robust control of a throttle body for drive by wire operation of automotive engines

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IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 8, NO. 6, NOVEMBER 2000 993 Robust Control of a Throttle Body for Drive by Wire Operation of Automotive Engines Carlo Rossi, Andrea Tilli, and Alberto Tonielli, Associate Member, IEEE Abstract—In recent years, ever more stringent requirements in terms of emissions control, driveability, and safety of automobiles have led to the development of the drive by wire (DBW) concept, a new architecture for engine control systems, with the purpose of managing air, fuel and ignition in an integrated way. The throttle control plays an important role in the development of DBW sys- tems. Despite its apparent simplicity, the position control of the throttle valve is quite a complex problem, due to application con- straints and system characteristics. Very high robustness must be linked with limited cost, as required by a mass production device. A cascaded control structure including a nonlinear trajectory gener- ator filter is adopted, allowing each different control problem to be solved with the most suitable control algorithm and implementa- tion technology. In this regard, the use of variable structure control techniques is the key element to reaching the solution. Extensive simulation tests are reported to show the performance of the pro- posed control algorithm. A throttle step from 0.5 to 89.5 indicates good position tracking under realistic operating conditions, with a position error smaller than 1 . The same simulation is performed at a battery voltage of 9 V to check the controller robustness. A pro- totype controller is presented. The experimental implementation of the controller for a step from 2.5 to 85.5 indicates a very smooth position trajectory with a maximum dynamic position error of 7 . A small throttle step from 1 to 7 (which contains the nonlinearity of the limp home mode spring) was also tested and resulted in very good position response with the maximum position error of 2 . Ap- plication specifications are fully satisfied both in terms of control performance and controller cost. Index Terms—Automotive, drive by wire, sliding mode, variable structure. I. INTRODUCTION I N AUTOMOTIVE spark ignition engines the air coming into the intake manifold, and therefore the power generated, strongly depends on the angular position of a throttle valve. In traditional systems, the throttle position is actuated by a me- chanical link with the accelerator pedal, directly operated by the driver. Automatic air flow regulation requires the introduction of additional actuators. In particular: 1) an actuator for control- ling idle speed and release, usually consisting of a bypass of the throttle valve whose section is regulated through a stepper motor and 2) other costly and bulky servomechanisms on the throttle for cruise control and/or traction control functions. In recent years new and increasing requirements in terms of emis- sions control, driveability, and safety have led to the develop- ment of drive by wire (DBW), a new architecture for engine con- Manuscript received April 1, 1998. Recommended by Associate Editor, F. Svaricek. This paper was supported in part by Magneti Marelli S.P.A. C. Rossi is with Magneti Marelli S.P.A., Engine Control Division, Bologna, Italy. A. Tilli and A. Tonielli are with the Department of Electronics, Computers and System Science, University of Bologna, Bologna, Italy. Publisher Item Identifier S 1063-6536(00)07350-4. trol systems, with the purpose of integrated air, fuel, and ignition management. The DBW architecture does not require any direct mechanical links between the accelerator pedal and the throttle valve. The throttle actuator is a motorized throttle body (MTB) electrically driven and controlled by an electronic system that mediates between: 1) a driver’s request, interpreted by an accel- erator pedal position sensor and 2) effective traction possibili- ties depending upon driveability, safety, and emission limitation constraints. The new architecture does not require additional air actuators, as they are replaced by the electric motor driving the throttle valve, and achieves noticeable improvements in relia- bility, performance, cost, size, and weight. There are a number of functions that can be achieved or improved with throttle position regulation in a DBW system, which can be divided into two main categories [10], [11]. The first one is related to the thermal engine performance and includes: • customized and variable accelerator pedal/throttle posi- tion mapping, as a function of operating conditions; • idle speed regulation and cold starting management; • dashpot management; • A/F ratio regulation during transients; • engine speed (r/min) limitation; • catalyst thermal management (light-off). The second category of functions refers to vehicle behavior and includes: • automatic vehicle speed control and intelligent cruise con- trol; • effective torque control, including traction control and ABS management; • vehicle speed and performance limitation; • smoother movement during acceleration/deceleration (driveability control); • integration with electronic, hydraulic and mechanical gear box; • vehicle dynamic control; • integration with anticollision and guidance systems. The basic function of a DBW system consists clearly in good control of the throttle position. The requirements to be achieved in terms of accuracy, response time, and robustness are severe, particularly when mass production constraints are imposed. MTB dynamical performance to large signal variation has to guarantee at least the same behavior of a traditional pedal/throttle body system. At the same time, the response to small signal vari- ations should be equally fast, especially during idle speed regula- tion, where also accuracy becomes a critical factor. From the control viewpoint this problem might appear to be one of simple position tracking control under variable load torque. Nevertheless, system operation close to the car 1063–6536/00$10.00 © 2000 IEEE

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Page 1: Robust control of a throttle body for drive by wire operation of automotive engines

IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 8, NO. 6, NOVEMBER 2000 993

