Modelling of electronic throttle body for position control system development

Transcription

1 Chapter 4 Modelling of electronic throttle body for position control system development 4.1. INTRODUCTION Based on the driver and other system requirements, the estimated throttle opening angle has to be precisely maintained in electronic throttle body (ETB) for providing better throttle response and drivability. Airflow into the intake duct of the engine is precisely controlled by proper positioning of butterfly valve which leads to allows enhanced fuel air mixture, thus optimizing combustion and reduced emissions. However, presence of multiple non-smooth nonlinearities such as limp-home position springs, different frictions, parameter variations, aging etc in the electronic throttle body affects the position accuracy of the throttle valve. Operation of ETB in the engine intake manifold, leads to create the nonlinearities and parameter uncertainties affects the system stability. The nonlinear characteristics in the system are also varied according to the operating conditions and as well the environmental conditions such as temperature, humidity and airflow. Hence there is a need of the control system to handle these nonlinearities present in the electronic throttle system. The nonlinearities predominantly exist in area near to the closed position of the throttle and the nonlinear effects are reduced as long as the valve opens. However the throttle control system has to track the reference throttle angle in its entire operating regime, particularly in the lower throttle valve angle for the idle speed control due to the prevailing of friction and opposing spring force are maximum in this region. The control system of electronic throttle should meet certain requirements, such as optimum settling time, no overshoot, less steady-state pointing error, low level of perturbations, should be robust and simple in its design to a range of plant parameter variations or disturbances. The accuracy and performances of the control system is largely depends on the type of control system employed. Control system design of an electronic throttle body is 66

2 challenging task, because of the throttle angle estimation complexities and also due to the presence of nonlinearities in the system NONLINEARITIES CHARACTERSTICS OF ETB Even though the electronic throttle body (ETB) is a simple device, but the system performance is significantly affected by various nonlinear characteristic such as limp home spring position, frictions, aerodynamic force of airflow across the throttle valve. In addition the system parameters are often uncertain due to aging, variations in working conditions and manufacturing tolerances. Mostly the literatures are addressing the nonlinearities created by the friction and spring. The present work addresses the nonlinearities created due to the limp home position spring and friction effect. The following section discuss about the nonlinear characteristic of limp home position spring and friction LIMP HOME POSITION SPRING NONLINEARITY Electronic throttle body has two inbuilt springs to keep the throttle valve open at a default open position. The throttle valve is opened for a default angle by the dual spring and this position is called as limp home position (LH) which is the fail safe location. To accomplish this, two springs are employed called as main spring is used to close the throttle and the other spring is in the plunger assembly of the valve, causes the throttle to be open in default angle. Hence, in the limp home position the spring forces the throttle valve to open for a certain angle ahead of the closed position. This is because, in the event of malfunction in the electronic throttle or other system malfunctions, the preload spring can bring back the valve to the limp-home position which is slightly above the closed position without an armature voltage to the motor. This causes the small amount of airflow is always ensured to operate the engine at a fixed condition even in case of failure in the system. By means of this the full closed position of throttle valve is prevented, which allows the driver to limp until it arrives at the nearest vehicle repair station. Due to this the throttle is trapped in the limp home region for a certain period of time until the spring force is overcomes. Also the operation of the idling and very low 67

3 load of an engine, the throttle angle is around the region of limp home position leads to create nonlinearity in controlling FRICTION NONLINEARITIES IN THROTTLE BODY As the throttle valve is moved by the motor, it has to overcome frictional forces created by the gearbox, LH springs and as well as in the throttle valve which act as a nonlinear phenomenon in the system. There are different types frictional forces developed on the throttle body such a Coulomb friction, static friction, stribeck friction, viscous and gear box friction. In the present work, Coulomb and viscous frictions are only considered in the control system development. I) COULOMB FRICTION The friction acting upon the system is related to the throttle movement direction (i.e. sign of velocity of throttle plate movement). Coulomb friction model does not rely on the magnitude of velocity, but rather just on direction of velocity. II) VISCOUS FRICTION Viscous friction happens in the situations where the throttle plate starts to rotate, which leads to reduces friction coefficient. Viscous friction is directly proportional to the throttle angular velocity and it increasing with increase in velocity. Hence, precise positioning of the throttle valve is important for regulating the airflow and torque requirements of the engine. However, the variation in the actual position of the throttle valve as compared to desired throttle angle input due to the nonlinearities described above such as friction and limp home position in the system DYNAMIC MODEL OF ELECTRONIC THROTTLE BODY In order to study the nonlinear effects on the angular position and throttle control system development, an integrated dynamic throttle body model has been developed in the present work and it is explained in the subsequent sections. A mathematical model 68

