International Journal of Automotive Technology, Vol. 14, No. 2, pp. 313−323 (2013) DOI 10.1007/s12239−013−0035−x

Copyright © 2013 KSAE/ 070−17 pISSN 1229−9138/ eISSN 1976−3832

EXPERIMENTAL STUDY OF AN ELECTRO-MECHANICAL CVT RATIO CONTROLLER B. SUPRIYO1)*, K. B. TAWI1) and H. JAMALUDDIN2) 1)

Automotive Engineering Department, Faculty of Mechanical Engineering, Universiti Teknologi, UTM Skudai, Johor 81310, Malaysia 2) Applied Mechanics Department, Faculty of Mechanical Engineering, Universiti Teknologi, UTM Skudai, Johor 81310, Malaysia (Received 13 March 2012 ; Revised 5 August 2012; Accepted 6 October 2012)

ABSTRACT−This paper introduces an electro-mechanical, dual acting pulley, continuously variable transmission (EMDAPCVT) and presents its real time ratio controller using a proportional-derivative-plus-conditional-integral (PDPCI) controller. The ratio controller system is developed based on primary (input) and secondary (output) pulley position controllers. Each position controller has two PID parameters, releasing and clamping, which are determined experimentally using a relay feedback method. A PC-based ratio controller system is implemented using Matlab/Simulink® software and a Keithley DAS1602 data acquisition system card. The experimental results show that the PDPCI controller system can control the CVT ratio adequately. KEY WORDS : Ratio controller, Conditional integral, Electro-mechanical CVT, PID tuning parameters, Relay feedback

1. INTRODUCTION

a smooth and quiet ride as well as driving comfort with no shift shocks. In general, CVT is grouped into belt and toroidal types (Asano, 2004). Until now, the metal pushing V-belt type CVT was the most accepted transmission. This type of CVT commonly utilizes a set of metal belts and a primary pulley and secondary pulley system and adopts a hydraulic cylinder system to deliver continuous pulley clamping forces to maintain a constant ratio and prevent belt slip. In fact, this continuous power consumption represents a major loss to the efficiency of the hydraulic CVT, thus partially decreasing the overall CVT efficiency (Micklem et al., 1996; Ide, 2000; Matthes, 2005). An electro-mechanical dual acting pulley (EMDAP) CVT offers a viable solution to overcome the constant ratio power loss by utilizing power screw mechanisms, as applied in Klaassen et al. (2004). When rotating, the power screw mechanisms shift movable pulley sheaves axially to change the CVT ratio. When stopping, the power screw mechanisms lock the current positions of the pulley sheaves to maintain a constant CVT ratio without consuming any power. The EMDAP CVT consumes electrical power only when shifting to a new CVT ratio. The applications of one movable and one fixed pulley sheaf in the majority of CVT systems may cause the metal belt to misalign. An intensive study of belt misalignment was conducted by Robertson and Tawi (1997). The longterm effect of belt misalignment causes the belt and the pulley to wear, which degrades the performance, efficiency, reliability and safety of the CVT system (Zang, 2009).

Recently, stricter government regulations on the automobile industry concerning environmental issues and energy efficiency have been enforced to challenge manufacturers to reduce both fuel consumption and greenhouse gas emissions in their new vehicles (Lutsei and Sperling, 2006). Engine efficiency plays an important role in improving fuel consumption and lowering gas emissions. The engine itself is not yet efficient because its efficiency is only 20 to 30 percent (Jayabalan and Emadi, 2004), and the remainder is lost in the form of heat, friction, etc. However, with the help of a continuously variable transmission (CVT), the engine can frequently run within its most efficient operating points to improve its fuel consumption performance (Ide, 2000). Ryu and Kim (2008) have achieved an overall system efficiency improvement of an engine-CVT configuration through a modified CVT ratio map by considering the losses in the CVT system. In addition, fuel economy improvements have been achieved through the implementation of CVT ratio control in a hybrid electric vehicle (Yeo et al., 2004; Lee and Kim, 2005). Unlike a traditional manual transmission, which provides different sets of fixed gears, CVT offers infinite numbers of transmission ratios between its minimum and maximum limits, which can be continuously shifted to give *Corresponding author. e-mail: [email protected] 313

