The verification of the developed controls are performed by extensive simulations using the MATLAB/SIMULINK environment. Then the best control method is chosen to extend it with the developed state observer and further tested on a real clutch bench. Finally, the performance of the observer based feedforward/feedback control is demonstrated on a test vehicle.
The aim of the performance test is to demonstrate the behavior of the designed controllers.
Thus, the system performance indexes correspond to the reference position tracking capability of the closed loop systems.
Two test sequences, which cover typical clutch applications, are chosen to examine the track-ing capability. First, two steps with 100% stroke are applied to derive the settltrack-ing times, then engagement test functions are used to get the settling times of the slipping phases and catch critical overshoots.
Four different lengths of time are distinguished according to the starting and reaching strokes during a step-response. The resulted time factors are the arithmetic mean of the corresponding measured times of the two steps. The starting and reaching strokes are noted in the factors subscript (Txx−xx%).
Six engagement slopes are tested afterwards. Each of them starts from 100% stroke and jumps down immediately to 70%, 60%, 50%, 40%, 30% and 20% respectively, then followed by a linear ramp, which lasts 2s and descends 20% stroke during this stretch of time. The time duration of reaching a 5% environment of the demanded slope is measured separately for each ramp (T1 −T6). Moreover, the critical overshoots, i.e. the positive errors in the clutch engagement domain, (s1 −s6) during the slopes are captured. The graphical interpretation of these performance indices are shown in Fig. 5.13.
−100
−50 0 50
ytoˆx Mag[dB]
EPC HGO
−300
−200
−100 0
ytoˆx Phase[deg]
0 20 40 60
yto
˙ ˆx
Mag[dB]
−100 0 100
yto
˙ ˆx
Phase[deg]
0 50 100
yto
¨ ˆx
Mag[dB]
100 101 102 103 104
−100 0 100 200
yto
¨ ˆx
Phase[deg]
Frequency [rad/s]
Figure 5.12: Magnitude and phase of the frequency response fromy to x,ˆ x˙ˆ and to x¨ˆ Besides the time factors and overshoots, the tracking errors are evaluated for both of the two sequences in L2 norm as:
|ǫ|2 = s
1 T
Z T
0
xref(t)−xpst(t)
¯ xref
2
dt, (5.30)
where the overline refers to the integral mean of the reference signal andT is the duration of the test case.
Finally the measure of the reference position tracking capability is defined by
χ= 1
qP18 i=1wiχ2i
, (5.31)
where χi corresponds to the performance indexes above (Txx, sx and |ǫ|2). Moreover, in order
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0
20 40 60 80 100
xpst[%]
time [s]
xref
xpst
xref−xpst
0 2 4 6 8 10 12 14 16 18
0 20 40 60 80 100
xpst[%]
time [s]
T0−5%
T0−95%
T100−95%
T100−5%
T1 T
2 T
3 T
4 T
5 T
6
s1 s
2 s
3 s
4 s
5
s6
Figure 5.13: Graphical interpretation of the performance indices
to achieve the weighted sum of the individual squared numberswi weights are used (see details later).
5.6.1 Simulation test
To obtain the simulation results the stiff ODE15s solver with variable step size is used, where the relative tolerance of the solver is set up to10−8. While the model runs at base sampling rate, the position control is placed into an atomic subsystem, with5msfixed step size. In the preliminary tests10ms update rate is considered also, but in this way the control loop has too much delay and cannot stabilize the system. Since the dynamics of the applied sensors are much higher than the dynamics of the EPC system the delay of the sensors are neglected. The parameter values considered in software-in-the-loop (SIL) tests, can be seen inTab. A.1.
In the first step, the simplified model M2 is used as the controlled plant to achieve an appropriate environment for quick controller tuning. Hence, the feedback controls (LQ,SM C, H∞) are tested only.
After some trials a trade-off between the performance and the stability is taken for all the three controls. The time graph of the step response test, in case of theM2 model, is shown in Fig. 5.14, while the time graph of the engagement test is shown in Fig. 5.15.