4 development place a major role while designing the appropriate control system for the plant. A typical mathematical model block diagram of Bosch s DV-E5 electronic throttle body is developed for the simulation purpose, by considering all the mechanical and electronic related components Figure.4.1 shows a typical electronic throttle body consisting of DC servo motor, gearbox and dual no-return spring. For the desired throttle angle input (, the throttle control system provides a motor voltage (U Motor ) signal to the H-Bridge driver circuit. For actuating the motor, H-bridge creates a motor armature current with an equivalent direction and duty cycle. In order to reduce the position error of the throttle valve a closed loop feedback control system is accomplished by using a throttle position sensor signal. Figure.4.1. Schematic of electronic throttle body system components DC MOTOR The precise positioning of the throttle valve angle is changed by using the DC motor and it consists of an inductor, resistor and a back emf voltage due to the motor rotation. U motor = (4.1) GEAR ARRANGEMENTS The gear arrangement in the throttle body connects the motor and the butterfly valve. Due to the gear ratios, the characteristic of actuation motor is the dominant 69

5 contributor of the whole ETB model. By means of the gear systems the torque produced by the motor is improved. Because of the torque improvement the size of the motor can be reduced and at the same time the gears system facilitates the motor to locate in parallel to the throttle shaft for a compact design. The butterfly valve is linked to the motor by means of the gear arrangements as shown in figure.4.1 and the photographic view is shown in figure.4.2. The gear set consist of pinion gear(n p ), motor gear(n m ), an intermediate gear(n i ) and valve gear(n v ). The equation for the gear ratio (G r ) between the motor shaft and throttle plate is give as, G r = = (4.2) By substituting eqn (4.2) and U motor = (4.3) Fig.4.2. Photographic view of gear arrangements in electronic throttle body LIMP HOME SPRING MODEL The default angle in the throttle valve accomplished by the dual non-return springs creates the nonlinearity in the operation of throttle control system due to asymmetric stiffness of the two springs. Each spring is acting independently on its respective direction, and both are pre-compressed. Both springs are pre-compressed by a specific angle and there is a minimum non-zero torque that is required to move throttle plate from its mean position. The spring torque is a piecewise linear function but the 70

6 spring constant differs greatly, and hence the spring torque depends on whether throttle valve is in the limp home forward or reverse position. A typical spring torque characteristic shown in Figure.4.3 of Bosch s DV-E5 electronic throttle body with spring balance point or the limp home position which varies between 14.5 (θ - Limp-home) and 15.5 (θ + Limp-home), also the lower mechanical stop (LMS) is at and upper mechanical stop (UMS) is at This variation in limp positive and negative is due to the construction flaws in the throttle body, aging, etc. The position of limp home, maximum and minimum angle for the throttle body is varied for the different category of engine throttle bodies according to the requirements. Figure.4.3. Variation of spring torque with the throttle angle Each spring is acting independently on its respective direction, and both are precompressed. Thus the resulting initial torque was non-zero. One of the non-linear moments acting on the throttle body was spring torque. The spring torque is a piecewise linear function but the spring constant differs greatly, and hence the spring torque depends on whether throttle valve is in the limp home forward or reverse position as shown in Figure.3. The spring torque applied to the throttle valve shaft is given as, T + spring = K + spring * (θ spring ) (4.4) Where spring compression related to the throttle angle, θ spring = (θ throttle - θ + Limp + θ + pre-load) 71