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Several works on minimizing the belt misalignment effects using various control strategies have been reported (Zang and Wu, 2009; Zang, 2010). The EMDAP CVT overcomes belt misalignment by adopting two movable pulley sheaves on each pulley shaft instead of one movable sheave. The belt is always clamped by primary and secondary movable pulley sheaves and aligned perpendicular to both the primary and secondary pulley shafts for all CVT ratios. A study involving the EMDAP CVT ratio controller was conducted by Ariyono et al. (2007). This work used the EMDAP CVT as a means of matching the power transfer between the engine and the transmission system. An inner loop control based on a proportional-derivative (PD) ratio controller was applied to follow the desired CVT ratio such that the engine speed could be maintained within its effective operating range for various loads and disturbances based on the maximum power driving strategy of the vehicle. This paper focuses on the real time implementation of PD and proportional-derivative-plus-conditional-integrator (PDPCI) ratio controllers for EMDAP CVT when no load torque is applied to the secondary shaft. In this case, the direct current (DC) motor supplies no-load belt clamping forces while coping with friction from the gear reducers and the power screw mechanisms. Various step input signals representing CVT ratio shifts and three CVT ratio conditional errors of 0.1, 0.2 and 0.3 are used to test the effectiveness of the proposed controllers. The control performance of each controller is then assessed in terms of the settling time response, the percent overshoot and the steady state error.

2. BASIC PRINCIPLE OF CVT The basic principle of a metal pushing V-belt CVT is similar to a speed variator. It consists of a primary pulley, a secondary pulley and a metal belt connecting these two pulleys. The schematic diagram of the variator geometry is shown in Figure 1. If the belt has a fixed length and moves perfectly without slip on the surfaces of the pulley sheaves with primary and secondary running radii, Rp and Rs, respectively, then the tangential velocity (vT) of both the pulleys and the belt will be the same. The relationship between speed and the running radii of

Figure 1. Variator geometry.

the variator are given as follows: ωsRs = ωpRp

(1)

rgs = ωp / ωs

(2)

rCVT = Rs /Rp

(3)

where Rp is primary pulley running radius, Rs is the secondary pulley running radius, ωp is the angular speed of the primary (input) shaft, ωs is the angular speed of the secondary (output) shaft, rgs is the geometrical speed ratio, and rCVT is the CVT ratio. The implicit relationship between the belt length, L, and the running radii are expressed as L = (π+2θ)Rp + (π-2θ)Rs + 2c cos(θ)

(4)

Rp = Rs + c sin (θ)

(5)

where c is the pulley center distance, and θ is half the increase of the wrapped angle on the primary pulley. The relationship between the running radii and the pulley positions can be written as Xp = (Rp- Rp0) tan (α)

(6)

Xs = (Rs- Rs0) tan (α)

(7)

where Rp0 is the minimum primary running radius, Rs0 is the minimum secondary running radius, α is the pulley wedge angle (11o), Xp is the primary pulley position, and Xs is the secondary pulley position. By solving equations (4) and (5) for L= 645.68 mm and c = 165 mm, the plot of the running radii for various values of the half increase in the wrapped angle is shown in Figure 2. Based on the graphs in Figure 2 and equation (3), the relationship between the running radii and the CVT ratio is shown in Figure 3. In addition, by using equations (6) and (7), the relationship between the pulley positions and the CVT ratio can be shown in Figure 4, and the relationship between primary and secondary pulley positions is shown in Figure 5.

Figure 2. Running radii versus half of the increase in the belt wrapped angle.

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Figure 6. EMDAP CVT. Figure 3. Running radii versus CVT ratio.

Figure 4. Pulley positions versus CVT ratio.

Figure 5. Primary versus secondary pulley positions.

Based on Figures 3 and 4, a CVT ratio controller is designed in which both the primary and secondary pulley positions are simultaneously controlled to achieve both desired primary and secondary pulley positions corresponding to the desired CVT ratio. To implement this ratio controller system, two position sensors are required to detect both the primary and secondary pulley positions.

