A comparative study of the new LQMCS control on an automotive electromechanical system
ABSTRACT This paper is concerned with the design and comparison of a new optimaladaptive control of an electronic throttle body. Numerical results are complemented by experiments.

Conference Paper: Experimental validation of a novel adaptive controller for piecewise affine systems.
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ABSTRACT: This paper presents the first digital implementation of a novel model reference adaptive scheme for the control of piecewise affine circuits and systems. The control law is implemented by using a lowcost commercial microcontroller. The aim is to control a piecewiselinear electrical circuit. The experimental validation process is made challenging by the presence of measure uncertainties, noise, quantization errors, unmodelled nonlinear dynamics, computational delays. Moreover, a digital microcontroller is used to implement an analogue continuoustime control law. Nevertheless, experiments confirm the effectiveness of the controller to cope with switching in the circuit dynamics, establishing the strategy as a viable control tool.International Symposium on Circuits and Systems (ISCAS 2010), May 30  June 2, 2010, Paris, France; 01/2010  [Show abstract] [Hide abstract]
ABSTRACT: This paper is concerned with the design of a novel adaptive controller, namely the linear quadratic new extended minimal control synthesis with integral action (LQNEMCSI). We present for the first time the analytical proof of asymptotic stability of the controller and experimental evidence of the algorithm effectiveness for controlling an electronic throttle body: an element of any drivebywire system in automotive engineering, affected by many nonlinear perturbations.IEEE Transactions on Control Systems Technology 12/2010; · 2.00 Impact Factor
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A comparative study of the new LQMCS control
on an automotive electromechanical system
Mario di Bernardo∗, Alessandro di Gaeta†, Umberto Montanaro∗and Stefania Santini∗
∗University of Naples Federico II, Italy
Email: {mario.dibernardo, umberto.montanaro, stefania.santini}@unina.it
†CNR, National Research Council, Istituto Motori, Naples,Italy
Email: a.digaeta@im.cnr.it
Abstract—This paper is concerned with the design and com
parison of a new optimaladaptive control of an electronic throttle
body. Numerical results are complemented by experiments.
I. INTRODUCTION
In automotive systems, the accurate control of the injection
timing and the precise regulation of the air/fuel mixture is
essential in order to guarantee high performance with respect
to traction, emissions, idle speed regime, cold starting manage
ment, thermal transient and smoother movement during tip/in
tip/out [2]. The main idea is to directly effect the mixture
formulation by the electronic control of the fuel injection and
the exact regulation of the air flow in the manifold by an
Electronic Throttle Body (ETB)(see for example [1]).
In the ETB system, a shaped body duct imposes the rela
tionship between the throttle valve position and the incoming
air flow into the manifold, while the desired plate position is
imposed by a microcomputer in a drivebywire configuration.
The control signal generated by the ECU becomes, by means
of a Hbrige power converter, the armature voltage of a DC
motor. The rotation motion is then transferred from the motor
shaft to the plate shaft through a gear system (some details
are in figure 1).
From the control perspective, the ETB is an highly nonlinear
plant since the transmission friction and the return spring limp
home nonlinearity significantly affect the system performance.
Moreover the wide variations of process parameters, which
can be caused by production deviations, variations of external
conditions (e.g., temperature) and aging, demand for a con
troller which is robust against uncertainties. Another control
requirement is the simplicity of the strategy that has to be
implemented on a typical lowcost automotive microcontroller.
Furthermore the feedback loop is closed only on the measure
of the plate angular position via a low resolution sensor.
The aim of this paper is to use the innovative LQMCS
(Linear Quadratic Minimal Control Synthesis) control scheme
to control the ETB system. In particular, the dynamics of the
new control are contrasted with those of a more traditional PI
scheme, applied to the problem in [5] where the closedloop
performances are enhanced by the joint action of a non linear
compensator and a self tuning approach for tuning of the PI
gains.
The robustness of the PI controller is proven by experiments
on the actual plant. The comparative analysis between the two
control philosophies is instead performed by simulation adopt
ing a mathematical model able to reproduce the experimental
behavior of the plant.
II. MATHEMATICAL MODEL AND IDENTIFICATION
The ETB system, shown in figure 1, is composed by a DC
motor, a reduction gear and a plate equipped with two springs.
These springs, named respectively default and return spring,
are necessary to lead the plate to the home position in case of
failure. Notice that, for security reasons, when a fault happens
and the motor does not generate a driving torque anymore, the
valve has to come back to a default position, called limp home
position, so the driver can limp until to reach the nearest car
service in a safe way. Obviously the valve is not completely
closed at the limp home.
Fig. 1. Throttle Body scheme
By assuming an ideal reduction gear and applying the
Newton’s law to the mechanical subsystem and the Kirchhoff’s
laws to the electrical part related to the armature coil, the
mathematical model of the system can be derived as:
⎧
⎪
All the variable meaning and the related symbols can be found
in Table I.