Robust Control of a Throttle Body for Drive by WireOperation of Automotive EnginesCarlo Rossi, Andrea Tilli, and Alberto Tonielli, Associate Member, IEEE

Abstract—In recent years, ever more stringent requirements interms of emissions control, driveability, and safety of automobileshave led to the development of the drive by wire (DBW) concept,a new architecture for engine control systems, with the purpose ofmanaging air, fuel and ignition in an integrated way. The throttlecontrol plays an important role in the development of DBW sys-tems. Despite its apparent simplicity, the position control of thethrottle valve is quite a complex problem, due to application con-straints and system characteristics. Very high robustness must belinked with limited cost, as required by a mass production device. Acascaded control structure including a nonlinear trajectory gener-ator filter is adopted, allowing each different control problem to besolved with the most suitable control algorithm and implementa-tion technology. In this regard, the use of variable structure controltechniques is the key element to reaching the solution. Extensivesimulation tests are reported to show the performance of the pro-posed control algorithm. A throttle step from 0.5 to 89.5 indicatesgood position tracking under realistic operating conditions, with aposition error smaller than 1 . The same simulation is performedat a battery voltage of 9 V to check the controller robustness. A pro-totype controller is presented. The experimental implementation ofthe controller for a step from 2.5 to 85.5 indicates a very smoothposition trajectory with a maximum dynamic position error of 7 .A small throttle step from 1 to 7 (which contains the nonlinearityof the limp home mode spring) was also tested and resulted in verygood position response with the maximum position error of 2. Ap-plication specifications are fully satisfied both in terms of controlperformance and controller cost.

Index Terms—Automotive, drive by wire, sliding mode, variablestructure.

I. INTRODUCTION

I N AUTOMOTIVE spark ignition engines the air cominginto the intake manifold, and therefore the power generated,

strongly depends on the angular position of a throttle valve. Intraditional systems, the throttle position is actuated by a me-chanical link with the accelerator pedal, directly operated by thedriver. Automatic air flow regulation requires the introductionof additional actuators. In particular: 1) an actuator for control-ling idle speed and release, usually consisting of a bypass ofthe throttle valve whose section is regulated through a steppermotor and 2) other costly and bulky servomechanisms on thethrottle for cruise control and/or traction control functions. Inrecent years new and increasing requirements in terms of emis-sions control, driveability, and safety have led to the develop-ment of drive by wire (DBW), a new architecture for engine con-

Manuscript received April 1, 1998. Recommended by Associate Editor, F.Svaricek. This paper was supported in part by Magneti Marelli S.P.A.

C. Rossi is with Magneti Marelli S.P.A., Engine Control Division, Bologna,Italy.

A. Tilli and A. Tonielli are with the Department of Electronics, Computersand System Science, University of Bologna, Bologna, Italy.

Publisher Item Identifier S 1063-6536(00)07350-4.

trol systems, with the purpose of integrated air, fuel, and ignitionmanagement. The DBW architecture does not require any directmechanical links between the accelerator pedal and the throttlevalve. The throttle actuator is a motorized throttle body (MTB)electrically driven and controlled by an electronic system thatmediates between: 1) a driver’s request, interpreted by an accel-erator pedal position sensor and 2) effective traction possibili-ties depending upon driveability, safety, and emission limitationconstraints. The new architecture does not require additional airactuators, as they are replaced by the electric motor driving thethrottle valve, and achieves noticeable improvements in relia-bility, performance, cost, size, and weight.

There are a number of functions that can be achieved orimproved with throttle position regulation in a DBW system,which can be divided into two main categories [10], [11].The first one is related to the thermal engine performance andincludes:

• customized and variable accelerator pedal/throttle posi-tion mapping, as a function of operating conditions;

• idle speed regulation and cold starting management;• dashpot management;• A/F ratio regulation during transients;• engine speed (r/min) limitation;• catalyst thermal management (light-off).

The second category of functions refers to vehicle behavior andincludes:

• automatic vehicle speed control and intelligent cruise con-trol;

• effective torque control, including traction control andABS management;

• vehicle speed and performance limitation;• smoother movement during acceleration/deceleration

(driveability control);• integration with electronic, hydraulic and mechanical gear

box;• vehicle dynamic control;• integration with anticollision and guidance systems.

The basic function of a DBW system consists clearly in goodcontrol of the throttle position. The requirements to be achievedin terms of accuracy, response time, and robustness are severe,particularly when mass production constraints are imposed.

MTB dynamical performance to large signal variation has toguarantee at least the same behavior of a traditional pedal/throttlebody system. At the same time, the response to small signal vari-ations should be equally fast, especially during idle speed regula-tion, where also accuracy becomes a critical factor.

