Sensing Device for Camless Engine Electromagnetic Actuators

Transcription

1 Sensing Device for Camless Engine Electromagnetic Actuators Fabio Ronchi, Carlo Rossi, Andrea Tilli Dept. of Electronics, Computer Science and Systems (DEIS), University of Bologna Viale Risorgimento n., 6 Bologna, ITALY Tel , Fax f fronchi, crossi, atilli g@deis.unibo.it Abstract A position reconstruction method for camless engine electromagnetic valve actuators control without direct position measurement is proposed. The method makes use of flux signals, obtained through integration of a secondary coil voltage added at each electromagnet. By this solution, both fluxes and position signals are available for the design of the feedback position controller. The paper discuss the accuracy that can be obtained for position reconstruction, linking it to the system parameters tolerances. Experimental results are reported to show the validity of the proposed solution. A x M B I. INTRODUCTION Electromagnetic actuators for internal combustion camless engine valve control has received an increased interest in the last years (see [], [] and included references). By adjusting the valve timing depending on engine operating condition it is possible to increase engine maximum power and efciency in the overall speed range. Moreover, additional strategies can be implemented, like separated cylinder cut-off, that have further benets in terms of emission reduction and fuel consumption. The adoption of an electromagnetic actuator for valve movement poses challenging control problems []. The main goal is the achievement of the so called soft-touch : valve should come to the full open and full close positions against mechanical hard stops with very limited speed, comparable to what is achievable with a mechanical cam, in order to reduce acoustical noise and wear of the valve itself. To realize the soft touch functionality, feedback position control is mandatory because system is unstable in positions near to mechanical stop. Given a position trajectory, the feedback controller have to stabilize the plant and achieve reference position tracking. For this reason, availability of a proper position measurement is one of the key factor. On the other side, direct use of a standard position sensor is unlikely in valve electromagnetic actuators, due to cost and reliability issues []. Owing to the fact that the adopted actuator is of a variable reluctance type, in this paper it is analyzed a virtual position sensor that reconstruct actuator position from electrical signal measurements and the knowledge of the electromagnetic characteristics of the actuator itself. In order to make use of the reluctance variation for position reconstruction, flux measurement should be available. Knowledge of flux in a variable reluctance actuator give additional benets: closed loop control is easier to realize and even more robust when compared with solutions using current Fig.. Valve sketch measurement. Differently from [], in this paper the use of a secondary coil is proposed for flux measurement purpose. This is useful by its own in designing the feedback controller and is instrumental in deriving the position reconstruction algorithm. The paper is organized as follows: in section II a schematic description of the system is given, together with basic mathematical relationships; section III presents the proposed method for flux and position reconstruction with associated limitations, and discuss how such limitations can be overcome in the overall position control system; section IV reports the sensitivity analysis of the position reconstruction to electromagnetic parameters variation, in order to evaluate what are the limits in the allowable system dispersion to achieve the desired accuracy from the position reconstruction; nally, section V gives some experimental results and section VI concludes the paper. II. SYSTEM DESCRIPTION AND MATHEMATICAL MODEL In Fig. a simplied scheme of the electrically actuated valve is reported. The system is composed by a mobile mechanical part (valve, levers) and two electromagnets (EMs) that develop the force needed to move the valve along the vertical axis x: EM closes the valve, whereas EM opens it. Two