3. EMDAP CVT SYSTEM The EMDAP CVT consists of two movable primary pulley sheaves at the primary (input) shaft, two movable secondary pulley sheaves at the secondary (output) shaft and a Van Doorne’s metal pushing V-belt connecting these two pulleys, as shown in Figure 6. The belt transfers both power and torque from the input to the output shaft based on friction developed between the belt and the contacts of

the pulley sheaves (Fushimi et al., 1996; Kanehara et al., 1996; Klaassen et al., 2004). In addition, two primary movable pulley sheaves and two secondary movable pulley sheaves always clamp the belt at the center of its respective shaft and keep the belt aligned perpendicular to both the primary and secondary shafts for all CVT ratios. This configuration mechanically eliminates belt misalignment. The EMDAP CVT has primary and secondary electromechanical actuated pulley sheaves (EMAPS) systems. Each EMAPS consists of a DC motor system, a gear reducer, two sets of pinion-helical gear reducers, two sets of power screw mechanisms and two movable pulley sheaves. The DC motor drives the mechanical actuator to axially shift two movable pulley sheaves in opposite directions to each other on its respective shaft to control the width of the pulley gap. The forward shift makes the pulley gap narrower, whereas the reverse shift makes the pulley gap wider. The axial positions of the primary and secondary pulley sheaves, Xp and Xs, are measured using position sensors. By applying equations (3), (6) and (7), the CVT ratio, rCVT, can be determined. The input of the EMAPS is a voltage used to adjust the speed of the DC motor, and its output is the actual pulley position, which represents how far the movable pulley sheave has been shifted from its origin point. The origin point represents the minimum position of the pulley sheaf. When a new desired CVT ratio is introduced, the DC motor systems adjust the axial positions of the primary and secondary pulleys to achieve their desired positions accordingly. When the desired CVT ratio is achieved, the DC motor systems are turned off; the power screw mechanisms stop and act as passive brakes to mechanically lock the current positions of pulley sheaves to maintain the current CVT ratio. The EMDAP CVT utilizes a pre-loaded disc spring placed at the back of each secondary pulley sheaf. Based on the disc spring characteristic, a compressive force of approximately 10 kN is required to flatten the spring. Because there are two disc springs at the secondary pulley sheaves, a total of approximately 20 kN of force are produced to clamp the metal belt. During CVT ratio calibration, when the desired ratio is achieved, the primary and secondary position controllers also achieve their desired axial positions and the springs are fully flattened by the secondary DC motor. Thus, the springs are at their flat

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conditions and supply approximately 20 kN of clamping force to keep the belt taut and minimize the occurrence of excessive slip, which can severely damage the belt (Bonsen et al., 2004; Pulles et al., 2005). In addition, the actual axial positions of both the primary and secondary pulleys in the steady state are measured using position sensors based on the flat condition of the disc spring.

Figure 7. Closed loop relay feedback structure for the primary pulley position controller.

4. CONTROL DEVELOPMENT The PID-based controller is a well-known method applied in industrial control systems. It has been the basis for simple and even advanced linear control systems due to its easy design, simple structure, straightforward control law, few tuning parameters and robust performance (Jianghua and Huihe, 2003;Valério and DaCosta, 2006). PID-based position controllers have been commonly implemented in practice and have provided adequate control performance in the vast majority of applications, especially where DC motors are commonly used as actuators (Cervantes and Alvarez-Ramirez, 2001; Yuxin et al., 2006). In this paper, the PID-based controller is selected to fit the EMDAP CVT ratio control application, which is developed based on the primary and secondary pulley position controls and utilizes DC motor systems as its actuators. The PID based control algorithms used in this paper are PD and PDPCI controllers. 4.1. Initial PID Parameters A PID-based controller requires suitable PID parameters of Kp, Ki and Kd to fit certain application objectives. A PID tuning method can be applied to determine these PID parameters. Many PID tuning methods are available today, but selecting the appropriate one is subjective and difficult. The fundamental selection should consider the system characteristics and be simple, easy to perform, safe and robust. Among other PID tuning methods, a combination of the Åström-Hägglund relay feedback tuning method and the Ziegler-Nichols formula was selected as a means of deriving the initial gains of the PID controllers for the control of the EMDAP CVT ratio. The relay feedback tuning method is easy to implement in practice and includes the dynamics of the system. Compared to the Ziegler-Nichols sustained oscillation method, the relay feedback tuning method is less time consuming and safer due to the bounded oscillations. Figures 7 and 8 show the structure of the closed loop relay feedback experiment for the primary and secondary pulley position controllers, respectively. For the primary pulley system, the CVT ratio reference value is rCVT_ref. The reference value is converted to its corresponding primary pulley position (Xpr) based on data related to the primary pulley position and the CVT ratio, as shown in Figure 4. This primary pulley position reference is then converted to its respective voltage (Vxpr) based on data related to the primary position sensor output, as shown in Figure 9. The output of the primary EMAPS is the actual primary pulley

Figure 8. Closed loop relay feedback structure for the secondary pulley position controller.

