energies Article
Robust Clamping Force Control of an Electro-Mechanical Brake System for Application to Commercial City Buses Sangjune Eum 1 , Jihun Choi 1 , Sang-Shin Park 1, *, Changhee Yoo 2 and Kanghyun Nam 1 1
2
*
Graduate School of Mechanical Engineering, Yeungnam University, Gyeongsan-si, Gyensangbuk-do 38541, Korea;
[email protected] (S.E.);
[email protected] (J.C.);
[email protected] (K.N.) Advanced Development Team, Sangsin Brake Co., Ltd., Dalsung-gun, Daegu Metropolitan City 43023, Korea;
[email protected] Correspondence:
[email protected]; Tel.: +82-53-810-3538
Academic Editor: Felipe Jimenez Received: 15 December 2016; Accepted: 7 February 2017; Published: 14 February 2017
Abstract: This paper proposes a sensor-less robust force control method for improving the control performance of an electro-mechanical brake (EMB) which is applicable to commercial city buses. The EMB generates the accurate clamping force commanded by a driver through an independent motor control at each wheel instead of using existing mechanical components. In general, an EMB undergoes parameter variation and a backdrivability problem. For this reason, the cascade control strategy (e.g., force-position cascade control structure) is proposed and the disturbance observer is employed to enhance control robustness against model variations. Additionally, this paper proposed the clamping force estimation method for a sensor-less control, i.e., the clamping force observer (CFO). Finally, in order to confirm the performance and effectiveness of a proposed robust control method, several experiments are performed and analyzed. Keywords: electro-mechanical brake; disturbance observer; clamping force control
1. Introduction As vehicle safety technology has developed, active safety systems with electronic and control technologies are actively proceeding. Especially, among the causes of vehicle and safety device accidents, the brake system represents a significantly large proportion. Thus, the importance of “brake by wire” technology [1–3], an electronic brake system which is combined with functions such as an antilock braking system (ABS), traction control system (TCS) and electronic stability program (ESP) is emphasized. Also, its study is consistently evolving. Since the brake by wire system is technology that controls a power of vehicle using electronic signals by eliminating mechanical and hydraulic connection lines, it has received a lot of attention in the automotive industry. Especially, to satisfy the driving stability, a brake by wire system such as electronic hydraulic brake (EHB) [4,5] and electro-mechanical brake (EMB) [6] are considered to be essential elements to develop the braking control system. Currently, there are two implementation of the brake by wire system, namely EHB and EMB. They also have advantages like light vehicle weight and better utilization of space as compared with past brake systems. However, because an EHB system uses hydraulic power, there are some drawbacks such as the fail-safe problem, the leakage of hydraulic fluid, the lack of power and cost. Compared with an EHB system, an EMB system has some advantages. It is more environmentally friendly than an EHB system. Also, it is possible to realize a faster response due to the fast actuator dynamics and it can control the braking force accurately and precisely. Energies 2017, 10, 220; doi:10.3390/en10020220
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Due to advantages of EMB systems, they have been studied for a long time. In 2008, [7] presented a method to estimate the clamping force based on other sensory information such as sensor–fusion methods. In 2010, a clamping force control algorithm was suggested along with a consideration of the frictional characteristics and the estimation of the clamping force. A designed model of an EMB system and the use of the triple-loop PI control method were discussed [8,9]. This algorithm can be divided into three parts: current-loop, velocity-loop and pressure-loop. In 2013 [10] introduced the electric parking brake system. This paper also analyzed the modeling and control of the system by designing a nonlinear P controller. Finally, a stability analysis was performed. Although studies about EMB systems have been widely presented, precisely controlling an EMB system is difficult due to the external disturbance elements such as the generated efficiency deterioration caused by the significantly large gear ratio and friction. To reduce these adverse effects, we suggest the disturbance observer (DOB) algorithm in this paper. A DOB is introduced by Ohnishi [11] for robust control. It has also been analyzed by many researchers [12–16]. A DOB is designed based on a system dynamics model and can estimate the external disturbances and eliminate them in real-time. Due to the good performance of a DOB, it has been applied in a variety of mechatronics fields. Today, cost reduction is very important in industry applications. Generally, the clamping force in an EMB system is measured by a load cell. It contributes to improving the control performance and accuracy at the same time. However, it is very expensive and makes the system complicated. Furthermore, its signal delay is fatal in control systems requiring fast control response. For