7 Where the preload torque on forward direction is give as T + pre-load = K + spring * θ + pre-load and the eqn (4.4) is given as, T + spring = K + spring * (θ throttle θ + Limp) + T + pre-load (4.5) Spring torque equation for acting on the reverse direction is derived as, T - spring = K - spring * (θ throttle θ - Limp) + T - pre-load (4.6) The analytical function of the restoring spring torque feature is given as four pieces of function and is expressed as in piecewise linear function, If θ throttle If θ limp θ throttle T spring = If θ limp θ throttle ---- (4.7) If θ throttle Figure.4.4.Variation of frictional torque with throttle angular velocity FRICTION MODELING As the throttle valve moved by the servo motor, it has to overcome frictional forces created by the gearbox and as well as in the throttle valve which act as a nonlinear phenomenon in the system. The frictional forces create a frictional torque (T static friction ) which opposes the direction of the motion. For the modeling of throttle body system, dry (Coulomb) friction and viscous friction are considered. A signum function is used to assess the direction of frictional torque depending on the direction of angular velocity. The signum function given as, Sign(x) = [ -1 for x<1, 0 for x=0, +1 for x>1] 72

8 As there are two different springs are acting in their respective active region, direction of friction is dependent on the direction of motion. Thus the frictional torque acting upon the system is related to the throttle movement direction (i.e. sign of velocity of throttle plate movement) as shown in figure.4.4. This condition is included by using signum function and the static frictional torque is modeled using coulomb friction which is represented in the following equation (4.8) Another friction factor is the viscous friction and is directly proportional to the throttle angular velocity. Its direction is always opposite to movement. Hence torque due to viscous friction will be as per the following equation (4.9) Figure.4.5. Dynamic model of electronic throttle body system DYNAMIC MOTION OF ETB The dynamic model of the electronic throttle body is formulated by considering the interaction between the each part of the system such as DC motor, dual springs and gearbox arrangements. The dynamic behavior the electronic throttle body is given by the torque acting on the throttle plate. The dynamic torque balance equation for motor will be as, 73

9 ---- (4.10) Behavior of the throttle valve load torque, which is transmitted through the reduction of gear trains, is governed as follows, (4.11) Combining the equation (4.10) and (4.11) gives the motor torque as follows, (4.12) Where J equivalent = J motor + J throttle ), C equivalent = C motor + C throttle ) and. The mathematical model of electronic throttle body on load side is given by the equation (4.12), considering the limp home position dual spring, dc motor with gear arrangements and friction. From the above mentioned dynamic behavior, a virtual model of electronic throttle body system is created in the SIMULINK workspace as shown in Appendix- A. The dynamic ETB model shown in figure.4.5 is useful in analyzing the dynamic behavior of electronic throttle body, parameter estimations and control system design process. Using the integrated model of the electronic throttle body, the nonlinearities which affect the throttle angle position accuracy such as friction and limp home spring position can be controlled by the robust control system design ESTIMATION OF MODEL PARAMETERS The various parameters in the mathematical model of the electronic throttle body such as motor constant, spring constant, preload torque, etc have to be estimated for the simulation and optimization of the electronic throttle body control system. In order to establish the various parameters of the throttle body, parameter estimation toolbox in MATLAB is used in this work. For the initial software in loop simulation of virtual throttle body. Model parameters of the throttle body are obtained by means of the multiple iterations and the final obtained values using estimation toolbox are tabulated in the Table

10 In order to validate the obtained data, the Bosch electronic throttle body is tested for the different operating voltages to evaluate some of the parameters experimentally by means of motor stall test. Thus, the obtained values of the motor are such as the resistance (R) is Ω, inductance (L) is 1.523mH and K back emf is Vs/rad. Hence the experimental values of the above mentioned parameters are closely matched with the estimated parameters. Table.4.1. Estimated parameters of the electronic throttle body Parameters Symbols Input Estimated Units used in model values Values Resistance on Motor R m Ω Coulomb frictional torque Nm Back EMF constant Vs/rad Inductance on Motor L m mh Motor torque constant Nm/A Equivalent moment of inertia Kg. m 2 Equivalent viscous friction coefficient C equivalent Nm.s/rad Preload torque on spring reverse Nm direction Preload torque on spring forward Nm direction Spring constant for reverse direction Nm/degree Spring constant for forward direction Nm/degree 4.4. PROPOSED THROTTLE VALVE POSITION CONTROL SYSTEM Based on the throttle angle requirement from the estimation module, the throttle control module has to adjust the position the throttle valve by considering the actual position ( ) of the valve by means of the throttle position sensor (TPS). There is a position error of throttle valve ( ) due to the nonlinear behavior of the spring 75