Figure 9. Primary position sensor output. position (Xpa). The primary pulley position sensor reads the actual pulley position and converts it into its corresponding output voltage (Vxpa). For the secondary pulley system, the reference value is converted to its corresponding secondary pulley radius, which is then used to calculate the secondary pulley position (Xsr) based on data related to the secondary pulley position and the CVT ratio, as shown in Figure 4. The secondary pulley position is then converted to its corresponding voltage (Vxsr) based on data related to the

Figure 10. Secondary position sensor output.

EXPERIMENTAL STUDY OF AN ELECTRO-MECHANICAL CVT RATIO CONTROLLER

secondary position sensor output, as shown in Figure 10. The output of the secondary EMAPS is the actual secondary pulley position (Xsa). The secondary pulley position sensor reads the actual pulley position and converts it to its corresponding output voltage (Vxsa). A step input corresponding to the middle point of the CVT ratio (1.35) is selected as a reference value for the relay feedback experiment, such that the EMDAP CVT can have a maximum symmetrical oscillatory output ratio from 0.7 to 2.0. The amplitude of the relay controller output is set to 5 volts. This value represents the maximum voltage input for the speed controller unit of the DC motor. 4.2. Ratio Controller During the execution of the EMDAP CVT ratio controller, the primary (Cp) and secondary (Cs) controllers have to work synchronously to move the primary and secondary pulley sheaves to their respective positions, which correspond to the desired CVT ratio, as shown in Figure 11. The two blocks consisting of rCVT_ref to Xpr and Xpr to Vxpr convert the CVT ratio reference into the voltage corresponding to the desired primary pulley position. The actual primary pulley position, Xpa, is sensed using the primary pulley position sensor. The output voltage of this sensor, Vxpa, is compared with the voltage value of the desired pulley position, Vxpr. The error between the desired and actual primary pulley positions is used to drive the primary controller, Cp. The output of the primary controller regulates the primary EMAPS such that the actual pulley position reaches the desired pulley position. For any given CVT ratio, the secondary controller (Cs) always tracks the actual primary pulley position (Xpa) to achieve the desired secondary pulley position, as shown in Figure 4. The block of Xpa to Vxsr indirectly converts the actual primary pulley position to a voltage value corresponding to the desired secondary pulley position. This conversion is performed by first converting the primary pulley position to its corresponding secondary pulley position based on the graph shown in Figure 5. Then, the secondary pulley position is converted to its corresponding voltage value based on the graph shown in

Figure 11. EMDAP CVT ratio controller scheme.

317

Figure 10. The two blocks of Xpa to Rpa and Xsa to Rsa convert the primary and secondary axial pulley positions to their corresponding belt-pulley running radii, respectively, to produce the actual CVT ratio. In this work, both controllers, Cp and Cs, can be either PD or PDPCI controllers. 4.2.1. PD controller PD control algorithm employs a proportional term that depends on current system error and a derivative term that depends on the derivative of the system error. A PD controller is commonly used to reduce the overshoot and the oscillation of the controlled variable. When controlling either the primary or secondary electro-mechanically actuated pulley sheaves, two sets of PD parameters are employed, as shown in Figure 12, namely, the clamping PD parameters (Kpc and Kdc) used to increase the pulley running radius and to tighten the belt and the releasing PD parameters (Kpr and Kdr) used to decrease the running radius and to loosen the belt. These two sets of PD parameters have different values and are listed in Tables 1 and 2. The selector block activates one of these two sets of the PD parameters based on the sign of the error input. Selector output Or activates the PID gains during the release of the belt or the widening of the pulley gap while output Oc activates the PID gains during the clamping of the belt or the narrowing of the pulley gap. When the error input is greater than zero, then the Or output will be disabled and the Oc output will be activated to select the clamping PD parameters. However, when the error input is less than zero, then the Oc output will be disabled and the Or output will be activated to select the releasing PD parameters. When the error input equals zero, then the two sets of PD parameters will be disabled, thus producing zero output. In this research, the PD controller system is initially tested using the step inputs with various amplitudes that represent discrete shifting patterns of the CVT ratios. 4.2.2. PDPCI controller The PDPCI controller utilizes proportional, integral and derivative terms, but its integral action will only be

Figure 12. PD controller with a gain switching scheme.