these problems, the clamping force observer (CFO) is proposed in this paper. A CFO based on a model dynamics is good solution to replace the load cell and reduce the system costs. Thus, a clamping force estimation is necessary for realizing the cost-effective EMB system. In this paper, the force sensor-less robust force control method for an EMB system is introduced. The structure of a proposed force control system consists of five parts: (1) a position mode-disturbance observer (P-DOB); (2) a force mode-disturbance observer (F-DOB); (3) a clamping force observer (CFO); (4) a position controller and (5) a force controller. In Section 2, an EMB system dynamics and results for system identification tests are shown. In Section 3, for a sensor-less robust force control, a controller design method is proposed and its performance and effectiveness are shown with several experimental results in Section 4. Finally, the conclusion and future works are presented in Section 5. 2. System Modeling of an EMB System This paper suggests the robust clamping force control method without using a force measuring device. However, with this we experience a couple of control problems such as a backdrivability and model variation. In order to overcome these challenging issues, we designed a robust position controller as an inner loop control and a robust force controller as an outer loop control. In order to design the aforemented two controllers, one needs accurate plant model information and model-based control technologies are required for providing the enhanced control performances. In this section, we derived simplified system dynamics for a driving motor and an EMB’s torque transfer mechanism. In addition, those system dynamics models are compared with models obtained from the system identification tests. Dynamics Model Figure 1 illustrates a schematic of the proposed EMB system that was developed by Sangsin Brake Co., Ltd. (Daegu, Korea), for commercial city bus applications. Figure 1a represents each component including a driving motor, a reduction gear set, a brake disk, etc. and Figure 1b shows the real view for an EMB system.
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(a) (a)
(b) (b)
Figure 1. A proposed EMB system: (a) EMB schematics; (b) Real view of an EMB system. Figure Figure 1. 1. A A proposed proposed EMB EMB system: system: (a) (a) EMB EMB schematics; schematics; (b) (b) Real Real view view of of an an EMB EMB system. system.
In order to describe an EMB system dynamics, we simply modeled an EMB system as shown in In order to describe an EMB system dynamics, we simply modeled an EMB system as shown in Figure 2. Fortoposition force system control dynamics, design, two models an areEMB required. Firstly, a motor In order describeand an EMB wedynamics simply modeled system as shown in Figure 2. For position and force control design, two dynamics models are required. Firstly, a motor dynamics forposition the precise control is derived as follows:models are required. Firstly, a motor Figure 2. For andposition force control design, two dynamics dynamics for the precise position control is derived as follows: dynamics for the precise position control is tderived = J w as+follows: B w (1) t m m= J m wm m m+ Bm wm m m (1) . τm = Jm ω m + Bm ωm (1) w (s) 1 (2) w m (ms ) = 1 (2) s1+ Bm ωtmt((mss())s )= J Jsm + Bm m = m (2) τm (s) Jm s + Bm
(a) (a)
(b) (b)
Figure2.2.AAproposed proposedEMB EMBsystem: system:(a) (a)EMB EMBschematics; schematics;(b) (b)Free Freebody bodydiagram diagramofofananEMB EMBsystem. system. Figure Figure 2. A proposed EMB system: (a) EMB schematics; (b) Free body diagram of an EMB system.
Here, we consider the further dynamics, illustrating the lagging effect between a reduction gear Here, Here, we consider the the further further dynamics, dynamics, illustrating illustrating the the lagging lagging effect effect between between aa reduction reduction gear gear and a brake pad, as a first-order low pass filter. Thus, a system transfer function from input tm to function from input τm t tom the to and a brake pad, as as aa first-order first-orderlow lowpass passfilter. filter.Thus, Thus,a asystem systemtransfer transfer function from input is obtained by the system output system output ωm is w obtained by the system output wm mis obtained by 11 ω wm 11 = 1 ´ 1 ( s ) =wmm = × (3) Pn (PsP )(ns= ´ 11+ ) =τm t m= JmJsm+ s +BB s (3) +tτs n mm tm J m s + Bm 1 + t s Toconfirm confirmthe themodel modelvalidity, validity,system systemidentification identificationtests testswere wereperformed performedand andresults resultsare are To To confirm the model validity, system identification tests were performed and results are representedininFigure Figure3.3. AA green green thick thick line line in inFigure Figure33isisthe thefrequency frequencyresponse responsefor forthe themodel model represented represented in Figure 3. A green thick line in Figure 3 is the frequency response for the model Equation(3) (3)and andother otherresults resultsare arefor forexperimentally-obtained experimentally-obtainedfrequency frequencyresponses responseswith withdifferent different Equation Equation (3) and other results are for experimentally-obtained frequency responses with different inputvoltages. voltages. input input voltages.
