regulation of a servo piezo mechanical hydraulic actuator for intake valves in camless ... ·...

Regulation of a Servo Piezo Mechanical Hydraulic Actuator forIntake Valves in Camless Combustion Engines

Paolo MercorelliLeuphana University of Lueneburg

Institute of Product and Process InnovationUniversitaetsallee 1, D-21335 Lueneburg

[email protected]

Abstract: In this paper a hybrid actuator is proposed. The hybrid actuator consists of a piezo mechanical structureand a hydraulic ratio displacement. Particular attention is paid to a liquid spring model of the displacement ratiowhich represents the hydraulic part of the mechanism. The proposed mechanism represents the fundamental partof a more complex one which consists of a supplementary hydraulic part to control intake valves of a combustionengine. The whole mechanism is controlled using a cascade repetitive control combined with a proportionalderivative (PD) controller and a feed-forward action to track a periodic signal. Measured results of the closed loopcarried out the suitability of the control approach.

Key–Words: Hybrid actuators, modelling, repetitive control, engines

Received: February 27, 2020. Revised: March 31, 2020. Accepted: April 29, 2020. Published: May 2, 2020.

1 IntroductionThe idea which this paper presents is to use a hy-brid actuator composed by a piezo, mechanical andhydraulic parts. Moreover, piezo actuators presentin general less problems of electromagnetic compat-ibility due to the quasi-absence of the inductance ef-fects. In fact, the piezoelectric actuator (PA) has beenused in precise positioning applications such as, forinstance, atomic force microscopy [1], [2]. The mainadvantages of PA are nanometer scale, high stiffness,and a fast response. However, since PA has a non-linear property which is called hysteresis effect, itleads to inaccuracy in positioning control with a highprecise performance. Very recent literature indicatesa clear interest in applications of piezo in mecha-tronic systems. In particular, for oscillations rejectionand soft landing recently piezo actuator were utilised.In [4] a novel active vibration control strategy us-ing piezoelectric actuators for metrological devices af-fected by low external loads is proposed. The con-trol strategy combines a classical sky-hook feedbackwith a feed-forward control. The effect of hystere-sis is minimized by compensating the sensitivity vari-ations of the actuator in oscillatory movements. Asalready mentioned soft landing and more in generalvelocity control are important issues. In [5] the ve-locity control of a large-range piezoelectrically actu-ated (piezo) stepper is analysed. In [6] a self-sensingtechnique for piezoelectric actuators used in precisepositioning applications like micromanipulation and

microassembly is presented. The main novelty is thatboth displacement and force signals can be simultane-ously estimated. This allows a feedback control usingone of these two signals with a display of the othersignal. In many technical applications periodical sig-nals are used and to correct the steady-state error arepetitive control can be taken into consideration. It isknown that the repetitive control is based on the prin-ciple of the internal model according to [7]. In orderto control periodic reference variables or for compen-sating periodic disturbances a repetitive control as in[8] is applied. The internal model principle is also ap-plied both for continuous and for discrete systems. Inaddition, an unstable controlled system must be firststabilized using an additional controller. Repetitivecontrol has a significant advantage that is very easyto be parameterized without transfer function of thecontrolled system. A crucial part of the actuator con-sists of a stroke displacement ratio with an oil cham-ber and because of possible faults of the sealings theright functioning of this part of the actuator can becompromised. To conclude, the main contribution ofthis paper consists of:

• presenting a new conception and modelling of ahybrid actuator

• proposing a repetitive controller together with anadaptive feed-forward controller.

Figure 1 shows the diagram of the positions of anengine intake and exhaust valves. In this figure the

PAOLO MERCORELLI

GERMANY

WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS DOI: 10.37394/232011.2020.15.7 Paolo Mercorelli

E-ISSN: 2224-3429 46 Volume 15, 2020

Figure 1: New structure of the engine

intake and the exhaust valve position profiles are in-dicated. Moreover, Fig. 1 shows the new enginestructure with, evidently, four piezo actuators. Anoverview on the complete hybrid actuator is depictedin Fig. 2. The paper is organised in the following way.Section 2 indicates a possible model of the hybrid ac-tuator. In Section 4 the proposed control scheme con-sisting of an adaptive feed-forward action based on afault detection is presented. Measured results togetherwith the conclusion close the paper.

KFL: stiffness constantKFL1: stiffness constant related to a large surface ofthe stroke ratioKFL2: stiffness constant related to a small surface ofthe stroke ratioA1: large surface of the stroke ratioA2: small surface of the stroke ratioVin(t): piezo input voltageVz(t): active piezo input voltageKx: internal piezo stiffness constantDx: piezo factorDxKx = Tem: transformer ratio

Figure 2: Model of the whole actuator

Fz(t) = Vz(t)DxKx: motor piezo forcemSK : mass of the servo pistonMv: mass of the servo valvex1(t): piezo positionx2(t): servo piston positionx2d(t) = Vz(t)Dx: motor piezo movementxV (t): valve piston positionKSK : servo piston spring constantDSK : damping factor of the servo piston springVM : steady-state factor of the mechanical systemVH : steady-state factor of the hydraulic systemp(t): pressureQth: volumetric flowAV P : surface of the servo pistonAL: leakage flow parameter

2 Model of the Hybrid ActuatorThe mathematical model is the same which is adoptedin [9] and in [10]; in this part of the paper the model ofthe actuator is presented again. The actuator consistsof different technical parts: a piezoelectric structure,a servo piston structure and a hydraulic one.