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activated under certain conditions. This condition involves the system absolute error value (e) and the conditional error value (ec). If the system absolute error is less than or equal to the conditional error value, then the integral term is activated, and the PDPCI acts as a standard PID controller, in which the integral term gradually eliminates the steady state error; otherwise, the integral term is disabled, and then PDPCI acts as a standard PD controller. The integral action used in the PDPCI is adapted from the conditional integration technique commonly used in integral anti windup applications to overcome the saturation of the controlled variable due to integral windup (Visioli, 2003). The objectives of the PDPCI ratio controller system are to improve the transient performance of the system with a minimum overshoot executed by the proportional and derivative terms and the steady state performance with the minimum steady state error found by the integral term activated at a certain CVT ratio error. According to the PD controller experimental results, when the CVT performs a minimum shift of 0.1, which is either an up-shift from 2.0 to 1.9 or a down-shift from 1.9 to 2.0, the system does not respond, thus producing the greatest steady state error. When starting the minimum ratio shift, its initial error of 0.1 is used as the smallest conditional error for the PDPCI controller system to start activating its integral part to correct the error. The conditional errors of 0.2 and 0.3 are also considered for comparison purposes and to observe how the system responds when the conditional error is two and three times greater than the minimum error. Three types of PDPCI controller systems with three conditional errors of 0.1, 0.2 and 0.3 are then determined to be the PDPCI-0.1, PDPCI-0.2 and PDPCI-0.3 controller systems, respectively. When controlling either the primary or the secondary electro-mechanically actuated pulley sheaves, two sets of PID parameters are employed, as shown in Figure 13, namely, the clamping PID parameters (Kpc, Kdc and Kic) and the releasing PID parameters (Kpr, Kdr and Kir). These two sets of PID parameters have different values and are listed in Tables 1 and 2. The selector block activates one set of these two sets of PID parameters based on the sign of the

error input. In this case, when the error input is greater than zero, then the Or output will be disabled, and the Oc output will be activated to select the clamping PID parameters. However, when the error input is less than zero, then the Oc output will be disabled, and the Or output will be activated to select the releasing PID parameters. When the error input equals zero, then the two sets of PID parameters will be disabled, thus producing zero output.

Figure 13. PDPCI controller with the gain switching scheme.

Figure 14. Block diagram of the EMDAP CVT test rig control unit.

5. EXPERIMENTAL TEST RIG An experimental test rig was set up to perform all experiments to test the performance of the EMDAP CVT ratio controllers. The block diagram of the EMDAP CVT test rig is shown in Figure 14, and the photograph of EMDAP CVT test rig is shown in Figure 15. The EMDAP CVT system is equipped with sensors, actuators, an interfacing unit, DAS-1602, a computer with MATLAB/ Simulink software installed, a power supply unit and an AC motor. This research uses a desktop computer to develop, edit and run the controller program and to record and plot the desired data using the MATLAB/Simulink software. The power supply unit consists of two 12 volt 60 ampere car batteries serially connected to each other to produce 24 volts and 60 amperes to power the DC motor systems. Each DC motor is a brushless DC motor with a rated voltage of 24 volts, a speed of 3000 rpm and a rated torque of 1 Nm. It is controlled using a speed controller unit operated using an external voltage between 0 to 5 volts supplied from an Analog Output Port from a DAS-1602 using the MATLAB/ Simulink software installed in the desktop computer to adjust the motor speed. Each axial position sensor uses a linearly precision 10turn-potentiometer connected by a gear reduction to the pinion shaft. This pinion shaft is driven by the output of the DC motor gear reducer. The potentiometer measures how many times the power screw mechanism rotates and indirectly measures the axial position of the movable pulley sheaves displaced from its origin. The potentiometer is supplied with a 5-volt reference voltage, and thus, its

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Figure 16. Relay feedback response of the primary pulley position controller system. Figure 15. Photograph of the EMDAP CVT test rig.

output voltage swings from 0 to 5 volts. The minimum axial positions of the primary and secondary pulleys are detected by the primary and secondary minimum pulley position sensors. The axial movements of the primary and secondary pulleys are monitored by the two position sensors: the primary pulley position sensor (primary PPS) and the secondary pulley position sensor (secondary PPS). The input shaft of the EMDAP CVT is coupled with an AC motor, which rotates at a constant speed of 1700 rpm.

