1. Introduction
Recently, many mechanical components used in vehicles have been replaced by electrical components to increase efficiency. These components are not only found in hybrid electric vehicles or electric vehicles but they have also been applied to gasoline and diesel vehicles such as Motor Driven Power Steering (MDPS) and Integrated Starter and Generator (ISG). These electric automotive components increase drive efficiency and reduce fossil fuel consumption. These changes are being applied to the transmission system and the engine valve system. Among these changes, the exhaust gas recirculation (EGR) valve is the mechanical component being targeted to replace the small DC motor [
1,
2,
3,
4,
5]. However, in general, the mechanical systems using the EGR valve have a low acceptable cost and a narrow space for implementation; therefore, the electrical system including the actuator should be cost-effective and small. To achieve this, the mechanical actuating system cannot avoid being roughly designed, which implies high friction forces. Also, the difference between coulomb friction and static friction is very large, so obtaining a correct and a fast response in terms of position control is almost impossible using a conventional linear control system such as P, PI, or PID.
To achieve position control given this friction torque, some research has been proposed [
6,
7,
8,
9,
10]. In [
6], H infinite control and impulse control were combined for a fast control response. Robust control was achieved using a disturbance observer [
7]. A fuzzy controller [
8] and a neural network controller [
9] were proposed to overcome this problem. In [
10], an adaptive control method for friction compensation was proposed. These methods can dramatically reduce the effect of friction; however, a large number of parameters have to be set and the processing burden for realization is also complex in a low-cost drive system.
This paper proposes a position control method for a low-cost system. The general position control method for this low-cost system is a P-PI control method, as described in [
11]. As mentioned above, correct and fast control cannot be achieved with this linear controller in mechanical systems that have this friction condition. Generally, in this case, feedforward compensation is adopted for improving the control performance [
11,
12,
13]. However, these feedforward data are incorrect because of the aging of the mechanical system and environmental changes, such as temperature and humidity. Moreover, feedforward compensation can improve the dynamics of the controller; however, it cannot be the solution for unstable control performance that is caused by the difference in static and coulomb friction torque. In this paper, to achieve the stable position control, we first analyze the EGR valve mechanical model, define the cause of the vibration. Then, a proposed novel and simple algorithm that may be adapted to low-cost system to solve this problem are illustrated. Finally, we compare the performance of the conventional method to our proposed method to verify its superiority using experiments.
3. Proposed Position Controller
Figure 5 shows the conventional P-PI controller and the proposed control system [
11]. As shown in the figure, the proposed control system does not use a speed controller. The main reason for this is that the motor position detection sensor is absent in the actual products to reduce the cost. Although the speed information can be obtained from the linear position sensor used for detecting the valve position, the sensing dynamics of the linear position sensor is insufficient to calculate the motor speed. Moreover, the speed information is the derivative component of the position information, so it is essential to use a filter to mitigate the noise. This worsens the restrictions on the bandwidth of the controller, which is already restricted due to the slow response of the linear position sensor.
For the same reason, the D controller cannot be used because the effective derivative component of the position error is difficult to obtain. Moreover, it can amplify the noise of the position information signal. Therefore, the PI controller was selected as the position controller in this system. Essentially, this position control system has performance problems.
First, proposed position control transfer function shown in
Figure 5 can be described as:
The control dynamic of the current controller is much faster than the position controller. The transfer function of the current controller
Gc(
s) can be approximated as the unity in the position control view. Assuming that the spring load torque is fully compensated by the feedforward path, the transfer function can be changed to:
where
km is
kt/
J.
Insert this transfer function into the final value theorem. The error of the step response can be obtained as:
From the above equation, the PI controller for position control has an error in the steady state. To solve this problem, the proposed control method was derived from the hysteresis control. The proposed control sets the allowable boundary to perceive that the practical position follows the reference. If the sensed linear position is inside the boundary, the timer is activated to observe that the controlled position is stably located in the boundary or it is just during a transient operation. In this paper, the time to perceive the controlled position to be in the steady state was 200 ms.
Figure 6 shows the problems experienced by the conventional PI controller. If the sensed position gradually reaches the reference position, the controller output is also reduced. It also reduces the generated current and the motor speed. In advance, if the speed is reduced below the Stribeck velocity, the static friction torque majorly affects the entire load torque. As a result, as indicated by the figure, the motor is stopped when the motor current does not overcome the static friction torque. Next, the I controller integrates the position error when the sensed position does not exactly follow the reference. This integrated error gradually increases or decreases the current reference. If the specific current value reached by the generated motor torque is above the static friction torque, it causes sudden speed variation shown in
Figure 4, which creates the position vibration.
To solve this problem, the variable I controller gain was adopted according to the position error. When the position error reached the boundary, I controller gain was reduced to the minimum accordance with the position error, as shown in
Figure 7. As mentioned above, the I controller is the root of the position control vibration, so this controller was inactivated, since the valve position was located inside the allowable range. In this case, only the P controller affects the current reference generation. As a result, position vibration did not occur with the proposed position control method. In this paper, this allowable range was 5% of the position reference.
4. Experimental Results
Figure 8 shows the experimental test setup. To compare our method with the conventional control method, a high performance DSP TMS320F28335 from TI was used. A speed sensor was also instantaneously implemented in the mechanical system. The sampling frequency of the current controller and the switching frequency were the same: 20 kHz. The position control frequency was 2 kHz. The motor parameters are shown in
Table 1.
Figure 9 shows the position dynamic responses of 10% and 100% of the valve reference. Due to the high static friction torque, if the position error was small, the I controller needed some time to generate the output for the suitable torque against the static friction torque. Therefore, the gain had to be tuned considering the maximum allowable control response time when the smallest position reference was applied. As shown in the figure, when the 10% reference was applied, the control response time was much longer than the result obtained when the 100% reference was applied because of the static friction torque. This control gain cannot be increased infinitely because of the overshoot restriction. Therefore, control gain tuning involves a trade-off by considering two aspects: response time and overshoot.
Figure 10 compares the experimental results obtained using both a conventional P-PI controller [
11] and the proposed controller. As shown in the figure, the position controlled by the conventional method vibrated due to the large difference between static and coulomb friction torque. When the current reaches 2.5 A for the forward direction, the position movement is limited because the static friction torque resists the movement, however, since the current is above the 10 A, the position is radically moved forward because of the sudden friction change to coulomb friction torque. Due to the I controller affection, the current reaches to almost 17 A, and then, the position is over the reference. When the current reaches 17 A, the conventional controller starts to operate to move the position to the reverse direction. However, the position is almost stuck because of the high static friction torque, resulting in a slow decrease of the current to 2.5 A due to a small error integration of I controller. Subsequently, the controller starts to operate, and the position moves forward repeatedly. This operation caused the vibration as shown in
Figure 10a. Note that the repeated current and the position are almost the same as shown in the figure, which meant that the static and coulomb friction torques at each position were hardly changed.
5. Conclusions
This paper proposed a position control method for a cost effective and a fast response time, which could be used in vehicle valve systems. Because the low-cost mechanical system has large differences in static friction and coulomb friction, the position and the current vibrations occur with the conventional P-PI linear controller. To solve this problem, this paper analyzed the EGR valve mechanical system and illustrated the procedure of extracting the parameters based on the predefined mathematical analysis. From this analysis, the proposed control method entailed acceptable boundary and selectable operation of the I controller. As a result, it could achieve the proper control performance which has an acceptable position error. The proposed method was verified by comparing our method with the conventional method in an experiment.