11 and friction characteristics in the throttle body, hence PID based closed loop control system along with compensators is followed for maintaining the throttle angle using the TPS signal act as a feedback shown in figure LIMP HOME SPRING COMPENSATOR In the limp home dynamic region of the throttle valve, the initial torque is nonzero and there will not be any spring force acting because of the dual return spring. When the throttle is moved from mean position, there is a variation in the spring torque which creates the nonlinearity in the system. To eliminate the non-linearity created by the dual return springs at the limp home position, a feedforward compensator was developed based on the spring model as discussed in Section Gain compensation is provided based on various reference throttle angle at the given limp home position. The spring torque compensation is calculated based on the different reference throttle angle using the different cases mentioned in the eqn (4.6). Hence the compensated voltage ( u LH ) is given in the following equations, and K m gives a relation between motor stall voltage and corresponding stall torque. The resulted spring compensation voltage is feedforward into the throttle body system. u LH = (4.13) Figure.4.6. Electronic throttle body control system module with compensators 76

12 FRICTION COMPENSATOR Throttle plate creates a frictional torque (T static ) which opposes the direction of motion of butterfly valve while opening or closing. Unlike viscous friction which is a linear function, dry friction has to be compensated because of its non-linear relationship due to the change in the direction of the throttle. The static friction compensation in the control system is based on equation (eqn.4.8) of friction model. Based on the angular velocity in the model, the friction value and sign are determined in the system. Hence, the parameters such as the throttle angle error, direction of throttle valve, and angular velocity are used for the estimating the friction compensation voltage ( u F ). The corresponding voltage is feedforward into the control system which will provide a smooth compensation, in order to compensate the effects of friction in the system. u F = (4.14) PID CONTROLLER PID controller provides the required correction (U PID ) by comparing the required throttle angle with the actual value obtained from the throttle position sensor and it continues till the required throttle angle is achieved by minimizing the error between the required and actual throttle angle values. The tuning of the PID is accomplished through the Ziegler- Nichols method, in order to give the better stability in the control system. u PID = K P (θ req θ actual ) + K I + K D (θ req θ actual ) (4.15) The final control system output voltage (U Motor ) to the motor in the electronic throttle system is the summation of the compensating voltages from limp home and friction compensators along with output from the PID controller (u PID ). U Motor = u PID + u LH + u F (4.16) 77

13 4.5. HARDWARE IN LOOP (HIL) EXPERIMENTAL SETUP Generally in the control algorithm development process Hardware in Loop (HIL) experimental setup is utilized to test the control algorithm in the component level approach. Hardware-in-the-Loop (HIL) testing is a standard V model technique shown in figure.4.7 that is used for testing the control algorithms in complex ECU systems. Some of advantages of HIL approach are enhancing the quality of testing, tight development schedules, actual plant in not needed, save time and money. Fig.4.7. Standard V model approach followed in the HIL testing In order to test the performance of the proposed throttle position control system, an hardware in loop (HIL) experimental test setup has been developed. The test setup consists of ETB, H-bridge driver circuit, battery source, DSP board to interface the simulink code and hardware is developed as shown in figure.4.8. Developed SIMULINK model is run on the target hardware and based on the control signal the PWM signal is fed into the H-bridge drover circuit. For the PWM signal the motor driver supplies the current to rotate the motor shaft. Then the actual position position of the throttle vavle is measred from the thorrtle position sensor and feedback into the microcontroller board for accomplishing the closed loop feedback ELECTRONIC THROTTLE BODY The electronic throttle body utilized for this work is Bosch DVE5 model and and its serial number is Its operating range is in between 8.3 degrees to

