Applied Mechanics and Materials Vols. 16-19 (2009) pp 145-149
© (2009) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMM.16-19.145
Online: 2009-10-12
Application of Compound PID Control in the DC Servo Motor
Xiaoyan Song1,a, Qingjie Yang2,b, Xueming Zhang2,c and Qigao Feng2,d
1
Pingdingshan University, Pingdingshan, China, 467002
2
Henan Institute of Science & Technology, Xinxiang, China, 453003
a
dymummy@163.com, byqingjie@vip.sina.com, cxmzh@hist.edu.cn, dfqg@hist.edu.cn
Keywords: PID control, DC servo system, Fuzzy PID control, Fuzzy rule
Abstract. Although the traditional PID controller is widely used in many fields, the system
parameters varying and external disturbances existing in the DC servo system will cause large
overshoot or poor stability. To improve the performance of the PID controller, a compound servo
control system combining the conventional PID control and the fuzzy control is presented to meet the
demand of a vehicular antenna servo system in this paper. Incorporating the fuzzy control and the
conventional PID control, this paper presents a design method of the fuzzy PID controller that is based
on the fuzzy tuning rules and formed by integrating two above control ideas. Simulation results are
presented to show the efficiency of the proposed controller. The practical control effect shows that the
control system that adopts the fuzzy PID controller has better performance than that of the traditional
PID control system, and meets the performance requirements of the servo system.
Introduction
Due to such advantages as easy use, high adaptability and flexibility, simple control principle, the
conventional PID controllers are widely used in a lot of automatic control systems of many
application fields. but it can not meet the needs of the servo system owing to lack of parameters
adjusting ability and disturbance rejection capability. Nevertheless, it usually takes a long time for the
PID controller to tune the process parameters, and its optimal parameters are difficult to select [1-3].
In addition, for the system existing varying process parameters, it will be difficult for the PID
controller to achieve effective in-line control.
Fuzzy control is an intelligent control method that imitates the logical thinking of human and is
independent on an accurate mathematical model of the controlled object. What is more, it is
insensitive to parameters variation, and has strong robustness. It is perfectly applied to overcome the
effects of nonlinearity, time variation and coupling of servo system [4-7]. The first fuzzy logic
controller was implemented by Mamdani on a steam engine in 1974. In the following years, combined
with other control strategies, fuzzy logic control has been widely used in many industrial applications
and has demonstrated significant achievements. Within these applications, the modeling and control
of some practical systems involve a considerable part because of their highly nonlinear and complex
structures. For the problem that the steady-state error is hard to be eliminated with a fuzzy controller,
a fuzzy PID controller for the servo system of the vehicular antenna is introduced in this paper. The
suggested controller incorporates in virtues of both control strategies, which has flexibility, perfect
anti-interference capability of the fuzzy control, and the high steady-state precision of PID control.
The application of the fuzzy PID controller in the servo system may increase the dynamic and the
static performances of the system, and better control effects can be attained.
Model of the Servo System
The vehicular antenna system consists of two parts, i.e., the outdoor equipment and the indoor
equipment. The outdoor equipment is the antenna servo tracking system, which mainly includes the
platform, the servo tracking system, the inertial sensor, GPS, and the satellite antenna. The indoor
equipment refers to main computer and the central controller, which mainly includes the sensor
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interfaces, data acquisition unit, the control unit, and the satellite receiver. The two parts are
connected together with cables and offer two main functions: receiving of satellite signals and steady
tracking in the course of fast moving.
The control unit uses TMS320LF2407A as the central controller. Only a few peripheral electronic
components need to be added to the whole circuit to constitute the main control unit and can
effectively perform the processing tasks, so the hardware circuit is very simple and has a high
reliability. An incremental photoelectric encoder is adopted to measure the rotor speed, the practical
position of the magnetic pole and its original position [8]. In this case, there will be no accumulating
errors as used in a stepper motor driving device. The schematic diagram for the fuzzy PID control of
vehicular antenna servo system is shown in Fig. 1.
Suppose the motor load is constant, and only the angular velocity of the motor is output, thus we
can obtain the transfer function of the DC servo motor, as shown in formula (1):
Ka
ω (S )
La J
=
G(s) = a
Va ( S ) s 2 + ( Ra J + La B ) s + Ra B + kt kv
La J
La J
(1)
where ωa is the angular velocity of the motor; Kv and Kt are speed and torque constants respectively,
which are determined by the magnetic flux density of permanent magnet, winding data of the rotor,
and the physical features of the ferric core; J is the rotary inertia of the rotor and the motor load; B is
the damping constant of the whole machinery rotary system. The values of motor parameters Ra, La,
Kv, Kt, and J can be obtained according to the features of the motor and the system. So we can get the
transfer function of the motor, as shown in formula (2).
G(s) =
326.5
(2)
2
s + 618.4s + 61.28
The block diagram of the DC motor servo subsystem under turntable is shown in figure 2, where
1/10 is the speed reducing ratio of worm to gear.
Fuzzy inference
de/dt
Kp
rin +
e
-
Ki
Kd
PID regulator
Vehicular antenna
servo system
Yout
Fig.1 Block diagram of fuzzy PID controller
Ideal position +
-
Practical position
G(s)
1/s
1/1
0
Fig.2 Block diagram of DC servo system
Design of the Control System
The hybrid controller is composed of a classical PID controller and a fuzzy controller based on
self-adjusting modifying factor. The fuzzy controller is used to control the motor when the practical
position is far away from the target position, and the PID controller is applied when the practical
position is near the desired position.