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Figure3.3.Results Results of of system system identification Figure identificationtests. tests. Figure Results of system identification Secondly, we need to obtain the3.dynamics for designing the tests. force controller which has a motor Secondly, we need to obtain the dynamics for designing the force controller which has a motor angle as an input and a clamping force as an output. Considering that a clamping force and a motor angle as has an input and a clamping as anaoutput. Considering a clamping force a motor Secondly, we need to obtainforce the dynamics for designing the force which has areduction motor K that angle a proportional relationship (i.e., proportional gain iscontroller obtained from the and angle asproportional an input and arelationship clamping force as aanproportional output. Considering that a clamping force and a motor gear angle has a (i.e., gain K is obtained from the reduction gear ratio and mechanical stiffness), it is reasonable to choose a simple first order model as below: has a proportional relationship (i.e., a proportional gain K first is obtained from the reduction ratio angle and mechanical stiffness), it is reasonable to choose a simple order model as below:
gear ratio and mechanical stiffness), it is reasonable Fˆ to choose K a simple first order model as below: . Pm ( s ) = cl » (4) ˆ 1 +Kt s Fqm PmP(s()s) = Fˆclcl ≈ K . . (4) (4) m θm 1 + τs 1 s m where a linear transfer function P is the relationship between a motor angle q and a clamping m
m
where a linear function Pm is relationship between a amotor θmmand a aclamping Pmthe where transfer function is the relationship between motor angle and clamping force Fˆcl a, linear t transfer is the model cut-off frequency that is the same value usedangle in Equation (3). force ˆ Fcl , τ force isTo theget cut-off frequency that is thein same value usedcontroller, inused Equation (3). identification Pm used a representative a force system tests Fˆmodel is the model model cut-off frequency that is the tracking same value in Equation (3). cl , To get a representative model Pm used in a force tracking controller, system identification tests were performed and results are represented in aFigure 4. A blue thin linesystem is the identification estimated clamping Pm used in To get a representative model force tracking controller, tests were performed results are linear represented in Figure 4. A blue thin line is(4)). the Since estimated clamping force and a red and thick line is the model that we designed (i.e., a clamping force-mode were performed and results are represented in Figure 4. A blue thinEquation line is the estimated force and a red thick line designed is the linear model that we designed (i.e.,Equation Equation (4)). Since disturbance based on this model, a modeling shown Figure 4 aisforce-mode properly force and aobserver red thickisline is the linear model that we designed (i.e.,error (4)).inSince a force-mode disturbance observer is designed based on this model, a modeling error shown in Figure 4 is properly compensated a realisplant is nominalized the linear model error we designed. disturbance and observer designed based on thistomodel, a modeling shown in Figure 4 is properly compensated andand a real plant is is nominalized modelwe wedesigned. designed. compensated a real plant nominalizedto tothe the linear linear model
Figure identificationtests. tests. Figure4.4.Results Results of of system system identification Figure 4. Results of system identification tests.
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3. Design of a Sensor-Less Robust Controller 3. Design of a Sensor-Less Robust Controller In this paper, we focus on two control objectives: (1) design of more robust and accurate position and force controllers forfocus enhancing braking force control performance; and (2) design of a position practical In this paper, we on twothe control objectives: (1) design of more robust and accurate clamping observer reduce thethe system cost.force Thus, we propose the force sensor-less and forceforce controllers fortoenhancing braking control performance; and (2) designrobust of a force control method.force Theobserver overall control structure is shown Figure The control scheme is given practical clamping to reduce the system cost.in Thus, we5.propose the force sensor-less force control method. The overall control structure is shown in Figure 5. The control scheme asrobust follows. is given as follows. • First, the desired clamping force F ∗ *is generated by a driver’s brake pedal command. Note that • the First, the desired clamping force F is generated by athe driver’s command. desired clamping force can be calculated by using brakebrake pedalpedal stroke sensor. Note that the desired clamping force can be calculated by using the brake pedal stroke sensor. • Second, the 2-degree-of-freedom position controller is designed based on the defined nominal • Second, the 2-degree-of-freedom position controller is designed based on the defined nominal motor model for improving the position tracking performances and an inner-loop disturbance motor model for improving the position tracking performances and an inner-loop disturbance observer (i.e., called a position-mode DOB) is designed for making the position controller robust observer (i.e., called a position-mode DOB) is designed for making the position controller robust against external disturbances. against external disturbances. • Third, a CFO is designed based on a nominal motor model and a reduction gear ratio. • Third, a CFO is designed based on a nominal motor model and a reduction gear ratio. • • Forth, DOB) is is designed designed to to Forth,the theouter-loop outer-loop disturbance disturbance observer observer (i.e., (i.e., called called aa force-mode force-mode DOB) compensate for model variations and to reject undesired disturbances. A F-DOB makes the compensate for model variations and to reject undesired disturbances. A F-DOB makes the complicated complicatedcalmping calmpingforce forcedynamics dynamicsbehave behaveas asaadefined defined nominal nominal clamping clamping force force model. model. • • Finally, the 2-degree-of-freedom clamping force controller is designed by using the nominal Finally, the 2-degree-of-freedom clamping force controller is designed by using the nominal clamping force model. clamping force model.