From the control viewpoint this problem might appear tobe one of simple position tracking control under variableload torque. Nevertheless, system operation close to the car

1063–6536/00$10.00 © 2000 IEEE

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994 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 8, NO. 6, NOVEMBER 2000

Fig. 1. Throttle body functional scheme.

engine and constraints on the cost imposed by mass productiontransform this apparently simple control problem into quite acomplex one. Joint methodological and technological designmust be performed to ensure the best tradeoff between controlcomplexity, technological feasibility, robustness, and cost limi-tation. The control algorithm adopted must be extremely robustalthough suitable for simple and inexpensive implementation.

Among all the robust control techniques proposed in the liter-ature a variable structure (VS) approach has been considered inthis project [1]. A three-level cascaded control structure is used[2]. The inner current controller is designed using hysteresiscontrol techniques [3]. The intermediate velocity controller isdesigned as a VS controller with integral action [6]. The outerposition controller is designed as a digital linear controller. Theposition reference signal is given by a smooth trajectory gener-ator (STG) able to generate position trajectories with variablebounds on velocity and acceleration [7], [12].

This paper is organized as follows. Section II contains thedescription of the problem. Section III describes the control ar-chitecture and the design of the different controllers. Simulationresults are reported in Section IV, while the experimental setupand results are given in Section V. The theoretical stability prooffor the velocity controller is reported in the Appendix.

II. PROBLEM DESCRIPTION

The motorized throttle body (MTB) used is manufactured byMagneti Marelli, Bologna, Italy. A schematic representation isgiven in Fig. 1. The main parts are:

• the throttle valve, driven by a permanent magnet dc motor(this motor is fed by a controlled four-quadrant dc/dc con-verter connected to the vehicle battery);

• thebodyduct,suitablyshapedtoensurethedesiredrelation-shipbetween theair flowand the throttlevalve position;

• a set of loaded springs ensuring a safety recovery position[referred to as limp home (LH) position] for the throttlewhen no driving torque is generated by the dc motor. Theresulting torque of the springs is reported in Fig. 2, whichshows that the LH position (5) lies inside the normal op-erating range ( ) of the throttle.

The main functional specification for a DBW system is afast throttle positioning with accurate reference tracking. Thesystem equations are as follows.

1) Motor Model:

(1)

(2)

(3)

Fig. 2. Safety spring torque (T ) as a function of throttle position (#).

TABLE ISYSTEM PARAMETERS FOR THEMTB CONSIDERED

wherethrottle position and velocity;armature current and voltage of DC motor; (both arelimited for technological reasons:

);motor torque coefficient;motor resistance and inductance;overall inertia (throttle motor);overall load torque.

2) Load Torque Model:

(4)

whereload torque generated by the safety springs,whose nonlinear characteristic is reported inFig. 2;friction torque, nonlinearly depending onthe throttle velocity;aerodynamic torque due to the engine airflow whose value is assumed to be unpre-dictable; bounded values are assumed for theaerodynamic torque and its derivative.

Owing to manufacturing tolerances (low-cost mass produc-tion), variable operating conditions and wear of mechanicalparts, nominal values of some system parameters are knownwith uncertainty while others may have a large variance aroundtheir nominal value.

Table I reports the nominal values of parameters and theirexpected range for the MTB considered.

The most important system parameters are strongly variable.For example:

• The electrical time constant can vary by a factor larger than5 (from 0.25 to 1.33 ms).

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ROSSIet al.: ROBUST CONTROL OF A THROTTLE BODY FOR DRIVE BY WIRE OPERATION OF AUTOMOTIVE ENGINES 995

Fig. 3. Control architecture adopted.

• The supply voltage, affecting the control gain, can vary bya factor of 3 (from 6 to 18 V).

• The safety spring torque is discontinuous at the LH po-sition; the LH position is defined with more than 10ofuncertainty; the torque discontinuity is relevant and corre-sponds to more than 40% of the motor nominal torque.

• the friction torque has strong variations in the specifiedtemperature range ( C C)

III. CONTROLLER DESIGN

A. Control Specifications

The main topic of this paper is the design of a posi-tion-tracking controller for the throttle valve, which is robustto MTB parameter variation and suitable for low cost massproduction. More specifically the requirements are as follows.

• The controller is not based on a detailed model of themotor-driven valve characteristics.

• The position reference is generated by the standard enginecontrol unit (ECU), remotely located with respect to MTB,where the expected sampling time for digital algorithmsimplemented on ECU is about 4 ms.

• The computational load added to ECU is very low.Besides, the control system must ensure the following.

• The position regulation error (static condition) is less than0.1 .

• The position tracking error (dynamic condition) is lessthan 7 .

• The valve opening time (0to 90 with 5% tolerance) isless than 130 ms with a supply voltage higher than 9 V.With between 6–9 V there are no specifications onopening time.

B. Control Architecture

A simple linear controller (analog or digital) cannot beadopted because of unknown or strongly time-variable systemparameters. A digital implementation can achieve a high levelof robustness through sophisticated self-tuning or on-lineadaptation algorithms, at the expense of heavy computationalload. Since ECU cannot handle significant added computa-tional load, another powerful microprocessor or DSP would be

required which would exceed cost constraints. Therefore, a spe-cial-purpose solution integrating robust control requirementsand technological implementation constraints is required.

