COMPARISON OF COMMON PID TUNING METHODS WITH FUZZY PID CONTROLLER FOR THE SPEED CONTROL OF A BLDC MOTOR DRIVE
Sri Latha Eti
1, Dr. N. Prema Kumar
21PG Scholar, 2 Associate Professor
Dept. of Electrical Engineering, A.U College of Engineering (A), Andhra University (India)
ABSTRACT
Brushless DC Motors are widely used for many industrial applications because of their high efficiency, high torque and low volume. This paper provides an overview of different tuning methods of PID Controller applied to control the speed of the mathematical model of the BLDC motor drive. This paper proposed an improved Fuzzy PID controller to control the speed of BLDC motor. The experimental results verify that Fuzzy PID controller has better control performance than the conventional PID controllers. The modeling, control and simulation of the BLDC motor have been done using the MATLAB/SIMULINK software. Also, the dynamic characteristics of the BLDC motor (i.e. speed and torque) as well as currents and voltages of the inverter components are observed by using the developed model.
Keywords - BLDC Motor, Conventional PID Controllers, Common PID Tuning Methods, Fuzzy PID Controller
I. INTRODUCTION
Speed and torque are the fundamental quantities used to describe the operation of rotating machinery. In adjustable speed drive applications, performance is usually discussed in terms of the speed, torque and other parameters that apply to the shaft of the motor. Speed Regulation is generally defined as the percentage speed change that results from a given load change. Permanent magnet brushless DC motors (PMBLDC) find wide applications in industries due to their high power density and ease of control. Although conventional PID controllers are widely used in the industry due to their simple control structure and ease of implementation, these controllers pose difficulties where there are some control complexity such as nonlinearity, load disturbances and parametric variations. Moreover PID controllers require precise linear mathematical models.
Fuzzy Logic Controller (FLC) for speed control of a BLDC leads to an improved dynamic behavior of the motor drive system and immune to load perturbations and parameter variations.
II. BLDC MOTOR MODELLING 2.1Simulation of BLDC motor
Brushless Direct Current (BLDC) motors are one of the motor types rapidly gaining popularity. BLDC motors are used in industries such as Appliances, Automotive, Aerospace, Consumer, Medical, Industrial Automation Equipment and Instrumentation. As the name implies, BLDC motors do not use brushes for commutation;
instead, they are electronically commutated. BLDC motors have many advantages over brushed DC motors and
induction motors as in [1]. A few of these are better speed vs torque characteristics, high dynamic response, high efficiency, long operating life and noiseless operation.
The equations that describe the model are as follows:
Or in shorter version
Since the resistances of all the phases are equal
Here, La, Lb and Lc are the self inductances of phases a, b, c;
Lab, Lbc and Lca are the self inductances of phases a, b, c;
ea, eb and ec are the phase back electromotive forces;
Since the self- and mutual inductances are constant for surface mounted permanent magnets and the winding is symmetrical:
Substituting equations (3), and (4) equation (1) gives the BLDCM model as
The stator phase currents are constrained to be balanced i.e.
This leads to the simplifications of the inductances matrix in the models as the
Therefore in the state space form
Fig.1 Position of the rotor with respect to the phase A The electromotive force induced in the phase A winding is
where: – Constant, – rotor angular speed
– Electrical angle (from fig.1) P – Number of pole pairs
For three-phase winding the electromotive forces written in the form of a matrix
where, (E=Ke.ωm)
Motion equation:
where, Torque due to Inertia, where, J – Moment of inertia, Torque due to viscous friction, , where, B – Friction coefficient,
Torque due to Coulomb friction, and, laod torque TL
Electromagnetic torque for 3-phase motor
2.2 Three phase Voltage source Inverter
Fig.2 Configuration of BLDC motor and Three Phase VSI system
Three phase bridge inverters are widely used for ac motor drives and general purpose ac supplies as shown in Fig.2. The output voltages obtained of the three phase VSI can be expressed in terms of switching functions Sa, Sb and Sc obtained from the hysteresis current controller.