2 F (A) Reluctances (H ) x 6 < x < Forces (N ) :6 mw b : mw b : mw b :6 mw b Fig x ' j (Wb) Magnetomotive force related to iron part of the magnetic flux x (m) x Fig.. Air-gap reluctances and Equivalent spring force (dotted) vs electromagnet forces for different fluxes springs A, B are present. Spring A deliver a force to close the valve, the B one to open it. The two springs can be modelled as an equivalent linear spring and they are preloaded to keep the valve in the center of its stroke (x =) when the EMs are not supplied. The two EMs considered are similar, with only differences in the geometrical conguration. Their magnetic hysteresis and Focault currents are neglected. They are completely magnetically decoupled when working in linear range. Equations describing each of the electric windings are _' j = N [v j ri j ] ; j =; () where the subscript j = ; indicates the EM considered according to the labels of Fig.. v j and i j are voltage and current of the electric circuits, ' j is the magnetic flux, r is the electrical resistance, N is the number of turns of the winding. A key point for a simple representation of the system model and for a performing control strategy is to express the current as a function of flux. This can be done [5] by splitting the magnetomotive force (MMF) into two components. The rst term refers to the iron portion of the magnetic flux path. It nonlinearly depends on the flux and it is assumed to be almost independent on the air-gap thickness. The second term takes into account the air-gap portion and it is assumed to be a linear function of flux and a nonlinear one of the air-gap thickness. Hence, the expression for the current i j is i j = N [F (' j)+<(ο j )' j ] ; j =; () where F (' j ) describes nonlinear effects in the iron part, whereas < j (ο j ) is the air-gap reluctance. Figs. and show respectively the behavior of functions < j (x) and F (') as derived by experimental measurements. The force developed by a single EM on the valve can be calculated [5] by means of the D Alembert principle and it is equal to F mj = r ' j j where r l is an equivalent lever ratio and the force is intended in the versus of increasing air-gap thickness. The sign of the force developed by a single actuator does not depend on the sign of the flux. It can be noted that the () decomposition makes the force expression independent from F (' j ) and therefore from the magnetic saturation. The air-gap thickness ο j can be expressed as a function of the valve vertical position x, as follows. ο = r l x L ; ο = r l L + x where L is the valve vertical stroke, x [ L=;L=]. Hence the air-gap reluctances <(ο j )=k e k ο jλ + k ο j ; j =; () can be expressed as direct functions of the valve position x: <(ο ) = < (x) and <(ο ) = < (x). In the same way, the forces () delivered by EMs can be written as functions of x: F m ' F m ' where the F m versus has been changed to assume positive forces in the versus of increasing x. Fig. compares EM forces for different flux values to equivalent spring force. According to (5), (6) the EM deliver positive force, whereas the EM a negative one. It can be noted that there is a range of position where EMs forces are less than the spring one. Considering also mechanical equations, the complete dynamical model for the system is [6] _x = v» _v = ' _' = N [v ri ] _' = N [v ri ] (7)

3 TABLE I TABLE OF MODEL PARAMETERS Trajectory generation Symbol Value Units L 8 mm N 5 turns M : kg r : Ω r l :578 k Λ N/m b Ns/m k :598 Λ 6 k : Λ k : Λ 8 <( ) () and Fig. F ( ) Fig. Position reconstruction Fig.. Flux current measures - Control Scheme Feedback position controller Reluctance derivative + Force to flux conversion Flux controller v j where kx is the equivalent spring force, bv is the viscous friction force and M is the equivalent mass of the moving part of the system. Note that the effect of the gravity force is negligible with respect to the other applied forces. The numerical parameters of the considered valve are reported in Table I, where the electromagnet parameters refers to EM. III. VIRTUAL FLUX AND POSITION SENSOR A magnetic flux direct or indirect measurement represents a key point for this kind of system for the following reasons. ffl The knowledge of the flux allows to better exploit the model formulation (7) in developing a valve position controller based on cascade structure (see Fig. where a possible control scheme is depicted). In fact a direct control of the flux trajectory allows a simpler position control based on force command. ffl Using current and flux values, () can be rearranged in order to obtain the following algebraic expression of the position based on electromagnetic properties of the system: ^x j = <» Nij F (' j ) ' j ; j =; (8) Therefore a static position estimator can be obtained. A. Fluxes reconstruction The windings currents can be easily measured via shunt resistors. Differently, direct measurements of the fluxes in the two EMs by means of Hall sensors is difcult to realize owing to hostile working conditions, mechanical constraints and tight cost limits. Equation () could be integrated to determine indirectly ' and ', but this solution is unlikely due to windings resistance and power stage electrical parameter variations. To achieve better accuracy in flux reconstruction, a secondary coil is added on the EM for measuring purposes. The voltages v m and v m at the terminals of the above open circuits have the following relation with the fluxes: v mj = m _' j = m N [v j ri j ] j =; (9) Fig. 5. v mj Flux measure scheme ' j μc where m is the number of turns of the additional windings. Therefore the fluxes determination can be achieved via a modelindependent integration of v m and v m. No current flows in the measuring circuits and the number of turns m can be selected smaller than N in order to keep the voltage level in the admissible measuring range. Starting from secondary coil voltages, flux can be reconstructed as: ' j (t) =' + m Z t t v mj ( )d () where ' is the initial condition assumed for the flux. A detailed analysis shows that, owing to the switching nature of v j in (9), a sampling time lower than μs is required to accurately reconstruct ' j by means of digital integration, whereas the available sampling period is T s = 5 μs. Hence, the integration is performed by an analog circuitry and the result is acquired by the digital calculator, as outlined in Fig.5. Rewriting the () from the digital part point of view, it follows that ' j (kt s )=' rst + ' j (kt s ) () ' j (kt s )= m Z kt s t rst v mj ( )d where ' rst is the flux assumed anytime a reset is performed. A periodical reset is needed to reduce the effects of integration drift due to offsets and uncertainties. Reset is commanded by the microcontroller when electromagnet is in a known operating condition, i.e. zero current that corresponds to zero flux, so that the initial condition ' rst is known.