2.1 Piezoelectric Structure

The mathematic model is the same which is adoptedin [11]. The details on this model can be found in[12]. Considering the whole system described in Fig.


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3 with the assumption of compressibility of the oil,the whole mechanical system can be represented bya spring mass structure as shown in the conceptualscheme of Fig. 4. Concerning the piezo actuator, ob-serving Fig. 4, K and D represent the elasticity andthe friction constant of the spring which is antagonistto the piezo effect and is incorporated in the PEA. Inthe technical literature, factor DxKx = Tem is knownwith the name ”transformer ratio” and states that themost important characteristic of the electromechani-cal transducer in which Kx is the elasticity constantfactor of the PEA and Dx is the parameter which isresponsible to transform voltage into movement. Infact, another well-known physical relation is Fz(t) =DxKxVz(t) which represents the piezo force in whichVz is the internal voltage. In the ideal case, we havethat Vz(t) = Vin(t) where Vin(t) states the input volt-age. According to [12], in Fig. 3 and in two schemeswhich represent the considered actuator are reported.

2.2 Servo Piston Structure

Figure 3: Scheme of the electrical part of the piezoactuator

The displacement ratio is calculated considering thesurface quotient between the piezo (radius = 40mm)and the servo piston (radius = 4mm):

iWeg =A1

A2. (1)

The oil compressibility is comparable with Hook’slaw of the material technique [13]. In [13] the concept

Figure 4: Mass spring model of the piezo servo pistonactuator

of a liquid spring is introduced and the fluid compress-ibility is modelled using an elasticity factor. Consider-ing [13], the coefficient of the liquid spring coefficientKoFL in a pressure form is calculated using the fol-lowing expression:

KoFL =V0

∆V (t)∆p(t), (2)

in which V0 represents the total volume in the cham-ber. ∆V (t) is the compressed volume because ofthe acting force which generates a pressure differenceequal to ∆p(t), see [13]. As shown in Fig. 4, twosurfaces A1 and A2 play a role in the hydraulic ratiodisplacement. This ratio states the steady-state gainposition factor of this part of the actuator. From Fig.4 it is possible to observe that the model consists oftwo hydraulic cylinders. The forces at the connectingsurfaces of both cylinders are calculated through thefollowing product:

FA1(t) = AF1KoFL1x1(t) =A1

A1 + A2KoFL1x1(t),

(3)and

FA2(t) = AF2KoFL2x2(t) =A2

A1 + A2KoFL2x2(t).

(4)

2.3 Hydraulic Structure

For constant pressures, the volumetric flow Qth(t) ofthe valve drive is proportional to the length of theopening slit that equals x2(t) − x2. Considering

Qth(t) = (x2(t) − x2(t))KSP (5)


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with KSP which represents a parameter depending onthe pressure and x2(t) represents the initial servo pis-ton position at which corresponds a Qth(t) = 0. InFig. 5 a possible model of its hydraulic part are shownas proposed in [13]. The model was presented in [13]but in a linear approximation form which is very oftenused in industrial applications.

Figure 5: Block diagram structure of the hydraulicpart of the actuator

xV (t) = KHQth(t), (6)

where xV (t) represents the velocity of the valve andQth(t) the volumetric flow. KH represents a physicalconstant which does not depend on the pressure p(t)and according to [13] it is expressed as follows:

KH =VHVMAV P

1 + VHVMAV P (AV P + AL), (7)

where, according to Fig. 5, VH is the steady-state pa-rameter between p(t) and Qth(t) −Qth(t) and VH isthe steady-state parameter between force and the ve-locity of the valve. More in depth, KH represents theclosed loop steady-state gain of the scheme of Fig. 5,see [13]. Equation (6) states the steady state conditionof the hydraulic valve system. In fact, Eq. (7) rep-resents the steady state constant of the linear systemproposed in [13] as a simplified model of the hydraulicvalve system which consists of a transfer function be-tween variables Qth(t) and xV (t).

3 Control Strategy

In Fig. 6 the adopted control scheme is shown. Thecontrol scheme presents a feed-forward action to com-pensate the steady state error because of the absence

of the integral action in the controller. Together withthe feed-forward action a repetitive control algorithmis used because of the presence of a periodic signalto be tracked. It is known that the control loop canneed to be stabilised and therefore a stabilising PDcontroller is considered in the loop.