The inverter output voltages are thus obtained as
2.3 Current Controller
The commanded value of current is compared to the actual phase currents of the motor and the errors are processed through a current controller as in [4]. The magnitude of the commanded value of current iref is
determined by using the reference torque Tref as (23) where, Kt is the torque constant.
Depending on the rotor position, the three phase reference currents are obtained by taking the value of reference current magnitude as iref. The table 1 below gives the dependency of the three phase reference currents on the rotor position.
TABLE I. ROTOR POSITION AND THREE PHASE REFERENCE CURRENTS Rotor
position (ɵ)
Reference Currents
These switching functions serve as the input to the three phase VSI.
2.4 Speed Controller
There are many types of controllers; each of them has a specified function to do. The P, PI, PD and PID are the basic types of controllers. Also the PID controller can be divided into parallel PID and series PID controller.
The success of the PID controllers is also enhanced by the fact that they often represent the fundamental component for more sophisticated control schemes that can be implemented when the basic control law is not sufficient to obtain the required performance or a more complicated control task is of concern. [11]
Fig.3 Speed Controller 2.4.1 Common PID Tuning methods:
Many various tuning methods have been proposed from 1942 up to now for gaining better and more acceptable control system response based on our desirable control objectives such as percent of overshoot, settling time, manipulated variable behavior etc. Some of these tuning methods have considered only one of these objectives as a criterion for their tuning algorithm and some of them have developed their algorithm by considering more
than one of the mentioned criterion. [11] The PID controller tuning methods are classified into two main categories.
Closed loop methods are:
-Ziegler-Nichols method -Tyreus-Luyben method Open loop methods are:
-Open loop Ziegler-Nichols method -C-H-R method -Cohen and Coon method 2.4.2 Adaptive Control Techniques:
Adaptive control use to change the control algorithm coefficients in real time to compensate for variations in environment or in the system itself. In drives, electrical and mechanical parameters do not remain constant. A sudden increase of Tl or J reduces speed[5]. Therefore real time adaptation of the controller is required.
One of the most successful expert system techniques applied to a wide range of control applications has been the Fuzzy Set Theory, which has made possible the establishment of "intelligent control".
2.5 Fuzzy Controller
Conventional PID controllers are generally insufficient to control process with additional complexities such as time delays, significant oscillatory behavior (complex poles with small damping), parameter variations, non-linearities and MIMO plants. Fuzzy logic has rapidly become one of the most successful of today’s technology for developing sophisticated control system[3]. The basic structure of a fuzzy logic controller is shown in Fig.4. Its fundamental components are Fuzzification, control rule base, inference mechanism and defuzzification[11].
2.6.1 Fuzzification:
The following functions are performed in the Fuzzification process:
1. Multiple measured crisp inputs first must be mapped into fuzzy membership function this process is called fuzzification.
2. Performs a scale mapping that transfers the range of values of input variables into corresponding universes of discourse.
Fig.4 The structure of a fuzzy logic controller
Fuzzy logic linguistic terms are often expressed in the form of logical implication, such as if then rules[3]. The inputs of the fuzzy controller are expressed in several linguistic levels. These levels can be described as Positive Big (PB), Positive Medium (PM), Positive Small (PS), Zero (Z), Negative Small (NS), Negative Medium (NM), Negative Big (NB) or in other levels. Each level is described by fuzzy set.
Fig. 5 Seven levels of Fuzzy membership functions
2.6.2 Fuzzy Inference:
Fuzzy inference is the process of formulating the mapping from a given input to an output using fuzzy logic[11]. There are two types of fuzzy inference systems that can be implemented in the Fuzzy Logic Toolbox:
Mamdani-type and Sugeno-type. These two types of inference systems vary somewhat in the way outputs are determined[10].