0 1 2 3 4 5 6 7 8 9
−0.02 0 0.02
σv[kg/s]
σmin,σmax
0 1 2 3 4 5 6 7 8 9
0 5x 105
pch[Pa]
0 1 2 3 4 5 6 7 8 9
0 50 100
xpst[%]
xref LQ H∞ SMC
0 1 2 3 4 5 6 7 8 9
−5
−3 0 3 5
ǫ[%]
time [s]
Figure 5.14: Step responses with 100% stroke in case of simplified model
0 2 4 6 8 10 12 14 16 18
−0.02 0 0.02
σv[kg/s]
σmin,σmax
0 2 4 6 8 10 12 14 16 18
0 5x 105
pch[Pa]
0 2 4 6 8 10 12 14 16 18
0 50 100
xpst[%]
xref LQ H∞ SMC
0 2 4 6 8 10 12 14 16 18
−5
−3 0 3 5
ǫ[%]
time [s]
Figure 5.15: Clutch engagement test functions in case of simplified model
The performance indexes are gathered in Tab. 5.1. When calculating the reference position tracking capability χ, the following weights are used: wi = 1 i = {1. . .4,6. . .11} in case of reaching times (Txx),wi = 0.75i={12. . .17}in case of overshoots (sx) andwi = 0.01i={5,18}
in case of tracking errors (|ǫ|x).
From the tests it can be seen that the LQ control cannot fulfill the requirements regarding the response timesT1-T4. Hence, theLQcontrol is not appropriate for advanced clutch control.
TheSM C has the best performance during the SIL tests. Although the H∞controller has also appropriate performance, it has not tested furthermore, since it has much larger computational cost than theSM C. This comes on one hand from the feedback linearization and on the other hand from the 5 th order nature.
In the second step, the SM C is tested using the detailed nonlinear dynamic hybrid model M0 of the clutch system. In this case not only the position control, but the mass flow rate control is integrated into the closed loop system.
In order to obtain the best solution, both the static and dynamic mass flow rate decomposition approaches are tested. Moreover, in case of the static mass flow rate decomposition approach the control system is tested not only with 5ms but with 1ms update rate as well, since the update rate has a high influence to the accuracy and the stability of the closed loop system. In the other case, the dynamic mass flow rate is run with 5ms update rate. This means that the dynamic mass flow rate controller can get the desired mass flow rate in every5ms and provides the appropriate opening time accordingly. The resolution of the opening time is 1µs.
The time graph of the step response test, in case of model M0, is shown in Fig. 5.16, while the time graph of the engagement test is shown in Fig. 5.17. In these tests SM C1 and SM C2 correspond to static mass flow rate decomposition with 5ms and 1ms update rate respectively, whileSM C3 corresponds to dynamic mass flow rate decomposition with 5ms update rate. The performance indexes are gathered in Tab. 5.1as well.
Table 5.1: Performance indices of step response and clutch slipping tests
Simplified model Detailed model Test b.
Nr. χi wi Spec. LQ H∞ SMC SMC1 SMC2 SMC3 SMC4 Unit
1 T0−95% 1 0.2 0.200 0.190 0.168 0.220 0.192 0.156 0.198 s
2 T100−95% 1 0.04 0.029 0.025 0.025 0.022 0.024 0.027 0.032 s
3 T0−5% 1 0.04 0.031 0.018 0.015 0.028 0.021 0.022 0.030 s
4 T100−5% 1 0.5 0.458 0.446 0.445 0.369 0.345 0.348 0.399 s
5 |ǫ|2 0.01 6 6.36 5.91 5.97 5.85 5.64 5.71 5.70
-6 T1 1 0.1 0.161 0.080 0.062 0.059 0.057 0.057 0.042 s
7 T2 1 0.13 0.193 0.092 0.074 0.134 0.112 0.076 0.057 s 8 T3 1 0.15 0.217 0.099 0.086 0.146 0.122 0.125 0.067 s
9 T4 1 0.2 0.243 0.110 0.099 0.191 0.139 0.134 0.084 s
10 T5 1 0.3 0.268 0.146 0.145 0.274 0.182 0.184 0.116 s
11 T6 1 0.4 0.284 0.231 0.230 0.323 0.209 0.209 0.200 s
12 s1 0.75 3 0.0 0.0 0.1 2.4 2.0 0.3 1.8 %
13 s2 0.75 3 0.0 0.0 0.0 0.4 0.0 0.2 1.3 %
14 s3 0.75 3 0.0 0.0 0.0 0.0 0.0 0.0 1.4 %
15 s4 0.75 3 0.0 0.0 0.0 0.0 0.0 0.0 1.3 %
16 s5 0.75 3 0.0 0.0 0.0 0.0 0.0 0.0 0.3 %
17 s6 0.75 3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 %
18 |ǫ|2 0.01 3 2.24 1.94 1.90 2.01 1.87 1.91 1.98
-χ 0.16 0.99 1.16 1.18 0.44 0.53 1.18 0.38
-0 1 2 3 4 5 6 7 8 9
−0.02 0 0.02
σv[kg/s]
σmin,σmax
0 1 2 3 4 5 6 7 8 9
0 5x 105
pch[Pa]
0 1 2 3 4 5 6 7 8 9
0 50 100
xpst[%]
xref SMC1 SMC2 SMC3
0 1 2 3 4 5 6 7 8 9
−5
−3 0 3 5
ǫ[%]
time [s]
Figure 5.16: Step responses with 100% stroke in case of detailed model
0 2 4 6 8 10 12 14 16 18
−0.02 0 0.02
σv[kg/s]
σmin,σmax
0 2 4 6 8 10 12 14 16 18
0 5x 105
pch[Pa]
0 2 4 6 8 10 12 14 16 18
0 50 100
xpst[%]
xref SMC1 SMC2 SMC3
0 2 4 6 8 10 12 14 16 18
−5
−3 0 3 5
ǫ[%]
time [s]
Figure 5.17: Clutch engagement test functions in case of detailed model
As can be seen from the results the SM C1 cannot fulfill the requirements, due to the step response settling time and the accuracy. Although theSM C2 has better performance it requires too high update rate for embedded application. The SM C3 control has the best performance just like in case of simplified model. Thus this control and through this the dynamic mass flow rate approach is proposed for further assessment in real environment.