Figure 5. Overall structure for a proposed robust clamping force control system: (1) 2-degree-ofFigure 5. Overall structure for a proposed robust clamping force control system: (1) 2-degree-offreedom clamping force controller; (2) 2-degree-of-freedom position controller; (3) Clamping force freedom clamping force controller; (2) 2-degree-of-freedom position controller; (3) Clamping force observer; (4) Position-mode DOB; (5) Force-mode DOB. observer; (4) Position-mode DOB; (5) Force-mode DOB.
3.1. Design of a Clamping Force Observer (CFO) 3.1. Design of a Clamping Force Observer (CFO) In the operation of an EMB, it is very important to know the clamping force in real time. Even if In the operation of an EMB, it is very important to know the clamping force in real time. Even if a load cell or force sensor can be used to measure the clamping force, it entails extra cost and space. a Therefore, load cell orinforce can bethe used to measure the it entails extra cost andmodel space. ordersensor to estimate clamping force, weclamping proposedforce, a CFO based on a nominal Pn and the second-order low pass filter Qi (s) as shown in Figure 6: Qi ( s) =
wi 2 s 2 + 2wi s + wi 2
(5)
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Therefore, in order to estimate the clamping force, we proposed a CFO based on a nominal model Pn and the second-order low pass filter Qi (s) as shown in Figure 6: Qi ( s ) = Energies 2017, 10, 220 Energies 2017, 10, 220
ωi 2 s2 + 2ωi s + ωi 2
(5) 6 of 13 6 of 13
Figure 6. Structure of a CFO. Figure Figure6.6.Structure Structureof ofaaCFO. CFO.
The estimation result for the CFO is shown in Figure 7. It is confirmed that the estimated Theestimation estimation for the is shown inthe Figure 7. measurement It is confirmed that the estimated clamping force (i.e.,result a result red for thin line inCFO Figure 7)intracks a noticeable The the CFO is shown Figure 7. sensor It is confirmed that thewithout estimated clamping clamping force (i.e., a red thin line in Figure 7) tracks the sensor measurement without a noticeable error. Noteathat reduction gear mechanism with a high gear ratio (i.e., 100:1) is applied in aerror. proposed force (i.e., red athin line in Figure 7) tracks the sensor measurement without a noticeable Note error. Note thatthe agear reduction gear mechanism with agear high gear (i.e.,friction, isaffect applied a proposed EMB nonlinear effects, by or thein estimation that a system, reduction mechanism withcaused a high gear ratiobacklash (i.e.,ratio 100:1) is100:1) applied in a proposed EMB EMB system, the nonlinear effects,bycaused by gear or friction, affect the estimation performance. system, the nonlinear effects, caused gear backlash or backlash friction, affect the estimation performance. performance.
Figure 7. Experimental results for a CFO. Figure 7. Experimental results for a CFO. Figure 7. Experimental results for a CFO.