To get high performance at low cost, control algorithm andimplementation technology cannot be considered indepen-dently. Strong interaction between the two design phases isrequired in order to maximize the performance/cost ratio. Theauthors have shown in [2] that a cascade of VS controllerscan lead to a simple and robust hardware implementation ofthe motor control system. Moreover, thanks to the flexibilityensured by the cascaded control structure, the three controlloops can be designed using, for each one, the best combinationof control method and implementation technology. Applyingthese concepts to the MTB control, the cascaded architectureshown in Fig. 3 has been defined. There are three separatesections:

1) the position controller, implemented at discrete-time inthe ECU;

2) the ECU/MTB interface;3) the two fast-dynamics velocity and current controller, im-

plemented at continuous-time in the MTB.A linear discrete-time feedback position controller with

feedforward action is used. To ensure that parameters of thereference trajectories (velocity, acceleration) are always setaccording to the time variable operating conditions of MTB,a nonlinear smooth trajectory generator (STG) operating withvariable velocity and acceleration bounds is added at thiscontrol level [7], [12]. According to specification on the posi-tion dynamics, the sampling time limitation on the algorithmsimplemented on ECU does not represent a serious problem. Onthe other hand, direct implementation in ECU software permitsstrong integration of the position controller into the completeDBW system.

A second-order filter is introduced in the ECU/MTB interfaceto smooth the digital to analog converter output (velocity setpoint). This is required to satisfy constraints on the set-pointderivative of the VS velocity controller.

The velocity loop is based on a VS velocity controller with in-tegral action. This ensures robustness to system parameter vari-ation and external load. A velocity estimator is included to re-construct the velocity from the valve position measurement.

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996 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 8, NO. 6, NOVEMBER 2000

Fig. 4. Typical current tracking.

The current loop is based on a simple fixed-frequency hys-teresis controller, suitable for direct integration into the powerconverter electronics.

C. Current Controller

It is well known from the literature (see, for example, [2]–[5])that current controlled pulse width modulators are simple VScontrollers ensuring fast dynamic response, high robustness andlow cost implementation. Among the different implementationsa fixed-frequency one is adopted to satisfy implementation con-straints imposed by the manufacturer of the power electronicscircuit. As explained in Fig. 4, at the beginning of each modula-tion period the control voltage sign is applied to themotor according to the sign of the current error. Once zeroerror is reached the control voltage is applied and main-tained up to the end of the modulation period.

After defining the current reference and the current error, the dynamical model (1) of the current can be

rewritten in error form as

or sign (5)

It is easy to demonstrate (see, for example, [2]) that sliding mode(SM) existence conditions (infinite switching frequency) can beused also to establish the stability of current controlled PWMmodulators operating at finite switching frequency.

The well-known condition for SM existence on “sur-face” is [1]

sign (6)

Substituting (5) in (6), after some simple computations it fol-lows that the stability of the proposed controller is ensured if

(7)

Both system parameters and the external reference affect thesystem stability. Robustness is achieved if enough controlvoltage is applied to compensate for internal and externaldisturbances. The control voltage is variable, depending onthe voltage level of the battery (see Table I). As a consequence,the current reference (the value and its derivative) must becarefully bounded to ensure the current tracking (i.e., currenterror stability) under all operating conditions. The smoothtrajectory generator and the velocity controller design imposethese bounds.

D. Velocity Controller

Owing to fast dynamics and robustness ensured by theadopted current controller, the assumption of the current-sourceconverter can be made and the velocity controller design canbe based on a first order model. This model is obtained joiningequation (2) with (4). In order to analyze and design thecontroller structure, the velocity-tracking control problem istransformed into the equivalent stability problem for the systemin error form. After defining the velocity reference and thevelocity error , the error model is

(8)

or, equivalently

(9)

where disturbance and input coefficient are given by

(10)

Under some hypotheses on the bounds of parameter, distur-bance and its derivative, the stability of system (7) can beensured by the following three-term controller:

sign sat (11)

where

satififif

(12)

Control law (11) and (12) is a modification of a VS control lawwith integral action originally proposed in [6]. By defining apositive velocity error bound , it can be proved that:

1) the system (9) is stabilized and, consequently, the velocitytracking is guaranteed;

2) the velocity error reaches the boundary layerin a finite time and lies inside ;

if the controller parameters ( ) in (11) and (12) satisfythe following inequalities:

(13)

(14)

where

(15)

reflect the assumptions that there are finite bounds on the deriva-tive of the disturbance and on the coefficient.

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ROSSIet al.: ROBUST CONTROL OF A THROTTLE BODY FOR DRIVE BY WIRE OPERATION OF AUTOMOTIVE ENGINES 997

The proof of the previous statement is quite complicated. Theinterested reader can refer to the Appendix, [2], [6] and [9].