5.6.2 Clutch bench test
In this phase the real actuator with the selected position and mass flow rate control is tested on a clutch test bench. In order to feed the controls with all the states the designed high-gain observer is integrated into the control algorithm as well, marked asSM C4.
The layout of the test bench is shown in Fig. 5.18. For the HIL test an electro-pneumatic Clutch Actuator Unit (CAU) with valve module and central release bearing is used.
Figure 5.18: Electro-pneumatic clutch system layout
The actuator is provided with a position sensor to measure the current position of the piston, which has a direct connection to the release bearing. Besides, a pressure sensor is connected to the chamber to measure the current pressure. The CAU is supplied from an air reservoir, whose nominal pressure level is 9.5bar (abs). The supply voltage is set to 28V. An acquisition PC is used to provide the reference signal for the Clutch Control Unit (CCU). Hence one gets an electro-pneumatically actuated Clutch-By-Wire system, which lets one to adjust the clutch position/torque arbitrary. Thus the reference signal (xref) is one of the input of the CCU.
Besides, the CCU gets the current position (xpst), which is the feedback signal from the CAU.
The CCU has analogue-to-digital converters with12bitresolution and has a16bitfixed point arithmetics, hence the effect of the quantization of the signal amplitude is not considerable. The control is run with 5ms update rate and has 1µsactuation time resolution similarly as in case of simulation.
The CCU outputs are the control signal of the valves (uxxv ). The valves and the power stages are integrated into the CAU. The actuator force acts against the load (Fl) and drives the Clutch Mechanism (CM) to the demanded position.
During the HIL test the same test cases are used as before. The time graph of the step response test in case of bench test, is shown inFig. 5.19, while the time graph of the engagement test is shown in Fig. 5.20. Moreover, the sliding surface and the state trajectory in the phase plane during a step response is shown inFig. 5.21. Starting from the initial condition, the state trajectory reaches the sliding surface in a finite time, and then slides along the surface towards
0 1 2 3 4 5 6 7 8 9
−0.02 0 0.02
σv[kg/s]
σmin,σmax
0 1 2 3 4 5 6 7 8 9
0 5x 105
pch[Pa]
0 1 2 3 4 5 6 7 8 9
0 50 100
xpst[%]
xref SMC4
0 1 2 3 4 5 6 7 8 9
−5
−3 0 3 5
ǫ[%]
time [s]
Figure 5.19: Step responses with 100% stroke in case of test bench
0 2 4 6 8 10 12 14 16 18
−0.02 0 0.02
σv[kg/s]
σmin,σmax
0 2 4 6 8 10 12 14 16 18
0 5x 105
pch[Pa]
0 2 4 6 8 10 12 14 16 18
0 50 100
xpst[%]
xref SMC4
0 2 4 6 8 10 12 14 16 18
−5
−3 0 3 5
ǫ[%]
time [s]
Figure 5.20: Clutch engagement test functions in case of test bench
−0.01
−0.005 0
0.005
0.01
−1
−0.5 0
0.5 1
−100
−50 0 50 100
˜ x[m]
˙˜
x£m s
¤
£m¨ ˜x2s
¤
Sliding phase
Reaching phase
Sliding surface
Figure 5.21: The sliding surface and the state trajectory in the phase plane
xd exponentially, with a time-constant equal to 1/λ. The performance indexes are gathered in Tab. 5.1 as well.
