⎝ ⎠(18)

where tf is the time when the input signal is zero. From the final value theorem, the steady-state values of θ is given by

( ) /{( ) }, ( 0)t lkθ α γ μ α∞ = − + < (19) Since it is assumed that θ(tf)=0 in (18). θ(∞) is the additional angular displacement of the motor after the power is cut off due to the inertia effect. Thus we can calculate the final clamping using (14) and (19). It is possible to reduce the error by shutting off the power before the estimated force reaches

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the target force. In Fig. 7, the additional angular displacement and the final clamping forces are plotted when the power is cut off at each target force.

74 76 78 80 82 84 86 88 90 92 94 96 98 1005.2

5.4

5.6

5.8

6

target force [kgf]

addi

tiona

l ang

ular

dis

plac

emen

t [re

v]

74 76 78 80 82 84 86 88 90 92 94 96 98 100

70

75

80

85

90

95

100

105

110fin

al c

lam

ping

forc

e [k

gf]

Fig. 7. The additional angular displacement and the final clamping force under each target force The left y axis is the additional angular displacement of the DC motor and the right y axis is the final clamping force.

IV. VALIDATION OF THE PROPOSED METHOD

A. Experiment environment

Fig.8. Experiment environment of the EPB system.

In order to control the clamping force of the EPB system, a

stretch type EPB system is used shown in Fig. 8. The system consists of a force indicator, a load cell measuring the absolute tension of parking cables, a controller board with a digital signal processor (TMS320F2812), a motor driver, and a module box including the motor, a gear box, and an encoder.

B. Control method Three control methods were evaluated in [13]: On-off,

linear Proportional (P), and nonlinear P. The nonlinear P controller had the best robustness and uniform tracking performance among them. However, the nonlinear P needs a PWM driver. For a low-cost control, we use an on-off control.

The simple on-off control applies the maximum input signal until the estimated clamping force reaches the target force for apply action. And the input signal becomes zero when the estimated force reaches or over the target force as (20),

max, 0

( )0, 0

u eu t

e>⎧

= ⎨ ≤⎩ (20)

where target est.e f f= − , u(t) is input voltage for the motor, umax is maximum voltage of the battery, and e is the error between the estimated clamping force and the target force.

C. Experimental results We controlled the EPB system using the clamping force

function (14) with the simple on-off controller (20). In order to validate the proposed method for different clearances, we performed experiments for three different target clamping forces under different clearances and the results are shown in Fig. 9.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

10

20

30

40

50

60

70

80

90

100

110EPB control with estimated force

forc

e [k

gf]

time[s]

80kgf from force sensor80kgf from estimated force90kgf from force sensor90kgf from estimated force100kgf from force sensor100kgf from estimated force

Fig. 9. Experimental results with the simple on-off control. In order to compare the estimated forces with the measured forces, which is gained from the force sensor embedded in the module of the EPB system, the measured forces are plotted by solid lines in Fig. 9. We see that there is a good agreement. The initial point where the estimated force follows the force sensor’s output is different since the experiment is performed under different clearance. And the maximum error between the estimated forces and the measured forces is about 3.5[kgf] which is within the error bound. We observed that the estimated force is much less than the measure force after the power is cut off. The reason is that the current ripple is not reliably detected after the power cut off. The EPB system has the maximum apply time of less than 0.8[s]. It thus satisfies the specification of the applying time. The average and the deviation of the errors are plotted in Fig. 10. We repeated 30 times applying and releasing for five different target clamping forces using the two on-off control methods (the simple on-off and the novel on-off).

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80 85 90 95 100-10

-8

-6

-4

-2

0

2

4

6

8

10

Erro

r[kg

f]

Target force[kgf]

Simple on-off control Novel on-off control

Fig. 10. The clamping force errors: Simple on-off control and novel on-off control method

In Fig. 10, negative error means that the over clamping force is applied. We see that every experiment satisfies the specification even no matter the inertia effect is considered or not. The novel on-off control, however, provides less averaged errors than the simple on-off control. Therefore, a low-cost control of the EPB system is possible using the novel on-off control.

V. CONCLUSION This paper proposed the clamping force control method of

EPB systems without using force sensors. This method used the relationship between the angular displacement of motor and the clamping force from the initial contact point between brake pads and a disk. We introduced how to approximately detect the initial contact point. The clamping force was estimated with the clamping force function of the angular displacement after the maximum angular velocity. We used on-off controller to make a simple control logics. We proposed the novel clamping force prediction method to decrease the inertia effect of DC motor. We executed experiments to validate the proposed method and showed that every experiment satisfied the specifications of the EPB systems. Due to its simple control structure, a low cost EPB system can be implemented with the proposed method.

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