14 degrees. The throttle position sensor located in ETB is a dual type potentiometer and the output voltage is varies in the range of 0V to 5V. Bosch throttle body consists of totally six pins in its construction, out of it two pins is for motor driving (positive and negative) and the remaining four pins is for throttle position sensor signal and supply. Figure.4.8. Experimental setup of the electronic throttle body system H-BRIDGE DRIVER CIRCUIT To operate the motor in a bi-directional manner and also to amplify the current, a driver circuit in the form H-bridge is required. In order to reduce the power consumption and also to smooth the current peaks the control signal from the microcontroller inside the EMS in the form of PWM signal is supplied to the H-bridge circuit. For this PWM signal information the H-bridge generates a motor driving power and based on the duty cycle the speed of the motor is controlled. The specification of H-bridge driver is employed to drive the motor is listed in Table

15 Table.4.2. Specification of the H-bridge driver circuit S.No Parameters Specification Units 1 Model No RKI Voltage rating V 3 Current rating 20 A 4 Absolute Maximum Peak Current 50 A 5 Output PWM - 6 No of pins 5-7 Frequency Hz DSP MICROCONTROLLER Digital signal processing (DSP) board is employed in the present work of 16 bit of for the evaluation of proposed control system in Matlab/Simulink platform. The DSP board acts as real time electronic control unit employed in the real engine control system application. The microcontroller board is connected to the throttle position sensor through four pin connection and the H-bridge is connected through 3 pin connections. Specification of the DSP board employed in the present work is tabulated in Table.4.3. Table.4.3. Specification of the H-bridge driver circuit S.No Parameters Specification Units 1 Chip No DSPIC33F - 2 Board name Explorer 16-3 Voltage rating V 4 Current from power supply ma 5 Operating Temperature + 25 C 6 No of pins Frequency 100 MHz 8 No of bits 8 bit 80

16 4.6. RESULTS AND DISCUSSIONS Performance of the proposed throttle position control system for tackling the nonlinearities such as friction and limp home spring position is examined for different throttle angle inputs to the control system. The proposed position control system along with HIL setup is developed in SIMULINK workspace and it is shown in Appendix-B. For testing the performance of the control system, the simulation is carried out in SIL and HIL mode. However, the results of HIL simulation are discussed in the following section for different throttle angle inputs. Hence position control system is simulated for sinusoidal and step, ramp based driving cycle throttle angle signals to the position control system. For these input signals performance output responses such as actual throttle angle measured from throttle position sensor (TPS) is compared with and without compensators. Also, the error between actual and reference throttle angle is compared between with and without compensators in the control system PERFORMANCE OF THE PROPOSED POSITION CONTROL SYSTEM FOR SINUSOIDAL THROTTLE ANGLE INPUT Figure.4.9. Actual throttle angle for sine input with and without compensators 81

17 Sinusoidal throttle angle input to the position control system is varied from 0 to 90 deg as shown in figure.4.9. Response of the actual and input throttle angle shows very minor difference with the presence of compensators in position control system. However, the variation is higher in lower and higher dip region of the sinusoidal curve. This is due to the mechanical limit of maximum angle 84.3 deg and minimum angle 8.3 deg is attained by the throttle valve. Though, the variation is minor very minor across in rest of the region between the input and actual throttle angle response. Variation between the actual responses of with and without compensators shows a higher diverge in the region of 40 to 84.5 deg. This is due to the existence of friction nonlinearity in this region and the friction is increased due to the variation of angle velocity is higher in this region. Figure Error between actual and required throttle angle without compensators Angular error between the actual and input throttle angle without compensators (limp home and friction) in position control system is shown in figure At the peak of sinusoidal curve the error is in the range of 5 deg and in the lower dip region error value is -11 deg. Such a higher value of error in the actual throttle angle shows the necessity of the position control system with compensators for handling the nonlinearities caused due to the frictions and limp home position springs. However, the error between actual and input throttle angle with compensators in control system shown in figure.4.11 depicts the error value in the range of -2.3 deg to +2.9 deg. This shows that the designed 82

18 compensator in the position control system is able handle the nonlinearities caused due to the friction and limp home position springs. Figure Error between actual and required throttle angle with compensators PERFORMANCE OF THE PROPOSED CONTROL SYSTEM FOR STEP SIGNAL BASED DRIVING CYCLE THROTTLE ANGLE INPUT Figure Actual throttle angle for step cycle with and without compensators 83

