Robust Discrete-Time MRAC With Minimal Controller Synthesis of an Electronic Throttle Body

524 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 19, NO. 2, APRIL 2014

Robust Discrete-Time MRAC With MinimalController Synthesis of an Electronic Throttle Body

Umberto Montanaro, Alessandro di Gaeta, Member, IEEE, and Veniero Giglio, Member, IEEE

Abstract—The electronic throttle body (ETB) is a fundamentalactuator for regulating the air mass coming into an internal com-bustion engine; hence, it is used to control the engine torque inany modern drive-by-wire configuration. To cope with the non-linear and discontinuous dynamics of this automotive device, inthis paper a novel discrete-time model reference adaptive control(MRAC) method is designed and experimentally tested on an ETBinstalled on a 2-L engine. The control strategy extends the class ofthe minimal control synthesis (MCS) algorithms for discrete-timesystems by adding an explicit discrete-time adaptive integral actionand an adaptive robust term. An in-depth experimental investiga-tion shows that the proposed control method is a viable solution asit is robust with respect to nonlinear torques acting on the plant,and it guarantees better performance than those provided by otherMRAC strategies especially for small reference signals around thelimp-home position where plant nonlinearities strongly affect theETB dynamics.

Index Terms—Automotive control, discrete-time model refer-ence adaptive control, electronic throttle body (ETB).

I. INTRODUCTION

THE electronic throttle body (ETB), see Fig. 1, is a mecha-tronic device dedicated to the regulation of the air mass

flow rate breathed by an internal combustion engine. Hence, itplays a fundamental role in the regulation of the engine torqueand the formation of pollutant emissions. These are the mostimportant engine variables to be controlled to meet both thedemanding engine performance, required by customers in termof drivability, and the emission constraints imposed by the in-creasingly restrictive emission standards [1], [2].

In the ETB system, a shaped body duct regulates the rela-tionship between the angular position of the throttle valve andthe air mass flow rate coming into the manifold. The referenceplate position is then designed by practitioners to solve a trade-off between the driver request (acceleration pedal position) andthe effective traction possibilities depending upon drivability,safety, and emission constraints.

The reference plate position is imposed by the electroniccontrol unit (ECU) in a drive-by-wire configuration. Precisely,the control signal generated by the ECU becomes, by means

Manuscript received April 12, 2012; revised October 25, 2012; acceptedJanuary 15, 2013. Date of publication March 11, 2013; date of current versionFebruary 20, 2014. Recommended by Technical Editor G. Herrmann.

The authors are with the Istituto Motori, National Research Council,Naples 80125, Italy (e-mail: [email protected]; [email protected];[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMECH.2013.2247614

Fig. 1. ETB: (a) picture and (b) schematic of the system.

of an H-bridge power converter, the armature voltage of a dcmotor. A couple of springs located on the ETB device assurethat when there is a failure of the dc motor the valve comes backto a safety position, named limp-home position. The limp-homeangle corresponds to the supply of a small amount of air intothe engine. This ensures that the throttle valve is not completelyclosed thus allowing the driver to “limp” until it reaches thenearest car service.

Despite its apparent simplicity, the behavior of the ETB is af-fected by many nonlinearities and aerodynamic disturbances [3]that can alter the ETB dynamics. Unwanted phenomena, likestick-slip, hysteresis, hunting limit cycles, and impacts, makethe tracking of a given reference a challenging control task(see [4] for the experimental evidence of the ETB nonlinearbehavior). Solving the control problem becomes even morearduous for reference signals around the limp-home positionwhere the elastic torque provided by the restoring springs canbe well approximated on a macroscopic scale as a piecewiselinear discontinuous function. Furthermore, the discontinuousfriction can jeopardize the closed-loop performance especiallywhen small variations of the plate position have to be carriedout.

Unfortunately, small variations of the plate position aroundthe limp-home are of great interest from the applicationviewpoint as they are required by ECUs when sophisticated

1083-4435 © 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

MONTANARO et al.: ROBUST DISCRETE-TIME MRAC WITH MINIMAL CONTROLLER SYNTHESIS OF AN ELECTRONIC THROTTLE BODY 525

high-level controllers, e.g., idle speed controllers [5], are imple-mented with the aim of improving fuel economy and reducingpollutant emissions. Another important issue when dealing withthe control of the ETB is the uncertainty affecting the systemparameters due to manufacturing tolerances, variable operatingconditions, or mechanical wears [6]. In addition, simple controlstrategies are required for solving the ETB control problem sothat they can be implemented in the ECUs with turnaround timessmaller than those required by the other engine control tasks.

The technical literature on the ETB is vast and often con-trollers with fixed gains have been proposed to tame its complexelectromechanical dynamics. For example, advanced controllersranging from model predictive control [7] to observer-basedcontrollers [8], [9] can be found.

Even though model-based strategies are efficient in control-ling the ETB device, their performance strongly relies on theknowledge of the plant model. Hence, their robustness with re-spect to disturbances and parameter variations is a critical issue.Furthermore, a satisfactory parameter identification of the ETBplant required by those strategies is time consuming and needsto be customized for just a single product.

To recover robustness, sliding-mode techniques [10]–[12] androbust controllers [6] can be used. On the other hand when suchstrategies are implemented, particular care has to be paid topossible onset of chattering on the control variable due to thediscontinuous nature of the control action. For example in [10],the control law is smoothed by continuous approximations ofthe signum function. This solution introduces boundary layersaround the sliding surfaces, so that vanishing steady-state errorscannot be guaranteed. An alternative way to solve the chatteringproblem is the use of second-order sliding-mode concepts, e.g.,the twisting algorithm in [11], or the integral-type switchinggain in [12]. Another issue regarding sliding-mode schemes isthat they require a high computational power due to the smallsampling time used for their implementation [8].

To tackle the ETB problem, control systems based on neuralnetwork [13] and fuzzy logic [14] also have been proposed. Inthis case, the storage for learning is the main drawback for thosestrategies as it is too large to be implemented on microcontrollersystems available for automotive applications [8].

To deal with uncertainties and nonlinear dynamics with a rea-sonable computational effort, it seems reasonable to implementsimple but robust adaptive control strategies where the controlgains are varied, or better adapted, according to the actual sys-tem behavior. Unfortunately, to our knowledge, only few andcustomized attempts in this direction are available in the tech-nical literature. In [15]–[17], different control algorithms basedon self-tuning PID strategies augmented with nonlinear com-pensators have been presented. From an engineering viewpoint,these strategies are effective and they indicate the need for moreflexible controllers for taming the ETB dynamics. On the otherhand, for these strategies only the plant parameters can be un-known, and a model of the ETB is required for their practicalimplementation. Moreover, robustness to aerodynamic torque,caused by pressure waves in the intake manifold, has not beeninvestigated as the ETB was not coupled to engine. Anotherdrawback is from a theoretical viewpoint, a consistent proof of

stability of the time-varying closed-loop systems is missing. Adifferent adaptive strategy has been proposed in [18], where again-scheduling PID is designed. Precisely, the adaptive mech-anism is given by a static map that maps the variation of thereference plant position onto the control gains. In this case, thestability of the resulting linear parameter varying closed-loopsystem is proven by studying the feasibility of a set of LMIs. Un-fortunately, as mentioned by the authors in [18], this approachrequires several experiments for the tuning of the control maps.