Figure 6: Block diagram of the control structure

3.1 Feed-forward Control

Thanks to modelling approximations described above,the inversion of the system described in Eq. (6) is asfollows:

Qth(t) = K−1H xVd

(t), (8)

in which xVd(t) represents the desired velocity of the

valve. The next step is to invert Eq. (5):

x2(t) = K−1SPQth(t) + x2. (9)

The steady-state feed-forward control can be sum-marized as follows: being Fz(t) = FA1(t) =

DxKxVinff (t) and p(t) = FA2(t)A2 = FA1(t)

A1 , thenFA2(t) = A2

A1Fz(t) and considering Eq. (4), then

AF2KFL2x2(t) = A2A1

DxKxVinff (t). It is straight-forward to obtain the following relation:

Vinff (t) =AF2KFL2(K

−1SPK

−1H xV d(t) + x2)

A2A1

DxKx

.

(10)

4 Experimental Results Using Repet-itive Control

According to the standard control scheme representedin Fig. 6 some measurements were done. It is known


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that a repetitive controller is characterised by the fol-lowing transfer function:

Gr(s) =1

1 − e−Tps. (11)

Parameter Tp represents the period of the periodicalsignal to be tracked. Normally, the repetitive con-troller is realised using a discrete technique and Eq.(11) becomes as follows:

Gr(z) =1

1 − z−Tp. (12)

Figure 7 shows the measured results of pressure insidethe stroke ratio, Fig. 8 shows the position measure-ments, Fig. 9 shows the position of the servo structureand finally Fig. 10 shows the trajectory position of theintake vale for 3000 rpm. A detailed scheme of therepetitive control idea is shown in Fig. 6. Measuredresults, in an experimental setup using a dSPACE sys-tem to implement the control and the fault detectionstructure, confirm that the inversions described in 3.1can be used as an effective feed-forward control forthe presented hybrid actuator.

Time (sec.)0 0.01 0.02 0.03 0.04 0.05 0.06

Pre

ssure

(bar)

10

15

20

253000 rpm

Figure 7: Pressure inside the stroke ratio

5 Conclusion and OutlookThe paper deals with modelling and control of a hy-brid actuator. Particular attention is paid to a hydraulicspring model of the ratio displacement which repre-sents the hydraulic part of the mechanism. A repet-itive controller is applied to track a periodical signal

Time (sec.)0 0.01 0.02 0.03 0.04 0.05 0.06

Pie

zo p

ositio

n (

mm

)

0.1

0.12

0.14

0.16

0.18

0.2

0.223000 rpm

Desired positionObtained position

Figure 8: Position of the piezo

Time (sec.)0 0.01 0.02 0.03 0.04 0.05 0.06

Serv

o p

ositio

n (

m)

×10-3

4.4

4.6

4.8

5

5.2

5.4

5.63000 rpm


Figure 9: Position of the servo piston

together with a PD-controller which is devoted to sta-bilise the feedback control loop. Measured results arepresented to demonstrate the effectiveness of the pro-posed method. Future advancements of this work caninclude a detailed friction model of the mechanicalsystem and its control using Sliding Mode Control asproposed in [14] and in [15]. Moreover, in order toreduce the number of sensors an implementation of aKalman Filter can be considered as proposed in [16].

Acknowledgements: The author wants to acknowl-edge Lucas Kohler, Guido Bergholz and Robert Zylla


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Time (sec.)0 0.01 0.02 0.03 0.04 0.05 0.06

Valv

e p

ositio

n (

m)

×10-3

-1

0

1

2

3

4

5

6

7

83000 rpm


Figure 10: Position of the valve

of Ostfalia University of Applied Sciences for thecollaboration in doing the measurements. The papercould not be accomplished without them.

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[9] P. Mercorelli and N. Werner. A model of aservo piezo mechanical hydraulic actuator andits regulation using repetitive control. In Proc. ofthe International Conference on Advanced Intel-ligent Mechatronics (AIM), 2014 IEEE/ASME,pages 186–191, Besancon, 2014.

[10] P. Mercorelli and N. Werner. An adaptiveresonance regulator design for motion controlof intake valves in camless engine systems.IEEE Transactions on Industrial Electronics,64(4):3413–3422, 2017.

[11] P. Mercorelli and N. Werner. A hybrid actuatormodelling and hysteresis effect identification incamless internal combustion engines control. In-ternational Journal of Modelling, Identificationand Control, 21(3):253–263, 2014.

[12] Y.-C. Yu and M.-K. Lee. A dynamic nonlinear-ity model for a piezo-actuated positioning sys-tem. In Proceedings of the 2005 IEEE Interna-tional Conference on Mechatronics, ICM 10th-12th July, Taipei, 2005.

[13] H. Murrenhoff. Servohydraulik. Shaker Verlag,Aachen, 2002.

[14] T. Ferch and P. Mercorelli. Vertical dynamics de-scription and its control in the presence of non-linear friction. WSEAS Transactions on Systems,18:198–212, 2019.

[15] K.-C. Schwab, L. Schrader, P. Mercorelli, andJ.T. Lassen. Sliding mode and model predictivecontrol for inverse pendulum. WSEAS Trans-actions on Systems and Control, 14:190–195,2019.

[16] J.T. Lassen and P. Mercorelli. Tuning kalmanfilter in linear systems. WSEAS Transactions onSystems and Control, 14:209–212, 2019.


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