19 Variation of the actual throttle angle for step signal based driving cycle input to the position control is shown in figure Driving cycle throttle angle input is varied in step sequence from 0 deg to 90 deg of angle. Variations between the input throttle angle to the actual throttle angle is higher across the entire operating region for the control system without compensators. However, the variation of actual throttle is higher for the control system with compensators in the lower region of 8 to 15 deg. This is due to the default position angle and limp home position spring. Since, the initial spring torque has to be overcome by the throttle movement creates the nonlinearities in the operation. Also the error is more in the middle operating range of the position control system with compensators and this due to the existence of friction nonlinearities in this region is high. Figure Error between actual and required throttle angle without compensators Maximum error is varied between input and actual throttle angle in the range of - 10 to + 12 for the control system without compensators as shown in figure Error is more than 5 deg across entire peak of the step signal curve rather than the other regions. This is due to the increased friction nonlinearity as the higher peak is attained. Whereas, the error is reduced by employing the compensators in the control system and it is in the range of 4 to deg as shown in figure This is due to the presence of compensators in the control system is able to tackle the friction and limp home position spring nonlinearities. 84

20 Figure Error between actual and required throttle angle with compensators PERFORMANCE OF THE PROPOSED CONTROL SYSTEM FOR RAMP SIGNAL BASED DRIVING CYCLE THROTTLE ANGLE INPUT Figure Actual throttle angle for ramp cycle with and without compensators Actual throttle angle response for ramp signal based driving cycle input to the position control system is plotted in figure Error between the input and measured actual throttle angle from throttle position sensor is high in the lower region of 8.3 deg to 28 deg. As this region is limp home position and the throttle angle has to spring torque and the error is more for the control system without compensators. Input and actual 85

21 throttle angle is following closely in rest of the region for the control system with compensators and this is due to the efficient handling the nonlinearities present on the electronic throttle body. Figure Error between actual and required throttle angle without compensators Figure Error between actual and required throttle angle with compensators The error value of 8 deg in the lower limp home region of the throttle position without compensators in the control system is noticeable in the curve shown in figure Whereas, the error value in the same region for the presence of compensators 86

22 is in the range of 5 deg as shown in figure In the rest of the place the error is limited and close to zero degrees of angle. Hence, the designed position control system is capable to reduce the effects of nonlinearities present in the electronic throttle body and the control system output is also able to follow the required input throttle angle closely in entire operating region ANGULAR ERROR OF PROPOSED POSITION CONTROL ALGORITHM FOR DIFFERENT THROTTLE ANGLE INPUTS In the proposed control system, the complexity in controlling the electronic throttle system due to the nonlinearities such as friction and limphome spring is also addressed in this strategy using the mathematical models and compensators. Performance of the proposed position control system with compensators (friction and limphome) based on PID controller has been tested by hardware in loop (HIL) test setup for its performance effectiveness by providing the desired throttle opening angle in the form random sine, ramp and step cycle inputs. Figure Angular error of throttle angle input to position control system 87

23 The actual throttle angle response for these three input signals obtained from the throttle position sensor (TPS) proves that the designed control system has the ability to follow the input throttle angle for both simulated and actual conditions. Maximum angular error (desired angle and actual angle) for the three signal inputs is depicted in figure.4.18 which shows maximum error for all three cases for the position control system without compensators. Proposed control strategy with compensators for friction and limp home nonlinearities has the ability to reduce the position error of 50% as compare to the control system without compensators. Hence, the proposed throttle position control system has ability to handle the nonlinearities such as friction and limp home position spring in the electronic throttle body (ETB) and improves the accurate positioning of the throttle valve. However, the developed position control system able to handle the nonlinearities has to be functioned at all operating conditions. Throttle position sensor (TPS) act as a feedback element in the position control system, which has to be monitored for its effective operation across the operating conditions. The consistency and reliability of the throttle position sensor output needs to be monitored appropriately to overcome hardware failure related problems. Hence, soft sensors or virtual sensor has to be developed to overcome the failures and malfunctions of the throttle position sensors in the position control system. 88