Recently, innovative and effective model reference adaptivecontrol (MRAC) methods based on the minimal control syn-thesis (MCS) algorithm have been proposed for generic LTIsystems affected by nonlinear disturbances [4], [19], [20], [21],[22], [23], [24] and for the control of switched systems [25]and piecewise affine systems [26]–[29], [36]. These strategieshave the advantage of not requiring a precise knowledge of theplant model or its parameters. Furthermore, their adaptive mech-anisms for updating the control parameters are simple; hence,they are particulary suitable for implementation in commercialECUs. Even though MCS algorithms have shown to be robustwith respect to the ETB nonlinearities, performance requiredby the automotive industry is not fulfilled in some operatingconditions, especially around the limp-home region.

This study proposes the first extension of the discrete-timeMCS algorithm recently presented in [30] by adding to the MCScontrol law an explicit adaptive discrete-time integral action andan adaptive robust term.

As in the continuous-time case [4], the advantage of introduc-ing these further control actions is the compensation of nonzeromean bias terms of the plant not only in steady-state condi-tions, but also during transients. On the other hand, as the novelcontrol action is directly designed in the discrete-time domain,stability issues due to the discretization of the adaptive mech-anism, which are typical when implementing continuous-timeMCS strategies as digital controllers [31], cannot arise. Hence,the resulting control algorithm, named discrete-time enhancedMCS (DEMCS), inherits the advantages of the continuous-timeand the discrete-time MCS methods and overcomes their limi-tations. We point out that different from the adaptive methodspresented in the literature [15]–[18], our algorithm is a directadaptive scheme and it does not require characterization of theETB nonlinearities. Furthermore, its applicability is not limitedonly to this automotive device as it is derived for generic systemsaffected by bounded disturbances.

After proving from an analytical viewpoint, the effectivenessof the DEMCS to tame the dynamics of a generic n-dimensionalLTI system with unknown parameters and when subjected toa bounded disturbance, its performance is experimentally as-sessed on a commercial ETB device.

To prove that the novel adaptive control algorithm is a viablesolution to steer the complex ETB dynamics in real scenarios,the experimental investigation is carried out on an ETB devicemounted on a 2-L gasoline engine. In doing so, the controllerhas to tackle not only the ETB nonlinearities, as friction andlimp-home effect, but also the aerodynamic torques due to in-take manifold pressure variations, which act on the system asa persistent time-varying disturbance. Furthermore, an in-depth


TABLE INOMENCLATURE RELATED TO THE DEMCS ALGORITHM

experimental analysis reveals that the DEMCS provides superiorperformance with respect to other MCS strategies and anotherrobust MRAC method previously proposed in the literature,especially around the limp-home region. Precisely, the compar-ison with other MCS strategies is used to confirm that the novelMCS algorithm is not just a theoretical extension of the MCScontrollers, but also is the most promising solution for imposingdemanding performance to complex plant dynamics, as those ofthe ETB device, with a minimal knowledge of the plant modeland its parameters. The comparison with another robust MRACalgorithm is instead exploited to show that better closed-loopperformance is achieved not only when the novel control strat-egy is compared with that of the same family, but also when itis compared to a well-known adaptive MRAC algorithm with adifferent design.

The experimental comparison is carried out in terms ofperformance indexes that are interesting from an automotiveviewpoint.

II. DEMCS ALGORITHM

The novel discrete-time MCS algorithm solves the model ref-erence adaptive control problem for discrete-time LTI systems incontrol canonical form when the plant parameters are unknownand the plant dynamics are affected by a bounded nonlinear un-known disturbance. Namely, given a plant of the form (see alsoTable I for a nomenclature of the following symbols)

x(k + 1) = Ax(k) + Bu(k) + f(x(k), k) (1)

where the system matrices are in control canonical form, i.e.,

A =

⎡⎢⎢⎢⎢⎣

0 1 . . . 00 0 . . . 0...

......

...0 0 . . . 1

−a1 −a2 . . . −an

⎤⎥⎥⎥⎥⎦

B =

⎡⎢⎢⎢⎢⎣

00...0b

⎤⎥⎥⎥⎥⎦

, b > 0 (2)

and f(x(k), k) ∈ Rn

f (x(k), k) = [ 0 0 · · · 0 d(x(k), k) ]T (3)

where d(x, k) models bounded unknown disturbances and un-modeled nonlinear perturbations (i.e., |d(x(k), k)| < D with Dan unknown positive constant).

The control objective is to impose to system (1) the dynamicsof a given asymptotically stable reference model

xm (k + 1) = Am xm (k) + Bm r(k) (4)

where the system matrices, Am and Bm , are in the same canon-ical form as those of the plant.

The control action provided by the DEMCS algorithm is

u(k) = uMCS(k) + uI (k) + uE (k) (5)

with

uMCS(k) = L(k)x(k) + LR (k)r(k) (6a)

uI (k) = LI (k)xI (k) (6b)

uE (k) = LE (k) sgn(ye(k + 1)) (6c)

and the adaptive gains computed as

L(k) = α

k∑i=0

ye(i + 1)xT (i) + βye(k + 1)xT (k) (7a)

LR (k) = α

k∑i=0

ye(i + 1)r(i) + βye(k + 1)r(k) (7b)

LI (k) = αI

k∑i=0

ye(i + 1)xTI (i) + βI ye(k + 1)xT

I (k) (7c)

LE (k) = ρ

k∑i=0

|ye(i + 1)| (7d)

where α, β, αI , βI , and ρ are positive scalar weights

xI (k) =k∑

i=0

xe(i) (8)

is the integral tracking error, and

ye(k) = BTe Pxe(k), xe(k) = xm (k) − x(k) (9)

where Be = [ 0 . . . 0 1 ]T ∈ Rn and P is a symmetric pos-itive definite matrix so that

ATm PAm − P = −Q, Q = QT > 0. (10)

Notice that equation (10) is always feasible as the referencemodel (4) is asymptotically stable by assumption.

Remarks:1) The control action in (6a) is that proposed in [19], [22],

and [30]. Hence, we extend the discrete-time MCS strategyby adding an explicit adaptive integral control action, i.e.,uI (k) in (6b), and an adaptive control action based on thesignum of the tracking error, i.e., uE (k) in (6c). Differentfrom [19], [22], and [30] in our problem formulation, we


consider an unknown perturbation term, f(x(k), k), thatpersistently acts on the plant dynamics.

2) The control action here proposed is the discrete-time coun-terpart of that presented in [4]. In doing so, unwantedphenomena that can arise when implementing MCS al-gorithms as digital controllers are avoided (see [31] fordetails on the possible onset of instability and unwantedovershoots emerging in closed-loop when the continuous-time MCS adaptive mechanism is discretized via standarddiscretization methods).

3) The adaptive mechanism (7) at the time k needs the knowl-edge of the output tracking error at the time k + 1, namelyye(k + 1). This problem, known in the model referenceadaptive control literature as one-delay problem, can besolved by estimating the sample ye(k + 1) with effectivemethods as those proposed in [32] and [30].

4) Similar to the discrete-time MCS in [19], [22], and [30],the DEMCS also can be applied to continuous-time sys-tems when the forward Euler method is used for their dis-cretization. We note that, even though the forward Eulermethod does not guarantee the stability of the discretizedplant, it is not restrictive as the DEMCS strategy can beapplied also to unstable plants and the stability of the dis-cretized reference model can always be assured as it ischosen by the designer.