4 (Wb) x (m) v (m=s) 'j ^F=^F =@ ^F (m=a) x x x x 5 ' ' x t (s) Fig. 6. Typical trajectory to open the valve: x; v; ' ;' B. Position reconstruction Substituting the flux measures into (8), two values for the valve position are obtained. Looking at the form of (8), it is clear that the best measure is the one relative to the higher flux. In the next section it will be shown that a flux greater than about : mw b is needed to have an accurate position measure. Based on the previous considerations, the position reconstruction is performed through a logic procedure, that select the most accurate measure based on the electromagnetic status. Let j f; g be the index of the greater between ' and ', then ^x =^x j if ' j : mw b () ^x not available if ' j < : mw b Control algorithm must take into account these considerations. In order to achieve a suitably soft-landing to mechanical stops, a feedback controller must be performed and therefore an accurate position measure must be available. Fig.6 shows a trajectory to open a valve. It can be noted that fluxes are high near to mechanical stops and hence position measure is accurate. There is a time range in which flux can not be sufciently high, hence feedforward actions have to be performed to ensure that when the valve approach mechanical stop the flux value is suitable for position measure. Finally it is worth underlining that the accuracy of the proposed virtual position sensor is strongly related to the flux reconstruction quality and the knowledge of the air-gap reluctance and iron saturation curves. In order to quantify the previous considerations, sensitivity analysis is reported in the next section. IV. SENSITIVITY ANALYSIS The position measure (8) is affected by the following uncertainties: the functions F ( ); < j ( ) are identied but not exactly known, the flux measure is not ideal. In principle, also the current measures affect position reconstruction. For the sake of brevity, the corresponding analysis is not reported, since the relative sensitivity is smaller than the other ones. Equation (8) can be rewritten to enlighten (by means of a hat) the terms affected 5 x x x ' (Wb) Fig. 7. Sensitivity analysis respect to ^F at different positions (; ; ; mm) and maximum relative error admissible for ^F to keep x <μm; % of half range by uncertainties. ^y = Ni ^F (^') ^' = ^<(^x) ^x = ^< (^y) () where the index of the considered EM has been omitted. In the following subsections, the upper EM is considered. The same considerations can be made for the lower EM. A. Sensitivity analysis respect to ^F Taking into account () and deriving respect to ^F, it follows ^F = ^< ' ^< (^y) ^< = r lhk k e kr l( L x) + k i (5) Fig.7 shows the results of (). It can be noted that the higher the flux and the smaller the air-gap thickness the better the sensitivity is. Equation () can be used to approximately evaluate the maximum error that is admissible for ^F in order to keep the error on ^x under a certain maximum value x max. j ^x ^F ^F j» x max =)j ^F ^< ' x max Fig.7 shows the maximum relative error allowed for ^F to keep j x j < μm; % of half range. It can be noted that signicant errors can be accepted if position is sufciently high and flux less than mw b, that corresponds to the value that keeps closed the valve (see Fig. 6).