Here some general considerations are made to better clarifyits use. The characteristics of MTB, as well as the external loadtorque and the external reference are all considered as boundeddisturbances in the design of the proposed controller [see (9)].The velocity tracking is achieved without an exact knowledge ofsystem and load parameters. Only bounds on parameter valuesand their derivatives are used in the design. Moreover, design in-equalities (14) ensure some degrees of freedom in the selectionof control coefficients and, since they are not a strictly neces-sary condition to ensure stability, they could even be violated,checking stability by simulations. It must be pointed out that thefinite bound on the total disturbance derivative [see (15)] isa strictly necessary condition for system stability. This means:

1) the velocity reference must have bounded first and secondderivatives;

2) the load torque and its derivative must be limited.

The first condition is ensured by the joint action of the STGin the position controller and the second-order filter that recon-structs a continuous velocity reference from the discrete one(see Fig. 3). Referring to the second condition, there are twostructural discontinuities in the load torque:

1) at LH position ( has a discontinuity) as shown in Fig. 2;2) for ( has a discontinuity due to static friction).

In these two isolated operating points the disturbance derivativeis not limited and the velocity tracking is lost. Since in

all other operating points is limited, the robustness of theproposed controller ensures a fast tracking recovery.

With respect to the controller originally proposed in [6], thismodified solution does not produce an SM motion withsince the discontinuous action in the control law has been re-placed with a high-gain saturated action. A limit cycle ariseswhose amplitude is always smaller than the design parameter

. This limit cycle is the equivalent of the chattering caused byoperation at finite switching frequency in VS controllers.

The control law (11) adopted has some significant advantagesif it is compared with classical VS control laws, since:

• the maximum amplitude of the residual tracking error is adesign parameter;

• under the above-mentioned smoothness conditions on, the velocity regulator produces a continuous

output (current reference). This condition is required in(7) to ensure SM existence on the current controller.

In order to bound the current reference, saturation is addedto the controller integral action. Moreover, to limit the current

reference derivative, parameters of the velocity controller mustsatisfy the added condition

(16)

where is the maximum achievable current derivative.It is quite difficult to strictly verify (16) for each oper-

ating condition, since the current derivative must be boundedaccording to actual value and MTB state [see (1)]. Asexplained in more detail in the next section, STG produces aposition reference complying with energetic constraints withdifferent . This means that the current reference, generatedby the VS velocity controller, will be automatically “near tosatisfying” (16) for each normal operating condition. Therefore,it is admissible to select controller parameters, , and inorder to satisfy (16) with reference only to the nominal case.

A direct measurement of the throttle velocity is not available.The velocity must be estimated from the position measurementmade by a linear potentiometer. Some care must be taken inperforming the signal derivative in such a noisy environment.Tradeoff between noise sensibility and bandwidth must be care-fully considered.

The proposed velocity controller is suitable for inexpensiveanalog implementation.

E. Reference Generation and Position Controller

Good position tracking can be achieved if the reference isalways consistent with MTB energetic limitations. The MTBmodel can be used to get the maximum positive and negativethrottle accelerations for every mechanical state of the valve andpower supply value, under the assumption of the worst caseexternal load.

Neglecting some small terms, the results are shown in (17)and (18) at the bottom of the page. The maximum positivethrottle acceleration as a function ofand is shown in Fig. 5,with V. These results are computed using typicalvalues of MTB parameters.

The fastest position and velocity reference consistent with thecurrent MTB state, are on-line generated by the trajectory gener-ator, built as a state-variable filter controlled by a VS controller,as shown in Fig. 6.

To explain the trajectory generator design, let us assume thatand are the input position reference and its derivative,and are the corresponding filtered output, and

are the variable positive bounds imposed on the outputvelocity and acceleration modules. Let us define the positionand velocity errors as

(17)

(18)

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998 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 8, NO. 6, NOVEMBER 2000

Fig. 5. Maximum positive acceleration as a function of# and!.

Fig. 6. Block diagram of trajectory generator.

The following discrete-time smooth trajectory generator (STG)is used to produce the position reference whose velocity andacceleration are bounded at and , respectively.

(19)

(20)

satsign sign

(21)

sat

(22)

satififif

(23)

Equations (19)–(23) are the discrete-time version of the STGproposed in [7]. They represent the cascade of two integrators(adopted to reconstruct the velocity feedforward signal) feed-back controlled by a VS controller derived from bang-bang con-trol. Bounds on acceleration and velocity ( and )can be arbitrarily imposed at run-time through dedicated con-troller parameters always keeping the filter stability. The maincharacteristic of this trajectory generator is that the output tra-jectory tracks the input reference without overshoot, in almostthe minimum time consistent with the selected bounds on accel-eration and velocity.

Further details on STG characteristics and a discussion on theadopted discrete-time implementation are given in [12]. In theMTB application considered, the velocity bounds are fixed to a

value depending on physical constraints, while the accelerationbounds are variable. Acceleration limits could be computed asa function of and according to (17) and (18). This solutionwas not adopted since values given by these expressions are notvery reliable, owing to uncertain and variable MTB parameters.A simpler approach is proposed. Three ranges are consid-ered: for each range, acceleration bounds are fixed to minimumvalues obtainable by (17) and (18) with the minimum supplyvoltage in the range. This is sufficient to satisfy requirements onthe throttle opening time and guarantees the controllers a “reg-ulation energetic margin.”