III. PROOF OF STABILITY

The proof lies in showing that the closed-loop error dynam-ics can be rewritten as an asymptotically hyperstable feedbacksystem, thus guaranteeing the asymptotic convergence of thetracking error to zero [32], [33].

Taking into account the canonical structure of the systemmatrices, after some algebraic manipulations the tracking errorsystem can be recast as

xe(k + 1) = Am xe(k) + BeΨ(k + 1) (11a)

ye(k) = BTe Pxe(k) (11b)

where

Ψ(k + 1) = φ(k)w(k) − [d(x, k)

+ bLE (k)sgn(ye(k + 1))] (12a)

w(k) = [xT (k) r(k) xTI (k) ]T (12b)

φ(k) = [ ΦX (k) ΦR (k) ΦI (k) ]T =

= [φ1(k) . . . φn (k) . . . φ2n+1(k) ] (12c)

with ΦX (k) = BTe (Am − A) − bL(k), ΦI (k) = −bLI (k) and

ΦR (k) = bm − bLR (k), where bm is the last entry of Bm .System (11a) and (11b) is the negative feedback interconnec-

tion of an LTI block with dynamic matrix Am , input matrix Be ,and output matrix BT

e P ; while the feedback path is a nonlin-ear time-varying block that maps ye(k) to −Ψ(k) (see Fig. 2for a schematization of the tracking error system). Accordingto [32], system (12) is an asymptotically hyperstable system ifthe feedforward block is strictly positive real and the feedback

Fig. 2. Closed-loop error dynamics represented as an equivalent feedbacksystem.

block satisfies Popov’s inequality, i.e.,

l∑k=0

−ye(k + 1)Ψ(k + 1) ≥ −c2 , c ∈ R (13)

with l being a generic time instant.In our case, the feedforward path is the same as that in [19],

[22], and [30]; hence, its strictly positive realness can be provedin the same way. On the other hand, the presence of the integraland the robust adaptive terms makes the feedback path differentfrom that in [22] and [30]; therefore, it is necessary to show thatPopov’s inequality is fulfilled also for the DEMCS algorithm.

To this aim, we note that the summation (13) can be decom-posed as follows:

l∑k=0

−ye(k + 1)Ψ(k + 1) =2n+1∑j=1

Sj (l) + SE (l), (14)

with

Sj (l)�=

l∑k=0

−ye(k + 1)φj (k)wj (k), (15)

and

SE (l)�=

l∑k=0

ye(k + 1) [d(x, k) + bLE sgn(ye(k + 1))]. (16)

We note that inequality (13) is satisfied if each term Sj , j =1, . . . 2n + 1, and SE can be made greater than some constants.

Taking advantage of the integral–proportional form of theadaptive gains (7), the generic component φj (k) of the vector φin (12c) can be decomposed as φj (k) = φαj (k) + φβj (k), j =1, . . . , 2n + 1, where the integral and the proportional adaptivecomponents are, respectively

φαj (k) = φαj (k − 1) − bαj ye(k + 1)wj (k) (17)

φβj (k) = −bβj ye(k + 1)wj (k) (18)

with the pair (αj , βj ) being

(αj , βj ) ={

(α, β), j = 1, . . . n + 1(αI , βI ), j = n + 2, . . . 2n + 1.

(19)

Now, from (17) and (18), we have −ye(k + 1)wj (k) =[φαj (k) − φαj (k − 1)] α−1b−1 = φβj β

−1b−1 and we substi-tute them into (15). After some algebraic manipulations, thegeneric term Sj (l) can be written as


Sj (l) =1

bαj

l∑k=0

φαj (k) [φαj (k) − φαj (k − 1)]

+1

bβj

l∑k=0

φ2βj (k). (20)

In what follows, given a generic vector η =[η1 η2 · · · ηm ]T ∈ Rm we define as Γ (η) the m-dimensionalvector

Γ (η) = [ 0 η1 η2 · · · ηm−1 ]T . (21)

Notice that, from (21), it is easy to show that

‖Γ (η)‖ � ‖η‖ (22)

where ‖·‖ is the Euclidean norm.By using definition (21), we have

Sj (l) =1

bαj

[‖Φαj‖2 − ΦT

αjΓ (Φαj ) − φαj (0)φαj (−1)]

+1

bβj

l∑k=0

φ2βj (k) (23)

with Φαj = [φαj (0) . . . φαj (l) ]T .Exploiting the Schwarz inequality and (22), the following

inequalities hold:

ΦTαjΓ (Φαj ) ≤

∣∣ΦTαjΓ (Φαj )

∣∣ ≤ ‖Φαj‖ ‖Γ (Φαj )‖ ≤ ‖Φαj‖2

(24)hence,

−ΦTαjΓ (Φαj ) ≥ −‖Φαj‖2 ⇒ ‖Φαj‖2 − ΦT

αjΓ (Φαj ) ≥ 0.(25)

From (23) and (25) we obtain

Sj (l) ≥ − 1bα

|φαj (0)φαj (−1)| := −c2j . (26)

Now, let’s focus on the SE -term in (16). Rewriting ye(k + 1) asye(k + 1) = |ye(k + 1)|sgn(ye(k + 1)), we have to prove that

SE (l) =l∑

k=0

b|ye(k + 1)|[d(x, k)

bsgn(ye(k + 1))

+LE (k)]≥ −c2

E (27)

with cE some constant.From the definition of the adaptation mechanism of LE in

(7d), it is apparent that the gain evolution is monotonouslyincreasing. Hence, for a given constant M > 0, there existsa time instant, say k∗ ∈ N, so that LE (k) > M for all k ≥ k∗.

Here, we set M = D/b > max(|d(x, k)|)/b ∀k, and we de-compose the SE -term as

SE (l) = SE0 + SE1 (l) (28)

where

SE0 =k ∗−1∑k=0

b|ye(k+1)|[d(x, k)

bsgn(ye(k+1))+LE (k)

](29a)

SE1 (l) =l∑

k=k ∗

b|ye(k+1)|[d(x, k)

bsgn(ye(k + 1)) + LE (k)

].

(29b)

Because the latter summation starts from k� , we have SE1 (l) >0, while from (29a) it is apparent that SE0 is a finite value.Hence,

SE (l) ≥ −|SE0 | := −c2E . (30)

The fulfillment of (26), j = 1, . . . , 2n + 1, and (30) impliesthat also (13) is verified. Consequently, the closed-loop stabilityis guaranteed in accordance with the hyperstability Theorem in( [32], Th. C-4, p. 386).

IV. DESIGN OF THE DEMCS ADAPTIVE

CONTROLLER FOR THE ETB

A. Fulfillment of the control canonical form assumption

The first step for the design of the DEMCS adaptive con-troller is to verify if the plant dynamics match the hypothesisof control canonical form. Appendix A shows how a complexthird-order nonlinear and discontinuous model of the ETB canbe roughly described as a second-order system in the requiredcanonical form (1), where x = [θth ωth ]T , with θth and ωth ,being the plate position and the velocity, respectively, and thecontrol input u = va with va being the armature voltage of thedc motor. Here, we just point out that in the case of the ETB,the disturbance term f(·) of model (1) is strongly nonlinear dueto the discontinuous characteristic of the restoring torque andthe friction torque, possible plant parameter variations, and thenonlinear aerodynamic torque caused by the operation of theengine.