The main nolinearity in the model is due to the friction
torque depending upon the low quality of the gearbox and
bearings. In engineering, friction plays an important role. It
is the source of selfsustained oscillations that often have
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
⎨
di
dt= −R
dωth
dt
dθ
dt= ωth
Li−Kv
=Kt
LGrωth+1
LGri−Tsp(θ)
Lva
−Tfric(ωth)
JJ
(1)
9781424416844/08/$25.00 ©2008 IEEE 552
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undesired effects in many areas of engineering [3]. The friction
in the ETB is a complex, nonlinear function of throttle angu
lar velocity which has been modeled by following different
approaches [10], [8], [11], [12]. Since it is important in
applications to conjugate simplicity with accuracy the friction
torque is modelled by assuming a Coulomb viscous Stribeck
function as (for further information see the relevant work of
Hensen [4]):
?
Another nonlinear effect also arises because the stiffness of
the default spring is always greater than stiffness of the return
spring. For this reason, the elastic torque is not simply a linear
function of all the admissible angles, but is a PWL (piecewise
linear) function given by:
Tfric(ωth) =
Tc+(Ts−Tc)e−ωth
ωs?
sign(ωth)+βωth.
(2)
Tsp(θ) =
⎧
⎪
⎪
⎪
⎪
⎩
⎨
Ks3
0
Ks1
Ks2
?θ−?θLH−Δθ
?θ−?θLH+Δθ
2
??−Tclose
??+Topen
if θ < θLH−Δθ
2≤ θ ≤ θLH+Δθ
if θLH+Δ
??+Topen
2
if θLH−Δθ
?ˆθ−?θLH+Δθ
2
22≤ˆθ
?θ−ˆθ?+Ks1
2
if θ >ˆθ
(3)
The parametric identification of the system model (1) on the
base of the experimental data has been performed by following
different approaches. In particular the parameters R, L, Kv, Kt
have been identified according to the procedures in the work
of Pavkvic et al. [13]. Values of the parameters J, β, Tc, ωs
have been estimated applying an optimization technique based
on a leastsquare algorithm. All the remaining parameters have
been derived by the knowledge of the experimental setup and
geometrical considerations.
The effectiveness of the identification procedure is shown
from the validation results in figure 2, where it is evident that
the model is able to capture the system behavior not only in
steadystate conditions, but also during the valve opening and
closing.
Fig. 2.
experimental data(dotted line) and model predictions (solid line). Results refer
to a triangular shaped input voltage.
Time history of the plate angular position. Comparison between
III. PI CONTROL
The experimental setup is composed by the throttle body, the
DC motor, the microcontroller and the DC power converter.
The DC power converter is based on the integrated circuit
TC4422, a diode RHRP15120, a mosfet IRFBF4710 (rise time
of 30[ns]) and a 4700[pF] capacitor. The control law has
been discretized and then implemented in a low cost micro
controller PIC PIC16F877A (RAM 368 byte, EEPROM 256
byte, maximum clock frequency 20[MHz]).
The design of the control scheme is based on a simplified
linearized version of model (1) derived under the following
assumptions:
1) the plateposition usually
?
simply reduces to Ks1
θ−
2) the friction action is given only by the term βωth(see
eq. (2))
The control loop, shown in figure 3, is composed by a
PI controller acting on the error between desiderated and
actual plate position and a model based feedforward action
to compensate nonlinear effects. The presence of a reference
governor, which is essentially a Smooth Trajectory Generator,
helps to reduce errors during rapid transients, while a filter
on the output reduce the noise on the feedback signal. The
worksintherange
θLH+Δθ
2,ˆθ
?
, thus the elastic force in equation (3)
??
θLH+Δθ
2
??
+Topen
Fig. 3. Control scheme
PI gains are tuned in order to ensure a phase margin for
the control system so that it is robust with respect to a
delay of 4ms determined by the ECU sampling time. The
parameters of the transfer functions of the output filter and
the STR filter are tuned heuristically by tacking into account
the main frequencies of the signals in the close loop system,
the necessary degree of attenuation of noise in the measured
signal, and the desiderate response of the closedloop plant.
The feedforward action is designed, starting form the friction
and the elastic torque models in eqs. (3)(2) and the effective
reference signal θrif, as:
Af f=?Tsp(θrif)+Tssign?˙θrif
The effectiveness of the proposed control scheme is verified
via experiments. Performances are summarized in figures 4
and 5 where the controlled signal well tracks the reference,
respectively a piecewise constant and a sawtooth signal. Notice
the presence of the delay in figure 5.
?+β?˙θrif
??
R
KtGr.
(4)
IV. LQMCS CONTROL SCHEME
The main disadvantages of the PI control are the time con
suming tuning of the control parameters and the impossibility
553
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Fig. 4.
results: plate angular position (blue solid line) against the PWC (piecewise
constant) reference signal.