6. RESULTS AND DISCUSSIONS 6.1. Initial PID Parameters The result of the relay feedback experiment for the primary DC motor system is shown in Figure 16. The signal Vxpr acts as reference input for the primary pulley position, the signal Vxpa represents the actual primary pulley position, and the signal Vprel is the relay controller output. Figure 17 shows the result of the relay feedback experiment for the secondary DC motor system. The signal Vxsr acts as a reference input for the secondary pulley position, the signal Vxsa represents the actual secondary pulley position, and the signal Vsrel is the relay controller output. In Figures 16 and 17, the waveform oscillations and the relay outputs of both the primary and secondary pulley systems are not symmetrical. Thus, the internal load torque overcome by the primary DC motor system is not always constant. This phenomenon can be understood because the DC motor torque used to clamp the belt is greater than that to release the belt. Consequently, two different gains are required for each position controller to clamp or release the belt. By taking the average of all data relating to the clamping conditions, the critical gain (Kc) and the period (Tc) in the clamping condition can be found. Similarly, by taking the average of all data relating to the releasing condition, the critical gain and the period in the releasing condition can be found. By applying the Ziegler-Nichols formula (Ho et al., 1996), all PID gains for clamping and

Figure 17. Relay feedback response of the secondary pulley position controller system.

Table 1. Initial PID parameters for the primary DC motor system. d

a

Tc

Kc

Kp

Kd

Ki

Clamping 5

0.16 2.67 39.77 23.86 17.90 7.95

Releasing 5

0.22 3,22 29.20 17.52 10.88 7.05

Table 2. Initial PID parameters for the secondary DC motor system. d

a

Tc

Kc

Kp

Kd

Ki

Clamping 5 0.167 2.90 38.21 22.93 15.82 8.31 Releasing 5 0.200 3,19 31.80 19.08 11.94 7.62 releasing the belt can be determined, as shown in Tables 1 and 2, where d is the output relay amplitude, and a is the wave oscillation amplitude (Åström and Hägglund, 1984). 6.2. Step Input Response The step input signals represent two CVT ratio shift patterns: up-shift and down-shift. Every up-shift pattern will start from a CVT ratio of 2.0 and shift to the desired CVT ratio of 0.7, 1.0, 1.3, 1.6 or 1.9, thus causing the angular speed of the secondary shaft to increase accordingly. Conversely, every down-shift pattern will start from any CVT ratio of 0.7, 1.0, 1.3, 1.6 or 1.9 and shift to

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Figure 21. Step response for 2.0-to-1.6 up-shift. Figure 18. Step response for 2.0-to-0.7 up-shift.

Figure 22. Step response for 2.0-to-1.9 up-shift. Figure 19. Step response for 2.0-to-1.0 up-shift.

Figure 23. Step response for 0.7-to-2.0 down-shift. Figure 20. Step response for 2.0-to-1.3 up-shift. the desired CVT ratio of 2.0, thus causing the angular speed of the secondary shaft to decrease. These CVT ratios represent the CVT ratio working ranges from 2.0 to 0.7. The step responses for the up-shifts are plotted in Figures 18 to 22 while those for down-shifts are shown in Figures 23 to 27. Overall, for all CVT ratio shift patterns, the PD ratio controller system does not reach its desired value (set point, SP), thus leading to a steady state error and no overshoot. However, the PDPCI ratio controller system significantly reduces the steady state errors, but the system creates overshoot at certain ratios. 6.2.1. Settling time In this paper, the settling time is the time required for the

Figure 24. Step response for 1.0-to-2.0 down-shift.

EMDAP CVT system response to reach and stay within 5 percent of its desired CVT ratio. In this case, the PD ratio controller system does not achieve the settling time

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rated torque of only 1 Nm. Future research will consider the use of a BLDC motor with a greater rated speed and torque to reduce the settling time. By using the greater torque, the gear reducer ratio can be reduced accordingly, thus increasing the axial pulley speed but still satisfying the desired torque to clamp the metal belt.

Figure 25. Step response for 1.3-to-2.0 down-shift.

Figure 26. Step response for 1.6-to-2.0 down-shift.