B. Control Specification

The achievable control specifications obviously depend onthe admissible performance of the adopted hardware, and essen-tially they are related to requirements on the system dynamicresponse. Here, we set the control objectives similar to thosein [6] as

1) the settling time is required to be 130 ms for a valveopening (notice that the settling time is defined as theminimum time after which the throttle plate angle remainswithin 5% of its steady-state value);

2) no overshoot should be present in the step response (fur-thermore, the throttle plate shall never hit the mechanicalend-stroke);

3) the average value of the steady-state tracking error is setto be 0.1◦; and

4) the maximum absolute dynamic error should be less than7◦.

Furthermore, the control system should be robust to variationsof the plant parameters, and the controller synthesis should besimple and automated as much as possible [7].


C. Details on the Implementation of the DEMCS Strategy

In implementing the control action (5), the following issueshave to be considered.

1) To satisfy control specifications “1” and “2” inSection IV-B, we select as reference model a second-ordersystem with real eigenvalues, unitary gain, and settlingtime of 130 ms.

2) The reference model is discretized with a sampling time Ts

of 1 ms, which guarantees asymptotically stable discrete-time reference dynamics, and it is often used in mod-ern ECUs for the implementation of control tasks. Wenote that, the choice of the sampling time does not af-fect closed-loop performance till the resulting discretizedreference model is asymptotically stable, as this is theonly assumption required by the DEMCS strategy for itsapplicability to systems in control canonical form.

3) The one-delay problem is solved estimating ye(k + 1) asin [30] and [32].

4) As usually happens when implementing the MCS strat-egy [24], the scalar quantities, which modulate the adap-tive gains in (7), have to be chosen heuristically as atradeoff between convergence time and reactivity of thecontrol action. According to the MCS empirical rule, weset β/α = 0.1. For reducing further the control parame-ters, we use the same rule for the integral weights, i.e.,βI /αI = 0.1, and we set αI = ρ = α. In doing so, onlythe parameter α has to be selected for tuning the entirecontrol action. Here, we have chosen α from a finite setso that the mean value of the tracking error is minimized.This value is approximately 1.2.

5) The presence of the switching function in (6c) introduceschattering (high-frequency switching of the control sig-nal). To avoid this unwanted phenomenon, the discontin-uous control action has be smoothed as

uE (k) = LE (k)ye(k + 1)

|ye(k + 1)| + ε(31)

where ε is a sufficiently small positive constant to be prop-erly chosen. Here, we have set ε = 10−3 .

6) A first-order filter as smooth trajectory reference (STR) isintroduced to limit the tracking error during rapid varia-tions of the reference signal [6].

7) Locking of the adaptive gains was implemented. In par-ticular, the adaptive gain LE of the robust action is frozenwhen it exceeds 15 % of the maximum allowable voltagevalue, i.e., the battery voltage.

V. EXPERIMENTAL RESULTS

The adaptive DEMCS algorithm has been tested on a commer-cial ETB (DV-E5, Bosch) installed on a 2-L naturally aspiratedgasoline engine. (Further details on the experimental rig can befound in Appendix B.)

The reference input to the control system is formed by con-catenating signals listed in Table II and it comprises square,sinusoidal, and step functions with different amplitude, bias,and frequency and it lasts about 23 min.

TABLE IISIGNALS THAT COMPOSE THE INPUT TO THE REFERENCE MODEL

Fig. 3. Experimental results: (a) engine speed; (b) intake manifold pressure;(c) intake manifold pressure for small plate positions; (d) Adaptive Gains, LR

(the dashed red line), L (the black solid line), LE (the dotted-dashed blue line),and LI (the dotted green line).

In particular, signal 26 is a sequence of steps of amplitude 15◦

starting from 15◦ and ranging to a maximum of 90◦ and back,while signal 28 is a sequence of steps of amplitude 5◦ startingfrom 10◦ and ranging to a maximum of 90◦ and back.

Over the long maneuver, the engine speed varies asshown in Fig. 3(a), which includes accelerations, decelera-tions, and engine speeds that are typical at idle speed regime


Fig. 4. Experimental results for wide throttle opening (Square wave with amplitude 35◦, bias 55◦, and period 5 s). (a) Angular plate position: θm , reference platetrajectory (the dashed red line), and θth , plate position (the black solid line). (b) Tracking error . (c) Controller output voltage.

Fig. 5. Experimental results when the reference input is a sinusoidal wave with amplitude 25◦, bias 55◦, and period 6 s. (a) Angular plate position: θm , referenceplate trajectory (the dashed red line), and θth , plate position (the black solid line). (b) Tracking error . (c) Controller output voltage.

(800-1000 r/min). Variations of the throttle plate position and ofthe engine speed induce those of the intake manifold pressure asshown in Fig. 3(b). These pressure variations act in turn on theplate of the ETB as an aerodynamic torque [3]. When the timeincreases, the control gains evolve as shown in Fig. 3(d) caus-ing an increasingly better tracking of the reference trajectory.As always happens in the practical implementation of adap-tive strategies, unavoidable presence of the residual mismatchprevents the convergence of the adaptive gains toward a finalsteady-state value [34]. In this specific case, the adaptive gainsincrease more when the valve plate is driven under the limp-home position (see signals 29–32 in Table II located at the endof the maneuver) to reject the nonsmooth stiffness characteristic(see Appendix A for its modeling). Furthermore, as shown inFig. 3(c), in this working condition the intake manifold pressureis much smaller than the ambient pressure (1000 mbar); and asa consequence, the disturbance due to the aerodynamic torqueis higher [3].

We point out that to keep the values of adaptive gains bounded,parameter projection and sigma modification methods [34], [35]can be used for large-scale production.

In what follows details on the tracking performance are givenfor some reference signals of automotive interest.

Fig. 4 shows the experimental results for a wide openingand closing maneuver that is required to open and close thevalve over a position range of about 70◦. This is a challengingproblem as the restoring torque slope changes on the basis ofthe actual plate position (see Appendix A for the restoring forcecharacteristic). Despite the lack of an explicit modeling of thespring torque, experiments confirm that the adaptive controllerdoes guarantee good tracking performance in this operatingcondition. Note that the maximum tracking error is below 7◦

during transients and it becomes less than 0.1◦ at steady state.Furthermore, as apparent from Fig. 4(a), the plate can be drivenclose to the end-stroke of the valve without any impact for thebenefit of the lifespan of the component.

We present next a sinusoidal maneuver. The complexity hereis to prevent the valve from getting stuck due to friction when theplate velocity changes the sign (see [4] for the experimental evi-dence of this phenomenon). As shown in Fig. 5, unwanted stickand slip phenomena are not preset in the closed-loop behaviorand tracking error is always below 1.5◦.

Now, we consider the case when the input command is a se-quence of rising steps from 15◦ to 90◦. As it is clear from Fig. 6,the closed-loop response closely follows that of the referencemodel with a maximum transient error always below 1.1◦.


Fig. 6. Experimental results for a sequence of rising steps. (a) Angular plate position: θm , reference plate trajectory (the dashed red line), and θth , plate position(the black solid line). (b) Tracking error . (c) Controller output voltage.

Fig. 7. Experimental results for a sequence of falling steps. (a) Angular plate position: θm , reference plate trajectory (dashed red line), and θth , plate position(the black solid line). (b) Tracking error and (c) Controller output voltage.