3.2. Design of an Inner-Loop Controller: Position Controller 3.2. 3.2. Design Design of ofan anInner-Loop Inner-LoopController: Controller: Position Position Controller Controller In this section, a robust position controller used as an inner-loop controller is introduced and its In section, position controller used inner-loop controller introduced and Inthis this section,aarobust robust position controller usedas asan an inner-loop controllerisis introduced andits its control effectiveness is explained from experimental results. A DOB-based inner-loop position control effectiveness is explained from experimental results. A DOB-based inner-loop position control control effectiveness is explained from experimental results. A DOB-based inner-loop position control is required to track the reference with a high control bandwidth and to make control system iscontrol required to track the reference with a high bandwidth and to make system robust is required to track the reference withcontrol a high control bandwidth and tocontrol make control robust against external disturbances and nonlinear effects. The structure is shown in Figure 8. system against external disturbances and nonlinear effects. The structure is shown in Figure 8. robust against external disturbances and nonlinear effects. The structure is shown in Figure 8.
C fp C fp ** θ
+
−
Cp Cp
d d
N N
+ + + dˆ− +
EMB EMB
dˆ
P-DOB P-DOB
m θm
3.2. Design of an Inner-Loop Controller: Position Controller In this section, a robust position controller used as an inner-loop controller is introduced and its control effectiveness is explained from experimental results. A DOB-based inner-loop position control2017, is required to track the reference with a high control bandwidth and to make control system Energies 10, 220 7 of 12 robust against external disturbances and nonlinear effects. The structure is shown in Figure 8.
C fp d
θ*
+ −
Cp
N
+ + + − +
EMB
θm
dˆ
P-DOB
Figure 8. Structure of a two-degree-of-freedom position controller with a position-mode disturbance Figure 8. Structure of a two-degree-of-freedom position controller with a position-mode disturbance observer (P-DOB). observer (P-DOB).
In order to accomplish the control goal, firstly, A P-DOB is designed to compensate the external disturbance and thereby makes the closed position control system robust. Secondly, a 2-DOF position controller (i.e., a feedback controller, C p (s) and feed-forward controller, C f p (s)) is designed to enhance the reference tracking performance and a residual vibration compensator (i.e., N (s)) is additionally designed based on frequency analysis for the tracking error. A transfer function between the reference position, θ ∗ , and the output θm is expressed as: Cp P θm = , ∗ θ 1 − Qi + C p P + PPn−1 Qi
(6)
where, if Qi ≈ 1 and P = Pn , Equation (6) can be simplified as: C p Pn ωp θm ≈ = ∗ θ 1 + C p Pn s + ωp
(7)
Here, in order to satisfy the Equation (7) condition, a feedback controller, designed based on a pole-zero cancellation method, should have a following form: C p (s) =
K pp s + Kip + Kdp s2 s
(8)
where, proportional, integral, and derivative gains are chosen as K pp = ω p ( Jm + Bm τ ), and Kdp = ω p Jm τ, respectively, ω p is the cut-off frequency deciding the position control bandwidth. In addition, an inverse model-based feed-forward controller is added to achieve fast response in the transient region as follows: C f p (s) =
ω1 3 s( Jm s + Bm )(1 + τs)
( s + ω1 ) 3
,
(9)
where, ω1 is the cut-off frequency of a feed-forward filter that is required to reject noises caused by numerical differentiation. To alleviate overshoot phenomenon at a certain frequency, a residual vibration compensator is applied and it is given by: s2 + 2ζωc s + ωc2 N (s) = 2 , (10) s + 2ωc s + ωc2 where, ζ and ωc are the damping coefficient and resonance frequency, respectively, and these values are obtained from the repeated experiment under various operating conditions.
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Several experiments are performed to confirm the frequency response for designed control system and those results are shown in Figure 9. It is examined that a maximum overshoot occurs in the vicinity of 12 Hz (i.e., a driving motor is the most oscillatory.). One can see that a vibration compensator,N (s), Energies 2017, 10, 220 8 of 13 contributes to reducing the maximum magnitude of the closed-loop frequency response by 45%.
Figure 9. Frequency response function for the closed-loop transfer function with a notch filter: Figure 9. Frequency response function for the closed-loop transfer function with a notch filter: (a) Magnitude plot; (b) Phase plot. (a) Magnitude plot; (b) Phase plot.