Fuzzy control involves fuzzification, a fuzzy rule base generalized from experts' experience, fuzzy
inference and defuzzification. However, self-adjustment of the fuzzy control rules is the key factor to
improve the controller's performance. On this basis, the modifying factor's fuzzy number model is
employed to regulate the fuzzy control rules in-line [9-12].
Applied Mechanics and Materials Vols. 16-19
147
The fuzzy inputs (error and the change rate of error) are classified into seven equal-span triangular
membership functions. NB, NM, NS, Z, PS, PM, PB are negative big, negative medium, negative
small, zero, positive small, positive medium and positive big.
A membership function characterizes a fuzzy set. The value of membership function represents a
degree of membership to the fuzzy set, which is between 0 and 1. A fuzzy set with the sharp
membership function curve has higher resolution and control sensitivity. With the smooth one, the
stability of system is better but resolution is lower [13].
The degree of interaction between two fuzzy sets, and it is generally given between 0.4~0.8. When
the value is small, the control sensitivity will be high. Otherwise, the system has strong robustness and
perfect adaptability. But excessively big or small may result worse control effect [14, 15].
Many of such sentences constitute a table of fuzzy control rules. Based on the features of PID
control, several important laws below should be followed:
(1) When the sign of E and EC is identical, the control variable u deviates to the desired value and
approaches to the desired value when they are different.
(2) When E is big, to accelerate the speed of response, avoid derivative saturation caused by
immediately rising to a large value of E in the early period and avoid large overshoot, a big Kp, a small
Kd and a small Ki are needed.
(3) When E is small, to keep reducing the error and prevent oscillation caused by large overshoot,
decrease the value of Kp, choose a small Ki and a moderate Kd.
(4) When E is quite small, to eliminate steady-state error, avoid overshoot and keep a good static
performance and strong capability of disturbance rejection, increase the value of Ki, choose a small Kp
and Kd.
According to the above laws and the control experience of engineers, the control rules of Kp, Ki and
Kd are shown in Table 1, 2, 3 respectively.
Computer Simulation Results
According to the controllers proposed above, the system was respectively modeled by the toolbox of
MATLAB. Computer simulations were executed for the servo system to verify the availability of the
proposed controller in practical implementation. The sampling frequency was selected to be 1 kHz.
With the same input of step signals, the outputs of systems with different controllers were plotted for
comparison. The simulation results are shown in Fig.3. From the simulation results we can see that the
self-tuning fuzzy PID controller exhibits a good unit step response with faster rising time and more
satisfactory settling time than that of the conventional PID control system.
E
NB
N
M
NS
Z
PS
PM
PB
Table 1 Rule table of fuzzy control of Kp
EC
NB NM NS
Z
PS PM
PB
PB PB PM PM PS
Z
Z
PB PB PM PS PS
Z
NS
P
M
P
M
PS
PS
Z
PM
PM
PS
Z
NS
NS
PM
PS
Z
NS
NM
NM
PS
Z
Z
Z
NS NS
NS NM NM
NM NM NM
NM
NM
NB
NM
NB
NB
148
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E
NB
N
M
NS
Z
PS
PM
PB
E
NB
N
M
NS
Z
PS
PM
PB
Table 2 Rule table of fuzzy control of Ki
EC
N
NB
NS
Z
PS
PM
M
PB PB PM PM
PS
PS
PB PB PM PM
PS
Z
P
M
P
M
PS
Z
Z
PB
Z
Z
PM
PM
PS
Z
NS
NM
PS
PS
Z
NS
NM
NM
PS
Z
NS
Z
NS
NS
NS
NM
NM
NS
NM
NM
NM
NM
NB
NM
NB
NB
Table 3 Rule table of fuzzy control of Kd
EC
NB NM NS
Z
PS PM
PB
NB NB NB NM NM
Z
Z
NB NB NM NS NS
Z
Z
NM NM
NM NS
NS NS
Z
Z
Z
Z
NS
NS
Z
PS
PS
NS
Z
PS
PM
PM
Z
PS
PS
PM
PB
PS
PS
PM
PB
PB
PS
PM
PM
PB
PB
(a) Step response of the PID Controller
(b) Step response of the fuzzy PID controller
Fig.3 Comparison of PID and fuzzy PID control
Conclusions
It’s easy to design for the linear time invariant systems, but it is a little difficult to design and requires
careful tuning of controller parameters for nonlinear systems. Traditional modeling techniques are
rather complex and time consuming. However, a fuzzy controller is usually a good choice because it
compensates for the shortcomings of the model, which cannot be estimated when modeling. The
vehicular antenna is usually in a varying environment, and thus may lead to the varying of the system
parameters. The conventional control strategy based on fixed parameters can not satisfy this kind of
requirements. To overcome the disadvantages of the traditional PID controller in the servo system,
this paper has successfully presented a fuzzy-PID controller which can self-adjust the values of the
parameters for the position control of a vehicular antenna servo system. The robustness and
effectiveness were verified through the computer simulations. We can arrive at the conclusion that,
for tracking performance in the vehicular antenna servo system, the fuzzy PID controller are better
than the conventional PID controller, and the practical application shows that the compound control
system has a faster response, a lower transient overshooting, a high anti-interference performance and
a better stability and dynamic performance. So we can arrive at the conclusion that the practical fuzzy
Applied Mechanics and Materials Vols. 16-19
149
PID control system had increased the dynamic and the static performances of the system and achieved
the desired control effect.
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10.4028/www.scientific.net/AMM.16-19
Application of Compound PID Control in the DC Servo Motor
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