The position controller implemented at the ECU level is de-signed as a digital PI controller with velocity feedforward ac-tion.

IV. SIMULATION EXPERIMENTS

Extensive simulation experiments were made to test the con-troller performance. The first set of experiments was made tocheck control performances of the two inner analog loops, whilethe second set was intended for the overall position controller. Inthe first set of experiments all system parameters are kept con-stant at their nominal value, as reported in Table I. This is nota limitation since the values of system parameters are not usedto tune the current and velocity controllers. Besides, constantsystem parameters in (4) mean variable load torque.

A. Current Controller

Two different simulations at the two different switching fre-quencies of 10 KHz and 20 KHz are reported in Fig. 7(a) and(b), respectively. Good tracking is achieved and little chatteringis observed when the highest switching frequency (20 KHz) isconsidered.

B. Velocity Controller

A smooth trapezoidal reference is used, similar to the onegenerated by the position controller. The controller parametersadopted are

A A s A/(rad/s)

A s A/(rad/s) A/s

s rad/s

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ROSSIet al.: ROBUST CONTROL OF A THROTTLE BODY FOR DRIVE BY WIRE OPERATION OF AUTOMOTIVE ENGINES 999

Fig. 7. Simulation of current control with continuous reference at differentswitching frequencies: (a) 10 KHz and (b) 20 KHz.

Fig. 8. Simulation of velocity control with filtered trapezoidal set-point:(a) set-point and actual velocity and (b) velocity error.

Very good tracking is reported in Fig. 8(a), confirmed by thesmall velocity tracking error reported in Fig. 8(b). Confirmingthe theoretical analysis, the velocity tracking is lost both at thestarting time s and at the time s, when theposition crosses the LH. As expected the tracking is quicklyrecovered after the load discontinuity.

C. Position Controller

A step command from to is assumed.Throttle velocity and acceleration are bounded to 2000/s (35rad/s) and 60 000/s (1047 rad/s).

The response of the STG is shown in Fig. 9, reporting filteredposition, bounded velocity, and acceleration.

A first set of experiments consists in testing the MTB con-troller under real operating conditions. A sampling time of 4 msis assumed, as imposed by time constraints on the ECU con-troller. A switching frequency of 10KHz is assumed in the cur-rent controller. Throttle velocity and acceleration are boundedto 2000 /s (35 rad/s) and 60 000/s (1047 rad/s). A good re-sponse is given in Fig. 10. The effects of the velocity feedfor-ward action are clearly reported in Fig. 10(a), where the actualposition seems to precede its reference. The discontinuous ve-locity reference, generated by the discrete controller, is filteredwith a second-order filter as reported in Section III-E.

The second set of simulations consists in testing the opera-tion under low battery voltage operating conditions. The sameoperating conditions as in the first set of simulations are consid-

Fig. 9. Smooth trajectory generator outputs: (a) position, (b) velocity, and(c) acceleration.

Fig. 10. Simulation of MDTB controller (discrete timeT = 4 ms):(a) position tracking and (b) velocity tracking.

Fig. 11. Simulation of MDTB controller when operating at 9 V (discrete time.T = 4 ms): (a) position tracking and (b) velocity tracking.

ered, but a supply voltage of 9V is assumed. The trajectory pa-rameters are (automatically) changed accordingly. The throttlevelocity is still bounded to 2000/s (35 rad/s) while the acceler-ation is limited to 40 000/s (700 rad/s).

Tracking performance comparable to that in the previous ex-periment is shown in Fig. 11. In particular the effect of a dif-ferent bound on acceleration can be observed in Fig. 11(b).

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1000 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 8, NO. 6, NOVEMBER 2000

Fig. 12. Simplified schematic diagram of current and velocity controller.

Fig. 13. First experiment on MDTB controller: (a) real position and (b) posi-tion error.

V. EXPERIMENTAL SETUP AND RESULTS

A prototype system was designed to perform experimentson an actual MTB. A custom analog board, equipped withMOS-FET power transistors and power supply, was designedfor current and velocity controllers. A simplified schematicdiagram is shown in Fig. 12.

To speed up the experiments, standard analog componentswere adopted. In the following figures some offset and noise ef-fects are still present. Better results would be obtained in termsof residual offset and noise if an optimized board, based on hy-brid electronics, was adopted.

The digital position controller and the STG were imple-mented on a rapid prototyping station developed by the authorsat the University of Bologna, Italy [8]. Powerful DSP andinput–output (I/O) (analog and digital) boards located on thebus of a standard personal computer, joined to a special purposeoperating system handling all the real-time and I/O drivers,simplifies the development of digital controllers. Built-inoscilloscope functions are useful to check performance andsave the most relevant waveforms.