Another significant test is the case of small-amplitude ref-erence signals when the presence of stick-slip motion due tofriction becomes particularly relevant as the position and the ve-locity variations are relatively low. To assess the DMCS strategyunder these working conditions, we consider as reference inputa sequence of small steps starting from 40◦ to 10◦ selected fromsignal 28 in Table II. As shown in Fig. 7(a), the novel discrete-time MCS controller copes well with such unmodeled nonlinearperturbations. In particular, Fig. 7(a) shows that the regulationperformance does not get worse when the reference trajectorycrosses through the limp-home position and the restoring torqueabruptly changes.

To visit persistently the limp-home region, we schedule asreference signal a small sinusoidal wave with amplitude 6◦, bias14◦, and period 4 s (see signal 31 in Table II). Because thelimp-home is located approximately at 13.3◦, the closed-looptrajectory enters and leaves the limp-home zone persistently.Again, we want to stress that this is the most hostile workingcondition as the controller has to cope with a discontinuous elas-tic torque, a nonlinear friction, and a high aerodynamic torquedue to the high difference between ambient pressure and intakemanifold pressure affecting the plant in this working regime (seeFig. 3(b) at the end of the maneuver and Fig. 3(c) for a zoom).

Nevertheless, as shown in Fig. 8, the novel adaptive controllerprovides good performance and can be effectively used to im-pose small plate positions as those required to implement effec-tive idle speed controllers without anya priori compensation ofthe limp-home effect [15]. Note that the control gains in Fig. 3(d)automatically increase at the end of the maneuver to face thisarduous operating condition. This self-organizing behavior can-not be obtained with controllers with fixed gains, which have tobe tuned by designers in different regions of interest.

Finally, we note that over the entire maneuver the correspond-ing control signal was within the acceptable bounds as shownin 4(c), 5(c), 6(c), 7(c), and 8(c).

VI. EXPERIMENTAL COMPARISON AMONG DIFFERENT

MRAC APPROACHES

In this section to confirm the effectiveness of the DEMCSalgorithm in controlling the complex ETB dynamics, we car-ried out an experimental comparison between the closed-loopperformance provided by the novel adaptive strategy and thosegiven by other MCS and MRAC algorithms proposed in thecontrol literature. More precisely we compare the closed-loopbehavior of the DEMCS with those provided by:


Fig. 8. Experimental results for small sinusoidal with amplitude 6◦, bias 14◦, and period 4 s. (a) Angular plate position: θm , reference plate trajectory (the dashedred line), and θth , plate position (the black solid line). (b) Tracking error . (c) Controller output voltage.

1) the New Extended Minimal Control Synthesis with In-tegral action (NEMCSI) algorithm presented in [4]. Thisis the continuous-time counterpart of the novel adaptivestrategy. Hence, a comparison between a continuous-timeMCS and a discrete-time MCS is carried out for the firsttime. Notice that, as any continuous-time MCS strategy,the NEMCSI also suffers from the discretization problemdiscussed in [31]. These problems have been overcome bythe novel DEMCS algorithm;

2) the Discrete time Minimal Control Synthesis (DMCS) al-gorithm proposed in [19], [22], and [30]. In doing so, weshow through experiments the enhancements provided bythe extra integral and the robust adaptive terms, i.e. (6b),(6c) respectively;

3) an output-based Robust Model Reference Adaptive Con-trol (RMRAC) strategy chosen from the literature [35],pp. 183–189]. Hence, we prove experimentally that theDEMCS strategy yields better performance with respectto that given by a powerful but different robust adaptivecontrol scheme.

For the sake of a fair comparison the same reference model,sample time, and reference input have been used for all the con-trollers. Furthermore, to visit all the state space regions wherethe plant is strongly nonlinear, i.e., the region around the limp-home position, zero plate velocity as well as positions close tothe end-stroke of the valve, the reference signal is again the longmaneuver composed of the signals listed in Table II.

In what follows closed-loop performance is analyzed by us-ing as performance indices 1) the mean value of the absolutetracking error; 2) its standard deviation; 3) the mean value ofthe absolute percentage tracking error;4) its standard deviation;5) the maximum absolute tracking error; and 6) the maximumabsolute percentage tracking error.

Precisely, defining

μ(ζ) =1T

∫ T

0|ζ(t)|dt (32a)

σ(ζ) =√

μ([|ζ(t)| − μ(ζ)]2

)(32b)

κ(ζ) = max0≤t≤T

|ζ(t)| (32c)

with ζ(t) being a generic signal and T the time interval of ob-servation, we compute for each controller the following indicesμ(e), σ(e), μ(e%), σ(e%), κ(e), and κ(e%), with e = θm − θth

and e% = 100e/θm , where θm and θth are the demanded refer-ence plate position provided by the reference model and θth isthe experimental plate position.

A. Tracking Performance

For testing the tracking capabilities of the adaptive algorithmsdescribed earlier, we split the reference signal in Table II in thefollowing relevant subsets.

(S1) Learning, from signals 2 to 8. After this first set of ma-neuvers the transient of the adaptive gains due to the activationof the controller is supposed to be extinguished. The trackingerror over this set is used for starting up the adaptive mechanismbecause the adaptive gains of each controller are initially set tozero. Hence, for this set of maneuvers it is permitted that theautomotive specifications are not fulfilled.

(S2) After learning, from signals 9 to signal 15. The sequenceof signals composing this set is the same as that of the Set S1,but now it is essential that the control objectives are satisfied.

(S3) Miscellaneous signals, from signals 16 to 25. This setcollects different signals whose bias and amplitude are thoserequired when gasoline engines work at medium and high loads.Hence, these are typical signals that have to be followed duringthe normal engine operations.

(S4) Small signals, from signals 29 to 32. This set containssignals with small amplitudes oscillating around the limp-homeposition. Hence, this is the most complex set of maneuvers toimpose on the ETB device. We note that this set contains typicalsignals that have to be effectively followed to use ETB as anactuator for implementing idle speed control schemes. In doingso, the traditional bypass valves can be removed.

(S5) Sequence of steps, signals 26 and 28. This set is com-posed of a sequence of steps included in the long maneuver.Hence, its study allows us to analyze the closed-loop perfor-mance for different steady-state regimes.

(S6) Square waves. This set collects all the square waves ofthe long maneuver (except those belonging to the Learning set).


Fig. 9. Performance indices for each set: (a) maximum absolute tracking error,κ(e) and (b) maximum absolute percentage tracking error, κ(e% ).

TABLE IIIPERCENTAGE REDUCTION OF THE MAXIMUM ABSOLUTE TRACKING

ERROR PROVIDED BY THE DEMCS STRATEGY WITH RESPECT TO OTHER

ADAPTIVE ALGORITHMS

It is used to test closed-loop performance in the presence ofsudden tip-in/tip-out maneuvers.

(S7) Sinusoidal waves. This set contains all the sinusoidalwaves of the entire input signal (except those belonging to theLearning set), and it is used to test closed-loop performance inthe presence of smooth tip-in/tip-out maneuvers.

For each set and adaptive controller, we have computed theperformance indices κ(e) and κ(e%). The results are shown inFig. 9. This figure clearly shows that the novel adaptive strategyprovides always the smallest maximum tracking error indepen-dently by the set of signals to follow. The percentage reductionof this index, when the DEMCS algorithm is used, is reported inTable III to show quantitatively how the tracking performancegets better with respect to those provided by the other controllerson each set of reference signals.