2.6.3 Defuzzification:
The output of the inference mechanism is fuzzy output variables. The fuzzy logic controller must convert its internal fuzzy output variables into crisp values so that the actual system can use these variables. This conversion is called defuzzification. The commonly used control defuzzification strategies are
(a) The MAX criterion method (b) The height method (c) The centroid method (or) Centre of Area method (COA)
2.6.4 Fuzzy Rule base:
The set of linguistic rules is the essential part of a fuzzy controller. In many cases it’s easy to translate an expert’s experience into these rules and any number of such rules can be created to define the actions of the controller. In the designed fuzzy system, conventional fuzzy conditions and relations such as “If e is A and e is B, then kis C” are used to create fuzzy rule base (7 x 7).
TABLE II. FUZZY RULE BASE FOR K
e/e NB NM NS Z PS PM PB
NB NB NB NB NB NM NS Z
NM NB NB NB NM NS Z PS
NS NB NB NM NS Z PS PM
Z NB NM NS Z PS PM PB
PS NM NS Z PS PM PB PB
PM NS Z PS PM PB PB PB
PB Z PS PM PB PB PB PB
III. MATLAB/SIMULINK MODELS
For a BLDC motor with the following specifications, the overall closed loop transfer function of the drive is developed:
0.5HP, 160V, 700rpm, 3-Ф BLDC motor with P=4; Ra=0.7Ω/ph; L=0.0272H; M=0.015H; Kb=0.5128V/ rad/
sec; Kt=0.49N-m/A; J=0.0002kg-m/s2; B=0.02N-m/ rad /sec; fc=2KHz; Vcm=10V 3.1 Mathematical model of the BLDC Drive
Fig. 6 Simulink model of BLDC Motor
3.2 Overall Speed Control loop of the Drive
Fig. 7 Overall Closed loop model of the drive 3.3 Speed Controller
Fig. 8 Fuzzy PID Controller IV. RESULTS
Conventional PID controller tuning methods are applied to the mathematical model of the drive and from the results it is observed that closed loop control techniques give better response for a step change in input compared to open loop control techniques. To reduce the peak overshoots, the results were then compared with fuzzy control technique. The fuzzy PID controller is further tuned with the above closed loop control techniques and it is observed that closed loop Tyreus-Lyuben tuning method with fuzzy controller gives better response with zero peak overshoot and zero steady state error.
TABLE III. COMPARISON OF DIFFERENT TUNING METHODS FOR MATHEMATICAL MODEL OF THE DRIVE
Controller type Responses
Rise time (sec)
Settling time (sec)
Peak overshoot
(rad/sec)
Steady state error
(rad/sec) Z-N Closed loop PI Controller 0.0025 0.004 0.05 0.383
Tyreus-Luyben PI Controller 0.003 0.004 0.124 0.507
Fuzzy Controller 0.02 0.03 0 2.633
Fuzzy+Z-N Closed loop PID Controller 0.015 0.03 0 1.518
Fuzzy+T-L PID Controller 0.02 0.03 0 0.1085
From the results, it is clear that Fuzzy + Tyreus-Luyben tuned PID Controller gives better response with zero peak overshoot and very less steady state error. Also, the torque response of the drive with this control is a smooth curve.
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0
1 2 3 4 5 6 7 8 9
time (sec) Te (N-m)
Torque
Fig. 9 Speed response of the Drive Fig.10 Electromagnetic torque developed in the drive
V. CONCLUSION
Conventional P/PI/PID controllers and fuzzy tuned P/PI/PID controllers are the Six control techniques which are used to control the Speed of BLDC drive. Rule base for the fuzzy tuned P/PI/PID techniques are designed for two inputs i.e error and change in error and one output i.e change in the gain. For inputs, 7 membership functions and for output also seven membership functions and totally 49 rules are designed.
Different PID Tuning methods have been applied on the the mathematical model of the BLDC motor drive. It is observed that the delay time is reduced, rise time is increased and settling time is reduced to more than half for fuzzy tuned PID controller when compared to conventional PID controller. Transient and steady state responses are improved by using fuzzy tuned controllers than using the conventional controllers.
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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 -10
0 10 20 30 40 50 60 70 80
time (sec) speed(rad/sec)
Fuzzy + T-L PID Tuning
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