A sampling time of 4 ms was adopted for the digital part and aswitching frequency of 10 KHz was set in the current controller.Two different experiments were performed.

The first experiment corresponds to the simulation shown inFig. 10, with a small difference in the two extreme positions, setto 2.5 and 85.5, respectively, for safety reasons.

A very smooth throttle position trajectory is shown inFig. 13(a). The position tracking error (within the specification)is given in Fig. 13(b). The rather long tail on the positionerror is due to some residual offset in the experimental analog

Fig. 14. First experiment on MDTB controller: (a) velocity reference and(b) actual velocity estimation.

Fig. 15. Second experiment on MDTB controller: (a) real position and(b) position error.

hardware that prevents the use of the best integral action gainin the position controller. The velocity reference and the actualvelocity estimation are given in Fig. 14.

The second experiment shows the effect of LH positioncrossing ( ). A small position step from 1 to 7 isapplied to the STG.

Still very good position response is shown in Fig. 15. Theposition scale has been selected to show the small residual effecton the actual position trajectory caused by the LH crossing.

VI. CONCLUSION

A robust position controller for motorized throttle body inautomotive applications is presented. Complexity of the controlproblem is explained and a control architecture is presented, en-suring very high robustness at limited cost. The cascaded con-trol structure adopted is illustrated. It enables the solution of thecontrol problem with the most suitable control algorithm andimplementation technology. The use of variable structure con-trol techniques represents the key element to achieving the solu-tion. The controllers designed at the different cascaded level arepresented and discussed. The extensive set of simulation testsreported shows good performance for the proposed control algo-rithm. The implemented prototype controller is also presented.The experimental results confirm the feasibility of the proposedapproach. Application specifications are fully satisfied both interms of control performance and controller cost.

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ROSSIet al.: ROBUST CONTROL OF A THROTTLE BODY FOR DRIVE BY WIRE OPERATION OF AUTOMOTIVE ENGINES 1001

APPENDIX

The velocity tracking problem in Section III-D has beentransformed into an equivalent stability problem for the systemin error form

(A1)

If the three-term VS stabilizing controller (11)–(12) is consid-ered, the resulting closed-loop second-order system is the fol-lowing:

sign sat

(A2)where .

Hypotheses:Based on physical bounds on unknown ortime-varying coefficients, the following mathematical hy-potheses can be formulated.

H1) The velocity error is a bounded variable and thestate dependent disturbance is a continuousfunction, with piecewise continuous derivative.

H2) The time derivative of is bounded

where is a known positive constant.H3) The coefficient is positive and bounded.

Then the following theorem can be stated:Theorem: Considering the closed-loop system (A2), if hy-

potheses H1, H2, H3 and design inequalities (11)–(12) are sat-isfied then for every initial state there is a finite timesuch that

where is arbitrary.Proof: System (A2) can be rewritten in state-space form

as

sat

sign(A3)

From H2 and (14) it follows that the sign ofin (A3) does notdepend on the term . The following four regions can bedetermined according to the sign ofand :

sat

where and

sat

where and

sat

where and

sat

where and (A4)

For every initial state and for each consistent with H1and H2, the system trajectories will always evolve from a region

to region , owing to state derivatives signs. Thus,each trajectory intersects the axis on a succession ofpoints individuated by ( ). In Fig. 16 a typical trajectory isgiven.

Fig. 16. VS controller typical trajectory in phase plane

As shown in [9], (13) and (14) guarantee that, with the worstdisturbance sign , a single asymptotically stablelimit cycle is present in region

(A5)

It will be proved that there are no other stable limit cycles for thesystem (A3) with the worst disturbance, under hypotheses H1,H2, H3 and (14). This implies that closed-loop system trajec-tories will converge to in a finite time, for each initial stateand for each consistent with H1 and H2.

Defining the region , contained by , as

(A6)

the proof proceeds in two steps.Step 1: In this part, initial states belonging to are consid-

ered.For each initial state in , with worst case disturbance, the

system behavior is the same as that analyzed in [9], thus systemtrajectories will converge to the unique asymptotically stablelimit cycle contained in .

Step 2: In this part initial states not belonging to are con-sidered.

As previously stated, each system trajectory intersects axison a succession of points ( ). Thus, with the worst

case disturbance sign , the following is necessaryand sufficient condition to ensure that there are not other limitcycles out of :

(A7)

With the worst disturbance, the system trajectories evolve instate-space according to:

satsign sign

(A8)

Let assume, without loss of generality, that at timesystem state is ( ), with [the case

follows by symmetry]. Starting from , the systemtrajectory evolves in and, at , reaches the surface

sat in . There are two cases.If , the trajectory will evolve as shown in [9] andit will converge to the sole limit cycle contained in ; in fact,

is smaller than . If [see (A1)] the tra-jectory will evolve in , it will intersect the axis at

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1002 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 8, NO. 6, NOVEMBER 2000

, in [ ], where is the solution of the fol-lowing equation:

(A9)Subsequently, the system trajectory will reach the axis ,in ( ), where is the solution of the following equa-tion:

(A10)

Due to hypotheses (14)

(A11)

From (A9), (A11) and (14) it follows that

(A12)

Hence, from (14), it follows that

(A13)

Consequently

(A14)

and, due to (14) and (A11)

(A15)

Thus

(A16)

This means that design inequalities (14) satisfy condition (A7).