Time history of the closedloop plate angular position. Experimental
Fig. 5.
results: plate angular position (blue solid line) against the sawtooth reference
signal.
Time history of the closedloop plate angular position. Experimental
to guarantee some optimality in the closedloop performances.
In order to overcome the drawbacks of the PI controller, we
propose an optimaladaptive model reference approach. This
control algorithm extends the family of the Minimal Control
Synthesis schemes [14], [15], [16].
The main idea is to integrate the classical LQ optimal
control approach with the MCS (Minimal Control Synthesis)
algorithm. In so doing we try to achieve the optimal perfor
mances of classical LQ control schemes while maintaining the
simplicity of use of the MCS algorithm and its benefits. The
MCS scheme is implemented on the actual plant by selecting,
as a reference model, the nominal model of the plant controlled
via a classical LQ optimal strategy, i.e. choosing the input to
reference model (um(t) in figure 6) as an optimal control input.
In so doing any mismatch between the nominal model and the
actual plant will be compensated by the adaptive action of the
MCS, which will also guarantee stability in those cases where
the LQ strategy alone would fail.
Figure 6 describes the LQMCS scheme. Further details,
proof of asymptotic stability based on the passivity theorem,
and performances of the controller on a representative case of
study can be found in [17], [9].
For the design of the ETB control via LQMCS, a linear
model is selected as nominal plant. Notice that it is the
same derived in section III for the PI synthesis. The weight
Fig. 6.LQMCS control scheme.
matrices Q and R are chosen to guarantee that bandwidth of
the reference model is equal to the closedloop plant controlled
via PI. Since the LQMCS control is a full state control, but
the velocity measure is not available in the actual plant, it is
necessary to derive the velocity information from the angular
potion measurement. To this aim a thirdorder Butterworth
filter is used, that ensures a zero phase offset in the useful
band and the maximum rolloff outside. The bandwidth of
the filter is tuned taking in account the tradeoff between the
accuracy of the reconstruction and the constraint imposed by
its numerical implementation.
Figure 7 shows the good matching between the LQ refer
ence model and the nonlinear model plant when the LQMCS
control is active.
Fig. 7.
signal; dotted line: output of the optimal reference model; solid line: plant
output
Closedloop system under LQMCS control. Dashed line: reference
The comparison results between the LQMCS and the PI
performances are reported in figure 8. It is noteworthy to high
light the importance of the feedforward action that improves
the tracking of the reference signal when the PI controller
is active. Notice that the exact compensation of all the plant
nonlinearities is impossible, since the parameters of the plant
change due to mechanical wear. for this reason, results suggest
the adaptive approach can be extremely useful to obtain zero
error in steady state regime even without compensation.
V. CONCLUSION
In this paper we have highlighted the advantages provided
by ETB control and related problems. In order to merge
optimality with robustness the use of a optimal adaptive
scheme, named LQMCS, is proposed. The effectiveness of
554
Page 4
Fig. 8. Comparison between PI control and LQMCS algorithm. Time history
of the reference signal (black dotted line) v.s. the plant output in the case of
the PI control without feedforward action (green dotted dashed line), the PI
control strategy with feedforward action (red dashed line) and the LQMCS
without feedforward action (blue solid line).
TABLE I
NOMENCLATURE
symbol
i[A]
ωth[rad/s]
θ[rad]
[θmin,θmax]
va[V]
R[Ω]
L[H]
Kv[Vs/rad]
description
armature current of the DC motor
plate velocity
plate angular position
minimum and the maximum plate position angles allowed
source voltage across the coil of the armature
equivalent armature coil resistance of the DC motor
equivalent armature coil inductance of the DC motor
velocity constant determined by the flux of the permanent
magnets into the DC motor
torque constant of the DC motor
gear ratio of the reduction gear
moment of inertia of the plate and motor
friction torque
Coulomb friction torque
stiction friction torque
Stribeck velocity
damping coefficient
elastic torque
stiffness coefficients in each region of interest
minimum torque to close the valve
minimum torque to open the valve
limp home position
clearance between the teeth of the gear
discontinuity point of the slope of the elastic torque
Kt[Nm/A]
Gr
J[Kgm2]
Tfric[Nm]
Tc[Nm]
Ts[Nm]
ωs[rad/s]
β[Nms/rad]
Tsp[Nm]
[Ks1,Ks2,Ks3]
Tclose[Nm]
Topen[Nm]
θLH[rad]
Δθ[rad]
ˆθ[rad]
the control action is verified by simulation results. Moreover
the performance of the proposed strategy has been compared
to the one achievable through a simple PI regulator.
VI. ACKNOWLEDGEMENTS
A special thank to Mario Vaccaro, a recent graduated in
Control Engineering at the Universit` a degli Studi di Napoli
Federico II, for his contribution in settingup the PI controller.
The next step in the future will be the experimental
verification of the LQMCS on the ETB problem.
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