In more detail, except for the DMCS strategy, the transientof the adaptive gains due to the activation of a generic adaptivecontroller is short because the performance indices computedon the first set (Learning set) are comparable to those obtainedanalyzing the second set (After Learning). Only for the DMCSstrategy does the tracking error reduces sensibly from the firstset to the second one. Nevertheless, the DMCS controller doesnot satisfy the control specification “4” in Section IV-B in thefirst set of signals and also over sets S2, S3, S4, S6, and S7.Furthermore, as is apparent in Fig. 9, the enhancements hereproposed for the DMCS strategy play a crucial role to keep themaximum tracking error small at the control startup. Indeed, byadding the adaptive actions (6b) and (6c) to the discrete-timeMCS [19], [22], [30], the maximum tracking error reduces fromabout 25◦ to 3.7◦. Hence, the novel MCS strategy improves thestartup response of the standard DMCS of about 85%.

The DEMCS provides better closed-loop performance alsowhen it is compared to its continuous-time counterpart (NEM-CSI controller). Indeed, because the DEMCS does not suf-fer from discretization problems affecting the continuous-timeMCS strategies [31], it is possible to increase the adaptiveweights to achieve a better tracking of the reference dynamicswithout triggering closed-loop instabilities. Similarly, superiortracking results are achieved by the DEMCS controller whencompared to those provided by the RMRAC strategy.

Except the DMCS, all the adaptive strategies verify the con-trol specification on maximum absolute dynamic error that re-mains always below 7◦ as shown in Fig. 9(a). In addition, abetter evaluation of the closed-loop performance can be doneby considering the maximum absolute percentage error κ(e%)in Fig. 9(b). In particular, the analysis of this index clearly showsthat only the novel adaptive control algorithm provides perfor-mances that are almost independent of the working conditionwith a maximum tracking error always below 12%. In particu-lar, the novel DEMCS is the only controller that is able to copeeffectively with small signals around the limp-home position.Indeed, the DEMCS drastically reduces the absolute percentagetracking error with respect to the other adaptive strategies byproviding a κ(e%) index of about 10% on the fourth set (smallsignals). Hence, among the proposed adaptive controllers, thenovel strategy is the best candidate to solve the ETB problemfor drive-by-wire systems in automotive engineering allowingto vary the valve position of few degrees around the limp-homezone.

The tracking performances provided by DMCS, NEMCSI,and RMRAC adaptive algorithms for this arduous but vitalworking condition are reported in Fig. 10 for the sake of com-pleteness. These performances are very poor when compared tothose given by the DEMCS strategy in Fig. 8(a).

B. Regulating Performance

We test the regulating capabilities of the proposed adaptivestrategies by evaluating the performance indices μ(e), σ(e),μ(e%), and σ(e%) in steady-state regime for a wide range ofconstant input reference commands. The experimental resultsare reported in Fig. 11, which shows these performance indicescomputed for each controller when the set point r belongs to{10 + 5k deg, k = 0,1, . . . 16}.

As shown in Fig. 11(a), only the novel algorithm is ableto satisfy the control specification on the mean value steady-state error providing a mean value absolute regulating error thatnever exceeds 0.1◦ [see the black dashed line in Fig. 11(a)]independent of the input set point. Furthermore, as shown in11(b), the standard deviation σ(e) given by the DEMCS strategyis always around 0.05◦ (only when the set point is 75◦, theσ(e) = 0.1◦).

The superior regulating performance provided by the DEMCScontroller can be better appreciated by evaluating the σ(e%) andμ(e%). In particular, the analysis of μ(e%) index shows thatwhen the reference command is 10◦ (set point below the limp-home position), the discrete-time MCS strategy without anyenhancement gives a mean percentage value of the tracking error


Fig. 10. Experimental results for small sinusoidal with amplitude 6◦, bias 14◦, and period 4 s. θm , reference plate trajectory (dashed red line), and θth , plateposition (black solid line) when the control strategy is: (a) NEMCSI algorithm, (b) DMCS algorithm, and (c) RMRAC algorithm.

Fig. 11. Performance indices computed for different set points: (a) meanvalue of the absolute tracking error μ(e), (b) standard deviation of the absolutetracking error σ(e), (c) mean value of the absolute percentage tracking errorμ(e% ), and (d) standard deviation of the absolute percentage tracking errorσ(e% ).

of about 25%, the continuous time counterpart of the DEMCSalgorithm (i.e., NEMCSI strategy) provides an error of 7.8%,while the RMRAC strategy gives a residual error of about 3.5%.(Notice that the performances provided by the NEMCSI andthe DMCS strategies are not shown in Fig. 11(c) as their μ(e%)values are out of the scale.)

The performances provided by these adaptive controllers arepoor when compared with those given by the DEMCS strategy,which at 10◦ has a μ(e%) index of 0.5 %. Moreover, also thepercentage standard deviation given by the novel algorithm is

always below that obtained with the other adaptive methods asconfirmed in Fig. 11(d).

VII. CONCLUSION

In this paper, we have presented the DEMCS adaptive algo-rithm and its application to the ETB automotive actuator de-vice. The controller extends the family of discrete-time MCScontrollers by adding an adaptive integral term and a robustadaptive action. The main advantage of the proposed approachis it requires a minimal knowledge of the plant and is robust tothe plant nonlinearities and the persistent aerodynamic torquesdue to the operation of the engine. An in-depth experimentalanalysis has shown that the DEMCS controller is a viable so-lution because automotive control specifications are satisfied inthe entire range of interest. Furthermore, an experimental com-parison with other MCS methods has revealed that the DMCS isthe best algorithm within the MCS family as it provides the besttracking performance especially around the limp-home zonewhere the discontinuous nonlinearities of the plant are located.Hence, we expect that the DEMCS algorithm can be exploited infuture to tackle different engineering control problems affectedby large model and parameter uncertainties.

APPENDIX A

MATHEMATICAL MODEL OF THE ETB

The adaptive law discussed in this paper extends the minimalcontrol synthesis approach; thus, it relies on a minimal knowl-edge of the plant. Hence, it can be implemented easily withoutrequiring time-consuming experiments for the precise charac-terization of the system nonlinear dynamics. Nevertheless, forthe sake of clarity and to emphasize the sources of nonlinearities,we briefly present an ETB model.

The ETB plant (shown in Fig. 1) mainly consists of a dcmotor, a reduction gear, and a plate where a couple of springsare also located to lead the plate to the limp-home position.The mathematical model of the plant is (see Table IV for a


TABLE IVNOMENCLATURE FOR THE ETB DEVICE

nomenclature of the symbols used in the rest of the Appendix)

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎩

di

dt= −R

Li − Kv

L

Gr

Kωth +

1L

va

dθth

dt= ωth ,

dωth

dt=

KKt

JGr i −

K

JTs (θth) − K

JTf (ωth)

−KJ Ta (θth , Pi)

(33)

with θth ∈ [θmin , θmax] and va ∈ [−Vbatt , Vbatt ].The elastic torque Ts is not simply a linear function of all

the admissible angles, but it is the following piecewise linearfunction with a sudden jump around the limp-home position

Ts(θ) =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

TS3 (θ) if θ ∈[θmin ; θLH − Δθ

2

[

0 if θ ∈[θLH − Δθ

2; θLH +

Δθ

2

]

TS1 (θ) if θ ∈]θLH +

Δθ

2; θ12

[

TS2 (θ) if θ ∈ [θ12 ; θmax]

(34)

TS1 (θ) = Ks1

[θ −

(θLH +

Δθ

2

)]+ Topen

TS2 (θ) = Ks2 (θ − θ12) + TS1 (θ12)

TS3 (θ) = −Ks3

[(θLH − Δθ

2

)− θ

]− Tclose . (35)

The model of the friction torque Tf is based on a staticCoulomb model modified in order to include the Stribeck effectas

Tf (ωth) =[Tc + (Tst − Tc) e−|

ω t hω s |

]sign (ωth) + βth

ωth

K.