3.3. Design of an Outer-Loop Controller: Force Controller
3.3. Design of an Outer-Loop Controller: Force Controller
The EMB control is challenged by the nonlinearities in the reduction gear mechanism, model The EMB control challenged by nonlinearities in undesired the reduction uncertainty, and lowisbackdrivability. Tothe compensate for such factorsgear and mechanism, unpredictablemodel terms, a DOB has been used in this study. In general, the DOB is used for rejecting disturbance and uncertainty, and low backdrivability. To compensate for such undesired factors and unpredictable compensating for variation of plant dynamics by treating the variations as an equivalent disturbances. terms, a DOB has been used in this study. In general, the DOB is used for rejecting disturbance and In the design DOB, theofselection of the low filterthe called a Q-filter important. It is compensating forofvariation plant dynamics bypass treating variations asisanvery equivalent disturbances. 1 Q ( s ) Q ( s ) required to select DOB such that QDOB (s) PDOB (s) is realizable. In general, the is DOB
In the design of DOB, the selection of the low pass filter called a Q-filter is very important. It is required designed as(as)low-pass filter, which the − dc1 gain of one, such that the closed-loop has a as a to select Q DOB such that Q DOB (s) Phas is realizable. In general, the Q DOB (ssystem ) is designed DOB ( s ) good disturbance rejection performance at low frequencies. From the general framework of a DOB low-pass filter, which has the dc gain of one, such that the closed-loop system has a good disturbance shown in Figure 10, characteristics of the DOB is analytically explained. A transfer function of a DOB, rejection performanceUat low frequencies. From the general framework of a DOB shown in Figure 10, i.e., from the input to the ouput Y , is expressed as: characteristics of the DOB is analytically explained. A transfer function of a DOB, i.e., from the input PPDOB U to the ouput Y, is expressed as:Y PDOB PDOB PQDOB QDOB PDOB
U
Y( If , Q 1) PPDOB U = PDOB DOB + PQ DOB − Q DOB PDOB
.
(11)
≈ PDOB
( I f , Q DOB ≈ 1)
.
(11)
d
The transfer function of Uthe input Y is expressedY as follows: d to the output Y d
=
P
PPDOB (1− Q DOB ) PDOB + PQ DOB − Q DOB PDOB
( I fdˆ, Q DOB ≈ 1)
PDOB
1
≈ 0
.
(12)
Based on a nominal clamping force model (i.e., Equation (4)), a F-DOB is designed and it QDOB contributed to alleviating the hysteresis effect during brake apply and release. In similar manner, a 2-DOF controller is designed by pole placement based on given control performance specifications Figure 10. General framework of a disturbance observer.
3.3. Design of an Outer-Loop Controller: Force Controller The EMB control is challenged by the nonlinearities in the reduction gear mechanism, model uncertainty, and low backdrivability. To compensate for such undesired factors and unpredictable terms, a DOB has been used in this study. In general, the DOB is used for rejecting disturbance and Energiescompensating 2017, 10, 220 for variation of plant dynamics by treating the variations as an equivalent disturbances. 9 of 12 In the design of DOB, the selection of the low pass filter called a Q-filter is very important. It is required to select QDOB (s) such that QDOB ( s ) PDOB ( s )-1 is realizable. In general, the QDOB (s) is
and two feedback gains (i.e., a proportional and integration gains) are chosen to make a closed-loop designed as a low-pass filter, which has the dc gain of one, such that the closed-loop system has a transfer function to be a 1st low-pass filter with a cut-off frequency of ω f : good disturbance rejection performance at low frequencies. From the general framework of a DOB shown in Figure 10, characteristics of the A transfer function of a DOB, C f DOB P is analytically explained. Cf P ωf Fˆcl = the ouput Y , is expressed ≈ = (13) i.e., from the input U∗ to as: −1
F
1 + Cf P
1 − Qo + C f P + PPn Qo
PPDOB Y = ≈ PDOB K p f s + Ki f U PDOB . C f +=PQDOB − QDOB PDOB s ( If , QDOB ≈ 1)
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ωf ω f τtransfer function of the input d to the output where, K p f = The k , Ki f = k .
U
+
+
9 of 13
(11) (14)
Y is expressed as follows:
PPDOB (1d− QDOB ) Y = ≈ 0 d PDOB + PQDOB − QDOB PDOB . P ( If , QDOB ≈ 1)
−
s + ωf
+
Y
(12)
Based on a nominal clamping force model (i.e., Equation (4)), a F-DOB is designed and it contributed to alleviating the hysteresis effect during brake apply and release. In similar manner, a dˆ PDOB −1control performance specifications 2-DOF controller is designed by pole placement based on given and two feedback gains (i.e., a proportional and integration gains) are chosen to make a closed-loop transfer function to be a 1st low-pass filter with aQcut-off frequency of w f :
− + DOB
Fˆcl *
=
Cf P -1
»
Cf P
=
wf
F General C f P + PPn Qo of a1disturbance s + wobserver. 1- Qo +framework + Cf P f Figure 10.