Figure 27. Step response for 1.9-to-2.0 down-shift. requirement. For all CVT ratio shift patterns, as shown in Figures 18 to 27, the PDPCI-0.3 mostly results in the fastest settling time while the PDPCI-0.1 results in the slowest one. In addition, PDPCI controller systems have faster responses during the down-shift than the up-shift because the primary DC motor, which is responsible for determining the transmission ratio, requires a greater torque to clamp the belt during up-shift than during downshift. For the maximum up-shift (Figure 18), the PDPCI-0.3, PDPCI-0.2 and PDPCI-0.1 systems require approximately 9.6, 10 and 10.1 seconds, respectively. For the maximum down-shift (Figure 23), they require approximately 7.4, 7.8 and 9.4 seconds, respectively. For this EMDAP CVT prototype, the slow settling time was due to the use of BLDC motor, which has a rated speed of 3000 rpm and a

6.2.3. Percent overshoot Because the system response for the PD ratio controller system does not reach the desired CVT ratio, the PD controller system produces no overshoot. For all CVT ratio shift patterns, as shown in Figures 18 to 27, the PDPCI-0.1 system generally has the smallest overshoot while the PDPCI-0.3 system has the greatest. During the maximum up-shift (Figure 18), the PDPCI-0.1, PDPCI-0.2 and PDPCI-0.3 systems produce approximately 0.5, 0.6 and 0.8 percent overshoot, respectively, while, during the maximum down-shift (Figure 23), they produce approximately 0.8, 1.6 and 2.2 percent overshoot, respectively, which are greater. In addition, among all of the up-shift responses, the smallest up-shift gives the largest overshoots while the smallest down-shift gives the worst overshoots for all CVT ratio shifts with 12.3, 18.2 and 24.9 percent for the PDPCI0.1, PDPCI-0.2 and PDPCI-0.3 systems, respectively. In this case, both a minimum up-shift and down-shift produce a ratio error of 0.1, which causes the PDPCI controller systems to activate their integral parts at earlier stages, thus creating significant overshoots. 6.2.4. Steady state error The PD controller system produces the greatest steady state error, which is approximately 50 percent for both the minimum up-shift and down-shift, because at this stage, the initial CVT ratio error of 0.1 is too small for the PD controllers to further reduce the steady state errors. In addition, the PD controller systems tend to produce greater steady state error when performing the down-shift than the up-shift for the same shift distances and when performing smaller up-shifts or down-shifts, for example, approximately 1 and 10 percent for 2.0-to-0.7 and 2.0-to-1.6 up-shifts, respectively, and 5 and 18 percent for 0.7-to-2.0 and 1.6-to2.0 down-shifts, respectively. Conversely, the PDPCI controller systems generally perform very well with steady state errors of approximately 2 percent or less for almost all ratios, except for the 1.9-to-2.0 down-shift (approximately 7 percent for both the PDPCI-0.1 and PDPCI-0.3 systems) and the 2.0-to-1.9 up-shift (approximately 6 percent for both the PDPCI-0.2 and PDPCI-0.3 systems).

7. CONCLUSION The real time application of a PC-based EMDAP CVT ratio controller based on primary and secondary pulley position controllers using PD and PDPCI control algorithms and implemented using Matlab/Simulink® software and a Keithley DAS-1602 data acquisition system was success-

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B. SUPRIYO, K. B. TAWI and H. JAMALUDDIN

fully carried out. In addition, a PID tuning method based on Astrom-Hagglund’s relay feedback and the Ziegler – Nichols formula was shown to be an effective and applicable tuning method to provide the initial PID parameters for the proposed controllers. The PDPCI controller systems have sufficiently improved the PD system performance, especially in terms of eliminating the steady state error and improving the settling time. In addition, the PDPCI controller system with the smallest conditional error produces acceptable overshoots (generally less than 5 percent). However, for the smallest up-shift (from 2.0 to 1.9) and down-shift (from 1.9 to 2.0) conditions, all PDPCI controller systems gave inadequate performances, especially in terms of the overshoot and the steady state error, due to the activation of the integral part at early stage. Further research to improve these weaknesses using intelligent controller algorithms, such as fuzzy logic control or neural networks, are suggested. For future works, no-load CVT data can be used as a reference to determine the belt slip values under various load torque conditions. These slip values will then be used to adjust the belt clamping forces optimally to improve the efficiency of the EMDAP CVT. ACKNOWLEDGMENT−The authors would like to express their appreciation to Malaysian Ministry of Science, Technology and Innovation (MOSTI) and Universiti Teknologi Malysia (UTM) for their continuous supports in the research work. This work was financially supported by Malaysia eSCIENCE Fund Vot. 79348.

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EXPERIMENTAL STUDY OF AN ELECTRO-MECHANICAL CVT RATIO CONTROLLER

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