(36)The aerodynamic disturbance torque Ta is due to the air

flow through the throttle and it depends mainly on the throt-tle position, the throttle plate geometry and the pressure ratioΔP = Pi/Pa . More in detail, this persistent disturbance actingon the plant can be described as

Ta (θth , Pi) =Pi

Paχ (θth , Pi) (37)

where χ (θth , Pi) is a function that can be well approximatedby means of a polynomial function [3].

A. Reduction to Control Canonical Form

As the electrical dynamics are faster than the mechanicalones, it is possible to neglect the electrical dynamics in (33) andconsider only the plate position and velocity as state variablesof the plant.

Defining x = [θth ωth ]T and u = va , after simple algebraicmanipulations the system dynamics can be rewritten as

x(t) = A0x(t) + B0u(t) + f(x, t) (38)

with

A0 =

⎡⎣

0 1

−KKs1

J− 1

J

(βth +

KtKvG2r

R

)⎤⎦ (39)

B0 =

[0

KKtGr

JR

], f(x, t) =

[0

K

JTnl(x, t)

](40)

where Tnl(x, t) = T snl(x1) + T f

nl(x2) + Ta (x2 , Pi(t)), withT s

nl(x1) = Ts(x1) − KS1 x1 and T fnl(x2) = Tf (x2) − βthx2

being the nonlinear part of the spring and the friction torques,respectively.

We note that system (38) is in the required control canonicalform. Hence, the DEMCS algorithm can be applied.

Further details on model derivation, identification and valida-tion as well as model parameters can be found in [4]. Here, wejust stress that neither the nonlinear term f(x, t) nor the entriesof the plant matrices A0 and B0 are necessary for the design ofthe novel DEMCS adaptive algorithm.

APPENDIX B

EXPERIMENTAL SETUP

The experimental setup consists of: 1) an ETB (DV-E5,Bosch), embedding a dc motor; 2) two dual resistive angularposition sensors; 3) a battery voltage sensor; 4) an H-bridgepower circuit (to drive the dc motor); 5) a Hall-effect currentsensor (LTA 50P/SP1, LEM); 6) signal-conditioning circuits; 7)a station for Rapid Control Prototyping (RCP). Furthermore, theETB is installed on a 2 L naturally aspirated port fuel injection


gasoline engine with a bore of 82 mm, stroke 72.65 mm, and anengine displacement of 1598 cc.

The RCP is a dSpace-based multiprocessor system equippedwith the DS1003 (DSP TMS320C40, 60 Mflops) and DS1004(DEC Alpha AXP 21164, 600 Mflops) processor boards. Ananalog DS2201 (20 ch., 12 bit, 30 kHz) and a digital DS4002(8 ch. CAP/CMP res. 30 bit/200 ns, freq. max. 833 kHz) boardallow the I/O handling. The DSP is programmed in MAT-LAB/Simulink (MathWorks) environment and the experimentsare managed and instrumented by a ControlDesk application(dSpace).

Note that, using the hardware described earlier, the executionof our control task is performed in 10 μs with a sample periodof 1 ms.

REFERENCES

[1] M. Corno and S. Savaresi, “Experimental identification of engine-to-slipdynamics for traction control applications,” Eur. J. Control, vol. 16, no. 1,pp. 88–108, 2010.

[2] T. Aono and T. Kowatari, “Throttle-control algorithm for improving engineresponse based on air-intake model and throttle-response model,” IEEETrans. Ind. Electron., vol. 53, no. 3, pp. 915–921, Jun. 2006.

[3] M. J. Morris and J. C. Dutton, “Aerodynamic torque characteristics ofbutterfly valves in compressible flow,” J. Fluids Eng., vol. 111, no. 4,pp. 392–399, 1989.

[4] M. di Bernardo, A. di Gaeta, U. Montanaro, and S. Santini, “Synthesisand experimental validation of the novel LQ-NEMCSI adaptive strategyon an electronic throttle valve,” Trans. Control Syst. Technol., vol. 18,no. 6, pp. 1325–1337, Nov. 2010.

[5] A. di Gaeta, U. Montanaro, and V. Giglio, “Idle speed control of GDI-SI engines via ECU-1D engine co-simulation,” presented at the SAEMeeting, San Diego, CA, USA, 2010, Tech. Paper 2010–01–2220.

[6] C. Rossi, A. Tilli, and A. Tonielli, “Robust control of a throttle body fordrive by wire operation of automotive engines,” IEEE Trans. Control Syst.Technol., vol. 8, no. 6, pp. 993–1002, Nov. 2000.

[7] M. Vaak, M. Baotic, I. Petrovic, and N. Peric, “Hybrid theory-based time-optimal control of an electronic throttle,” IEEE Trans. Ind. Electron., vol.54, no. 3, pp. 1483-1494, Jun. 2007.

[8] H. Yunfeng, L. Qifang, S. Pengyuan, C. Hong, and L. Jun, “Design ofan adrc-based electronic throttle controller,” in Proc. 30th Chinese Contr.Conf., 2011, pp. 6340–6344.

[9] C.-H. Chen, H. C. Jiao, and H.-L. Tsai, “Engine throttle control withdisturbance observer,” in Proc. 8th Asian Control Conf., May 2011, pp.1105–1110.

[10] Y. Pan, U. Ozguner, and O. Dagci, “Variable-structure control of electronicthrottle valve,” IEEE Trans. Ind. Electron., vol. 55, no. 11, pp. 3899–3907,Nov. 2008.

[11] M. Reichhartinger and M. Horn, “Application of higher order sliding-mode concepts to a throttle actuator for gasoline engines,” IEEE Trans.Ind. Electron., vol. 56, no. 9, pp. 3322–3329, Sep. 2009.

[12] Y. Zhang and N. Kurihara, “An integral variable structure compensationmethod for electronic throttle control with input constraint,” in Proc. 3rdInt. Conf. Adv. Comput. Contr., 2011, pp. 492–496.

[13] X. Yuan, Y. Wang, L. Wu, X. Zhang, and W. Sun, “Neural network basedself-learning control strategy for electronic throttle valve,” IEEE Trans.Veh. Technol., vol. 59, no. 8, pp. 3757–3765, Oct. 2010.

[14] X. Yuan and Y. Wang, “A novel electronic-throttle-valve controller basedon approximate model method,” IEEE Trans. Ind. Electron., vol. 56, no. 3,pp. 883–890, Mar. 2009.

[15] D. Pavkovic, J. Deur, M. Jansz, and N. Peric, “Adaptive control of automo-tive electronic throttle,” Control Eng. Pract., vol. 14, no. 2, pp. 121–136,2006.