(13)
Figure 10. General framework of a disturbance observer. Cf =
K pf s + K if
(14)
A feed-forward controller is also designeds based on an inverse nominal model, i.e., w f)t, and w1st Pm −1 (s) =where, K −1 (1K+=τs low-pass filter, i.e., ω2 /(s + ω2 ), is used for rejecting the f , Kif = . pf k k amplified noise: A feed-forward controller is also designed ω (based 1 + τson ) an inverse nominal model, i.e., C f f (si.e., ) =w2 /(s2+ w2 ) , is used for rejecting the amplified noise: (15) Pm-1 (s) = K -1 (1 + ts) , and 1st low-pass filter, K ( s + ω2 ) 4. Experiments
C ff (s) =
w2 (1 + t s) K (s + w2 )
(15)
In this section, an experimental setup for the EMB system is introduced and experimental results 4. Experiments are presented to confirm the tracking performance of a proposed controller. In this section, an experimental setup for the EMB system is introduced and experimental results are presented 4.1. Experimental Setupto confirm the tracking performance of a proposed controller. 4.1.11 Experimental Setup Figure shows the experimental setup for the EMB system. An EMB system consists of an AC motor, mechanical brake andfor a load cell. It should besystem noted that aofload Figure 11 shows thecomponents experimental setup the EMB system. An EMB consists an ACcell is very brake components andpaper, a load it cell. should be noted a load cell very expensive,motor, e.g., mechanical more than $1000. In this is Itonly used as a that reference forisvalidating the expensive, e.g., more than $1000. In this paper, it is only used as a reference for validating the proposed clamping force estimation algorithm. The MATLAB/SIMULINK software is used to realize proposed clamping force estimation algorithm. The MATLAB/SIMULINK software is used to realize the real-time control.control. Additionally, in order totomeasure the data, a Quanser DAQfrom board from Quanser the real-time Additionally, in order measure the data, a Quanser DAQ board Quanser CompanyCompany (Markham, ON, Canada) is used. (Markham, ON, Canada) is used.
Figure 11. Configuration of experimental setup.
Figure 11. Configuration of experimental setup.
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4.2. Experimental Experimental Results Results 4.2. A proposed proposed estimation estimation and and clamping clamping force force control control methods, methods, illustrated illustrated in in Figure Figure 5, 5, are are A implemented on an EMB system shown in Figure 11. To simulate the driver’s brake command, the implemented on an EMB system shown in Figure 11. To simulate the driver’s brake command, sinusoidal braking maneuver hashas been Hz the sinusoidal braking maneuver beendone doneunder undervarious variousfrequency frequency conditions conditions (e.g., (e.g., 22 Hz sinusoidal command, 3 Hz sinusoidal command). Considering the possible foot-braking frequency sinusoidal command, 3 Hz sinusoidal command). Considering the possible foot-braking frequency thataa driver driver makes makes is is about about 0–3 0–3 Hz, Hz, test test scenarios scenarios are are reasonable. reasonable. Figure Figure 12 12 represents representsthe the test test results results that foraaproposed proposedclamping clampingforce force control. Figure 12a–d results for control the control a 2and Hzaand for control. Figure 12a–d areare thethe results for the withwith a 2 Hz 3 Hza 3 Hz clamping force commands, respectively. We can see that the estimated clamping force (i.e., clamping force commands, respectively. We can see that the estimated clamping force (i.e., a feedbacka feedbackwell variable) tracks theclamping generated clamping force command fromAlso, Figure 12a.the Also, under variable) trackswell the generated force command from Figure 12a. under same test the same test conditions, a driving motor’s angle tracks the control angle command generated from conditions, a driving motor’s angle tracks the control angle command generated from the outer-loop the outer-loop controller as shown in Figure 12b. From the results, similar control results, Figure 12c,d, force controller force as shown in Figure 12b. From the similar control Figure 12c,d, it is confirmed it isa confirmed thatcontrol a propose EMB control system shows the satisfactory reference without tracking that propose EMB system shows the satisfactory reference tracking performance performance without noticeable errors. Considering that the braking control bandwidth in noticeable errors. Considering that the braking control bandwidth in commercial ABS for heavy commercial ABS for heavy vehicles is under 3 Hz, it is expected that control performances of an ABS, vehicles is under 3 Hz, it is expected that control performances of an ABS, based on a proposed EMB based on a proposed EMB control systems,As are significantly improved. AsEMB aforementioned, mostthe of control systems, are significantly improved. aforementioned, most of the systems undergo the EMB systems undergo the backdrivability problem and have challenging control issues backdrivability problem and have challenging control issues accordingly. In this paper, to overcome accordingly. paper,atodual overcome that problem, we proposed a dualisloop control and that problem, In wethis proposed loop control strategy and its effectiveness verified fromstrategy test results, its effectiveness verifieditfrom test results, 12. In addition, it is confirmed the force i.e., Figure 12. In is addition, is confirmed thati.e., theFigure force sensor-less force control method that is practically sensor-less force control method is practically applicable to an EMB control system. applicable to an EMB control system.