REFERENCES

[1] V. I. Utkin, “Variable structure systems with sliding modes,”IEEETrans. Automat. Contr., vol. AC-22, pp. 212–222, Feb. 1977.

[2] C. Rossi and A. Tonielli, “Robust control of permanent magnet motors:VSS techniques lead to simple hardware implementations,”IEEE Trans.Ind. Electron., vol. 41, Apr. 1994.

[3] J. Holtz, “Pulsewidth modulation—A survey,”IEEE Trans. Ind. Elec-tron., vol. 39, pp. 410–420, Oct. 1992.

[4] D. M. Brod and D. W. Novotny, “Current control of VSI-PWM in-verters,”IEEE Trans. Ind. Applicat., vol. IA-21, pp. 562–570, May/June1985.

[5] C. Rossi and A. Tonielli, “Robust current controller for a three-phaseinverter using finite-state automaton,”IEEE Trans. Ind. Electron., vol.42, Feb. 1995.

[6] R. Zanasi, “Sliding mode using discontinuous control algorithm of inte-gral type,”Int. J. Contr., vol. 57, no. 5, pp. 1079–1099, 1993.

[7] C. G. Lo Bianco, A. Tonielli, and R. Zanasi, “Nonlinear trajectory gen-erator,” inProc. IEEE—IECON’96 Int. Conf., Taipei, Taiwan, R.O.C.,Aug. 1996.

[8] R. Morici, C. Rossi, and A. Tonielli, “Fast prototyping of nonlinear con-trollers for electric motor drives,” inIFAC World Congr. 1993, Sydney,Australia, Aug. 1993.

[9] C. Bonivento and R. Zanasi, “Discontinuous integral control applied tothe orientation of a spacecraft,” inIFAC Symp. Robust Control Design,Rio de Janeiro, Brazil, Sept. 1994.

[10] R. J. Tudor, “Electronic throttle control as an emission reduction device,”in Annual SAE Congr., 1996, Paper 930 939.

[11] H. M. Streib and H. Bischof, “Electronic throttle control (ETC): A costeffective system for improved emissions, fuel economy, and drivability,”in Annu. SAE Congr., 1996, Paper number: 960 338.

[12] R. Zanasi, C. G. Lo Bianco, and A. Tonielli, “Nonlinear filters for thegeneration of smooth trajectories,”Automatica, vol. 36, no. 3, Mar.2000.

Carlo Rossi was born in Fabriano, Ancona, Italy, on January 3, 1964. He re-ceived the Dr. Ing. degree in electronic engineering and the Ph.D. degree insystem science and engineering from the University of Bologna, Italy, in 1989and 1993, respectively.

In 1989, he joined the Department of Electronics, Computer, and System Sci-ence (DEIS) of the University of Bologna. In 1993, he spent six months at theUniversity of California, Santa Barbara, as a Visiting Researcher from the ItalianNational Council of Research. In 1995, he joined the “Engine Control SystemDivision” of Magneti Marelli S.p.A., Bologna, where he is currently SystemAnalysis and Simulation Manager. His research interests include electric motordrives, geometric approach to nonlinear control, nonlinear observers, variablestructure systems, and hybrid control applied to automotive systems.

Andrea Tilli was born in Bologna, Italy, on April 4,1971. He received the Dr. Ing. degree in electronic en-gineering and the Ph.D. degree in system science andengineering from the University of Bologna, Italy, in1996 and 2000, respectively.

Since 1997, he has been at the Department of Elec-tronics, Computer, and System Science (DEIS) of theUniversity of Bologna. His current research interestsinclude nonlinear control techniques, variable struc-ture systems, electric drives, active power filters, andDSP-based control architectures.

Alberto Tonielli (A’92) was born in Tossignano,Bologna, Italy, on April 1, 1949. He received theDr. Ing. degree in electronic engineering from theUniversity of Bologna, Italy, in 1974.

In 1975, he joined the Department of Electronics,Computer and System Science (DEIS) of the Univer-sity of Bologna, with a grant from the Ministry ofPublic Instruction. In 1979, he started teaching as anAssistant Professor. In 1980, he became PermanentResearcher. In 1981, he spent two quarters at the Uni-versity of Florida, Gainesville, as Visiting Associate

Professor. In 1985, he became Associate Professor of Control System Technolo-gies at the University of Bologna. Currently, he is Full Professor of AutomaticControl at the same university. His current research interests are in the fieldsof nonlinear and sliding mode control for electric motors, nonlinear observers,robotics, and DSP-based control architectures.