[16] P. Mercorelli, “Robust feedback linearization using an adaptive PD regu-lator for a sensorless control of a throttle valve,” Mechatronics, vol. 19,no. 8, pp. 1334–1345, 2009.

[17] B. Alt, J. P. Blath, F. Svaricek, and M. Schultalbers, “Self-tuning controldesign strategy for an electronic throttle with experimental robustnessanalysis,” in Proc. Amer. Contr. Conf., Jun. 2010, pp. 6127–6132.

[18] S. S. L. F. M. Corno and M. Tanelli, “Design and validation of a gain-scheduled controller for the electronic throttle body in ride-by-wire racingmotorcycle,” IEEE Trans. Control Syst. Technol., vol. 19, no. 1, pp. 18–30,Jan. 2011.

[19] M. di Bernardo, A. di Gaeta, U. Montanaro, J. M. Olm, and S. Santini, “Ex-perimental validation of the discrete-time MCS adaptive strategy,” ControlEng. Pract., to be published, DOI: 10.1016/j.conengprac.2012.12.004.

[20] U. Montanaro, A. di Gaeta, and V. Giglio, “Adaptive tracking controlof a common rail injection system for gasoline engines: A discrete timeintegral minimal control synthesis approach,” IEEE Trans. Control Syst.Technol., to be published, DOI: 10.1109/TCST.2012.2220772.

[21] M. di Bernardo, A. di Gaeta, V. Giglio, U. Montanaro, and S. Santini,“Design and validation of a novel model reference adaptive algorithm tocontrol ETB for drive-by-wire applications,” Int. J. Passenger Cars-Mech.Syst., vol. 2, no. 1, pp. 1268–1284, Oct. 2009.

[22] M. di Bernardo, A. di Gaeta, U. Montanaro, J. M. Olm, and S. Santini,“Discrete-time MRAC with minimal controller synthesis of an electronicthrottle body,” in Proc. IFAC World Congr., Aug. 2011, pp. 5064–5069.

[23] U. Montanaro, A. di Gaeta, and V. Giglio, “An MRAC approach for track-ing and ripple attenuation of the common rail pressure for GDI engines,”in Proc. 18th IFAC World Congr., Milan, Italy, Aug. 2011, pp. 4173–4180.

[24] D. Stoten and E. Gomez, “Adaptive control of shaking tables using theminimal controller synthesis algorithm,” Philos. Trans. R. Soc. Lond.,vol. 357, pp. 1697–1723, 2001.

[25] M. di Bernardo, U. Montanaro, and S. Santini, “Novel hybrid MRAC-LQcontrol schemes: Synthesis, analysis, and applications,” Int. J. Control,vol. 81, no. 6, p. 940–961, Jun. 2008.

[26] M. di Bernardo, U. Montanaro, and S. Santini, “Hybrid model referenceadaptive control of piecewise affine systems,” IEEE Trans. Autom. Control,vol. 58 , no. 2, pp. 304–316, Feb. 2013.

[27] M. di Bernardo, C. I. H. Velasco, U. Montanaro, and S. Santini, “Experi-mental implementation and validation of a novel minimal control synthe-sis adaptive controller for continuous bimodal piecewise affine systems,”Control Eng. Pract., vol. 20, no. 3, pp. 269–281, Mar. 2012.

[28] M. di Bernardo, U. Montanaro, and S. Santini, “Minimal control synthesisadaptive control of continuous bimodal piecewise affine systems,” SIAMJ. Control Optim., vol. 48, no. 7, pp. 4242–4261, Jun. 2010.

[29] M. di Bernardo, U. Montanaro, J. M. Olm, and S. Santini, “Model ref-erence adaptive control of discrete-time piecewise linear systems,” Int. J.Robust Nonlinear Control, to be published, DOI:: 10.1002/rnc.2786.

[30] M. di Bernardo, F. di Gennaro, J. M. Olm, and S. Santini, “Discrete-timeminimal control synthesis adaptive algorithm,” Int. J. Control, vol. 83,no. 4, pp. 2641–2657, Dec. 2010.

[31] O. Bursi, D. Stoten, and L. Vulcan, “Convergence and frequency-domainanalysis of a discrete first-order model reference adaptive controller,”Struct. Control Health Monitoring., vol. 14, no. 5, pp. 777–807, 2007.

[32] Y. D. Landau, Adaptive Control: The Model Reference Approach. NewYork, NY, USA: Marcel Dekker, 1979.

[33] V. Popov, Hyperstability of Automatic Control Systems. New York, NY,USA: Springer-Verlag, 1973.

[34] S. E. M. Sebusang and D. P. Stoten, “Controller gain bounding in theminimal control synthesis algorithm,” in Proc. 13th Southeastern Symp.Syst. Theor., Mar. 1998, pp. 141–145.

[35] P. Ioannou and B. Fidan, Adaptive Control Tutorial. Philadelphia, PA,USA: SIAM, 2006.

[36] U. Montanaro, “Model reference adaptive control of piecewise affine sys-tems and applications,” Ph.D. thesis, Faculty Eng., Univ. Naples FedericoII, Naples, Italy, 2009.

Umberto Montanaro received the “Laurea” degree(M.Sc.) in computer science engineering (cum laudefirst class with Hons.) and the Ph.D. degree in auto-matic control from the University of Naples FedericoII, Naples, Italy, in 2005 and 2009, respectively.

He is currently a Postdoctoral Research Fellow atthe Istituto Motori, Italian National Research Coun-cil, Naples. In addition, he is also a temporary Lec-turer in Automation and Process Control at the Uni-versity of Naples Federico II. His Ph.D. research workfocused mainly on developing adaptive control strate-

gies for piecewise affine systems. His current research interests include controltheory to control application and include automotive control, modeling and con-trol of nonlinear dynamical systems, adaptive control, and control of piecewiseaffine systems.


Alessandro di Gaeta (M’12) received the “Laurea”degree (M.Sc.) (cum laude) in computer science en-gineering and the Ph.D. degree in automatic controlfrom the University of Naples Federico II, Naples,Italy, in 1999 and 2003, respectively.

From 2003 to 2006, he was a Postdoctoral Re-search Fellow at the Istituto Motori, Italian NationalResearch Council, Naples, where since 2007 he hasbeen a Researcher in the High Efficiency Spark Igni-tion Engines Division. His research interests includethe modeling, analysis, and control of automotive

mechatronic systems, and of gasoline direct injection (GDI) engines.

Veniero Giglio (M’12) received the “Laurea” degree(M.Sc.) (cum laude) in mechanical engineering fromthe University of Naples Federico II, Naples, Italy, in1988.

Since 1990, he has been with the Istituto Motori,Italian National Research Council, Naples, where heis a Senior Researcher. His main experiences are inthe field of spark ignition engine, in both experimen-tal and modeling areas. His research interests includeSI engine downsizing by turbo-charging and variablevalve timing, gasoline direct injection, combustion

modeling, investigation of knock and simulation of the related auto-ignitionphenomena, and nonintrusive combustion diagnostics by flame ionization de-tection at spark plug electrodes.

Robust Discrete-Time MRAC With Minimal Controller Synthesis of an Electronic Throttle Body

Documents

Transcript of Robust Discrete-Time MRAC With Minimal Controller Synthesis of an Electronic Throttle Body