Figure 12. Experimental results for braking force apply and release mode: (a) A result for the clamping Figure 12. Experimental results for braking force apply and release mode: (a) A result for the clamping force tracking control with the 2 Hz force command; (b) A result for the position tracking control with force tracking control with the 2 Hz force command; (b) A result for the position tracking control the 2 Hz force command; (c) A result for the clamping force tracking control with the 3 Hz force with the 2 Hz force command; (c) A result for the clamping force tracking control with the 3 Hz force command;(d) (d)A Aresult resultfor forthe theposition positiontracking trackingcontrol controlwith withthe the33Hz Hzforce forcecommand. command. command;
5. Conclusions This paper has presented a robust clamping force control method for EMB control system applications. In order to overcome challenging issues in precise force control, a dual loop control
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5. Conclusions This paper has presented a robust clamping force control method for EMB control system applications. In order to overcome challenging issues in precise force control, a dual loop control technique is employed and its performance is verified by several control results. Since the EMB undergoes parameter variations and a backdrivability problem under various operating conditions, a disturbance compensation technique based on a DOB is used for enhancing the robustness and a 2-DOF control method is used to improve the reference tracking performance. Additionally, a model-based clamping force estimation method for realizing the sensor-less control is proposed and its effectiveness is also verified by brake apply-release tests. Although there exists an estimation error that is caused by nonlinear effects such as gear backlash or friction, the trajectory of the estimate is well-matched with that of the sensor measurement without any noticeable errors. As a cost-effective control solution, proposed estimation and control methods can be practically applied to EMB systems for commercial city buses. In future works, precise friction modeling should be done and non-linear clamping force estimation methods will be studied. In addition, the closed-loop stability analysis will be done by employing the robust stability theorem as shown in the authors’ other publication [17]. Acknowledgments: This research was supported by the Ministry of Trade, Industry & Energy (MOTIE), Korea Institute for Advancement of Technology (KIAT) through the Encouragement Program for The Industries of Economic Cooperation Region. Author Contributions: Kanghyun Nam has equally contributed to this paper and performed the numerical simulations and proposed the overall control method. Changhee Yoo provided critical comments in experiment. Sangjune Eum performed the experiment and wrote a manuscript. Jihun Choi, and Sang-Shin Park revised the manuscript and build experimental setup. Conflicts of Interest: The authors declare no conflict of interest.
Nomenclature Bm Cf Cp Cf f Cf p d dˆ Fcl Fˆcl Jm Kp f Ki f K pp Kip Kdp Kt k N Pn Pm Qi Qo θm τm τ ωm ω1
a damping coefficient in a motor model a force controller a position controller a force feed-forward controller a position feed-forward controller external disturbances estimated disturbances a clamping force an estimated clamping force a moment of inertia for a driving motor a proportional gain used in the force controller an integral gain used in the force controller a proportional gain used in the position controller an integral gain used in the position controller a derivative gain used in the position controller a force gain a brake pad coefficient a residual vibration compensator a nominal model between τm and ωm a nominal model between θm and Fˆd a low pass filter used in an inner position control loop a low pass filter used in an outer force control loop an angle of a driving motor a torque of a driving motor a time constant an angular velocity of a driving motor a cutoff frequency of a feedforward filter used in the position control
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a cutoff frequency of a feedforward filter used in the force control a bandwidth of the residual vibration compensator, N a bandwidth of the force controller a cutoff frequency of Qi a cutoff frequency of Qo a bandwidth of the position controller stroke of the brake pad a damping coefficient used in a residual vibration compensator, N
ω2 ωc ωf ωi ωo ωp x ζ
References 1. 2. 3. 4.
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