5 ^'= ^' ^< (m H) ^' (m=w b) ^<= ^< x x x x (m) Fig. 8. Sensitivity analysis respect and Maximum relative error admissible for ^< to keep x <μm B. Sensitivity analysis respect to ^< Taking into account () and deriving respect to ^<, it follows ^< = ^< ^< (^y) Fig.8 shows the results of (6). It can be noted that the lower the air-gap thickness the better the sensitivity is. Equation (6) can be used to approximately evaluate the maximum error that is admissible for ^< in order to keep the error on ^x under a certain maximum value x max. j ^x j' ^< ^< j ^< j» x max =)j ^< j» x max Fig.8 shows the maximum relative error allowed for ^< to keep x < μm. It can be noted that relevant errors are admissible only for positions greater than mm, when the valve is approaching the upper mechanical stop and a feedback control is needed. C. Sensitivity analysis respect to ^' Taking into account () and deriving respect to ^', it follows that ^' = "@ ^F + ^< ^' ^' ^< ^< (^y) Fig.9 shows the results of (7). It can be noted that the smaller the air-gap thickness the better the sensitivity is, whereas the flux should be sufciently high but not in the saturation range. Equation (7) can be used to approximately evaluate the maximum error that is admissible for ^' in order to keep the error on ^x under a certain maximum value x max. j ^x ^' ^'» x max x x ' (Wb) Fig. 9. Sensitivity analysis respect to ^' at different positions (; ; ; mm) and Maximum relative error admissible for ' to keep x <μm =)j ^' ^' x max Fig.9 shows the maximum relative error allowed for ^' to keep x < μm. Relevant errors can be admissible only for positions greater than mm and fluxes less than mw b, that corresponds to the value that keeps closed the valve (see Fig. 6). Looking at Figs. 7, 8, 9 it can be noted that, in the same conditions of flux and position, the maximum relative error acceptable on the flux measure is the lowest. This consideration justies the particular attention that has been devoted to the flux measurement. Considering Fig. 6 and the results of the sensitivity analysis, it can be stated that position measure is less affected by uncertainties when it is needed to perform a feedback control action to ensure soft-landing on the mechanical stop. In fact position measure is accurate near the mechanical stops, that correspond to the only conditions in which EMs are able to deliver signicantly forces to move the valve (see Fig. ). Hence the proposed flux and position sensor is suitable for the use in integration with the valve control. V. EXPERIMENTAL RESULTS In order to validate the considerations of the previous sections, some experimental tests have been performed. A typical result is presented in Fig., where interferometric laser output is compared with the position reconstruction. According to the relative flux values, the reconstruction by EM is selected for positions less than about mm, whereas the one by EM is chosen for positions greater than mm. In middle position fluxes are not sufciently high to ensure accurate position measure. However, the position reconstruction has been derived also for fluxes smaller than : mw b threshold to enlighten error under these operating conditions. Note the jump in position when switching between the two magnets for reconstruction is performed. The accuracy of position reconstruction is higher when EM is used: this is due to the fact that same model has been used for both EMs, whose parameters have been tuned on EM.

6 x (m) x t (s) Interferometric laser measure (dashed), position reconstruction (con- Fig.. tinuous) VI. CONCLUSIONS The paper discuss the possible use of a secondary coil as a mean to obtain flux and position reconstruction in a electromagnetic actuator for camless engine. This is a basic step in realizing feedback position control for achieving the soft-touch functionality in these actuators. The functional characteristics of position reconstruction and its accuracy seems to be compatible with the required applications. Integration within the feedback controller is a matter of current research and will be reported in future works. REFERENCES [] T. Ahmad, M. A. Theobald A survey of variable valve actuation technology, SAE paper, no. 8967, (989). [] M. M. Schechter, M. B. Levin Camless engine, SAE paper, no. 98, (998). [] M. S. Ashhab, A. G. Stefanopoulou, J.A. Cook, M. Levin Camless engine control for robust unthrottled operation, SAE paper, no. 9658, (996). [] S. Butzmann, J. Melbert, A. Koch Sensorless control of electromagnetic actuators for variable valve train, SAE paper, no. --5, (). [5] F. Filicori, C. Guarino Lo Bianco, A. Tonielli Modeling and control strategies for a variable reluctance direct-drive motor, IEEE Trans. Ind. Electron., volume, no., pp. 5 5, (Feb. 99). [6] Y. Wang, A. Stefanopoulou, M. Haghgooie, I. Kolmanovsky, M. Hammoud Modeling of an electromechanical valve actuator for a camless engine, Proc. AVEC, ()