Although the amplitude of the sensor noise is up to 2% and thus it modifies the values of the overshoots the requirements regarding this factor are fulfilled. Furthermore, the time factors are similar to those of the SIL tests. Hence the control algorithm is appropriate for vehicle test.
5.6.3 Vehicle test
For the vehicle test a heavy duty truck, equipped with automated mechanical transmission, is used, hence the reference position comes from the transmission control unit. During the test the vehicle is not loaded so that the driver can better feel the effect of the clutch slipping.
Firstly, the attention is focused to the smooth launch of the vehicle, where a low dynamics, but very accurate position tracking is needed.
In the beginning of the test, the engine is off, the gear box is in neutral gear and the clutch is disengaged (seeFig. 5.22).
In the current test case, when the engine is started (at0.8s), a touch point learning process is started immediately as well. In this phase, the stroke of the clutch actuator, regarding the touch point, where the pressure plate reaches the friction disc is determined. When the engine speed (ωe) reaches its idle value, the clutch is engaged immediately. Thus, the input shaft speed of the gearbox (ωg) is brought up to the engine speed (at 1.4s). Then the clutch is disengaged fully to allow for a second engagement along a ramp (2.3s−3.9s). When the clutch is disengaged,
0 5 10 15 20 25 0
T
ts[s]
tsls tbls tses tbes
0 5 10 15 20 25
0 2 4 6x 105
pch[Pa]
0 5 10 15 20 25
0 50 100
xpst[%]
xref xpst
0 5 10 15 20 25
−5
−3 0 3 5
ǫ[%]
0 5 10 15 20 25
0 1000 2000
ω[rpm]
time [s]
0 5 10 15 20 25 0
5 10
v[km/h]
ωg ωe v
Figure 5.22: Smooth launch of the vehicle
the input shaft speed starts to decrease till the clutch stroke reaches the touch point. At the touch point, the gradient of the decrease is changed (at 3.8s), and then the input shaft speed starts to increase. At the end of the touch point learning process, the learned stroke is checked.
Hence, the input shaft speed increases again to reach the engine speed, and then the clutch is disengaged in order to let input shaft speed drop. The clutch stroke is set to the newly learned touch point ( xpst = 40%) along a ramp as well (4.6s−5.2s). When the stroke reaches it, the gradient of the input shaft speed is changed slightly. In order to find the touch point correctly a very accurate control is needed.
After the successful learning, a smooth vehicle launch is executed. The gearbox is shifted into an appropriate gear (at14.2s) and the clutch actuator is set to disengaged state (xpst= 65%).
When the driver pushes the accelerator pedal, the reference position jumps immediately to the touch point (at 19s). Then the clutch is engaged further to reach the appropriate transmitted torque for the smooth vehicle launch. This phase is one of the most important parts in the clutch control. Since, on one hand, the delay of the touch point reaching time causes unwanted increase in engine speed and through this higher friction disc wear. On the other hand, the overshoot can cause driveline oscillations and through this reduced driver comfort or can stall the engine
completely. When the vehicle is launched and the clutch slip is decreased to zero, the clutch is fully engaged (at 23.3s).
A dynamic vehicle launch and gear shifting processes are tested afterwards (see Fig. 5.23).
In case of a dynamic start, the reference position jumps immediately to the touch point as well (at 0.8s). Then along a ramp an appropriate torque is set (1.1s−1.7s). When the vehicle is launched and the clutch slip is decreased to zero, the clutch is fully engaged again (at2.6s).
0 2 4 6 8 10 12 14 16 18 20
0 T
ts[s]
tsls tbls tses tbes
0 2 4 6 8 10 12 14 16 18 20
0 2 4 6x 105
pch[Pa]
0 2 4 6 8 10 12 14 16 18 20
0 50 100
xpst[%]
xref xpst
0 2 4 6 8 10 12 14 16 18 20
−5
−3 0 3 5
ǫ[%]
0 2 4 6 8 10 12 14 16 18 20
0 500 1000 1500 2000
ω[rpm]
time [s]
0 2 4 6 8 10 12 14 16 18 20 0
10 20 30
v[km/h]
ωg ωe v
Figure 5.23: Dynamic launch and gearshifting
The gearshifting is started with a rapid disengagement (at 6.4s) and with a controlled slip to engage (7s−7.4s). At higher gears the reference is a step function only.
As seen from the measurement, the error is in the tolerance band (dashed lines). Only when the reference changed instantaneously, is the error out of this range. This is the consequence of the limited actuator dynamics. Hence, the accuracy of the closed loop system is acceptable.
There are no critical overshoots, the step response times are within the allowed range and the driver feeling is satisfactory as well.