ABSTRACT:
This paper presents an insight into the speed control of D.C motor using a fuzzy logic controller to meet the desired speed. Fuzzy logic is one of the most successful applications of fuzzy set in which the variables are linguistic rather than numeric. A fuzzy logic controller (FLC) is based on a set of control rules (fuzzy rules) among linguistic variables. The personal computer provides the necessary flexibility in setting any speed profile with the use of fuzzy packages. Basically a D.C shunt motor has drooping speed-torque characteristics. The proposed fuzzy controller results in a better response compared to the basic fuzzy controller and normal response of D.C motor. The step response parameters can be closely controlled with the help of simple operations within the controller. The simulation is carried out and the simulation results present the flexibility of the motor speed control.
KEY WORDS: fuzzy controller, speed-torque characteristics, fuzzification,
De- fuzzification.
INTRODUCTION:
DC motor converts electrical energy into mechanical energy. DC motor is used in applications where wide speed ranges are required. DC shunt motor exhibits a drooping speed-torque characteristic. The speed of the DC motor is given by
Hence, the speed can be controlled by varying,
i) Flux/pole (j). Field Control Method
ii) Voltage of armature circuit, by varying Ra, Armature Control Method.
FIELD CONTROL METHOD:
The speed is inversely proportional to flux. By decreasing the flux, the speed can be increased and vive versa. The flux of the DC motor is changed by changing
field current with help of a shunt field rheostat.
ARMATURE CONTROL METHOD:
This method is used when speeds below base speed are required. As supply voltage is normally constant, the voltage across the armature is varied by inserting a variable resistance in series with the armature circuit. As resistance is increased, armature voltage is decreased, thereby decreasing the armature speed.
FUZZY LOGIC CONTROL SYSTEM:
A fuzzy logic controller (FLC) is based on a set of control rules (fuzzy rules) among linguistic variables. Usually these rules are expression in the form of conditional statements (if x is small, then y is large). The execution of these rules is given by the compositional title. A basic architecture of FLC is shown in Fig 1. This structure consists of following four modules:
Fig1: Basic structure of Fuzzy logic controller
THE COMPLETE SPEED CONTROL SYSTEM:
The block diagram of the dc motor speed control system is as shown in Fig2. The inputs for the proposed fuzzy logic controller are the speed error (e) and the derivative of the speed error (de/dt). The output of the controller is the change in the motor voltage DV. The linguistic variables for the input and output sets are Negative Large (NL), Negative Small (NS), ZERO, Positive Small (PS) and Positive Large (PL). The shapes of the fuzzy sets are isosceles triangles and trapezoid for large term sets (NL, PL) as shown in Fig 3. The Rule Base used in the design of the fuzzy logic controller is shown in Fig 4. The basic location of the singletons which are at the centre of gravity of the triangular sets are –3,-1,0,+1,+3 for NL, NS, ZERO, PS, and PL respectively.
e
Ref Speed de/dt
Actual Speed Vc
Fig2: Block Diagram of speed control system
Fig(a) Derivative of Speed error
Fig(b) Speed error
Fig 3: Fuzzy sets used
NL NS ZERO PS PL
PL / NL / NLPS / ZERO / NS / NL / NL
PL / PS / ZERO / NS / NL
PL / PL / PS / ZERO / NS
PL / PL / PS
PL
PS
ZERO
NS
NL
Fig 4: Fuzzy control rules
PROPOSED FUZZY LOGIC CONTROLLER:
In most of the adaptive fuzzy controllers, attempt is made to change the Rule Base to make the system adaptive. In the scheme proposed, such a result is achieved by adjusting the defuzzifier as a function of the system response. Also it is possible to regulate the parameters of the time – domain response. The block diagram of the system with the proposed FLC is shown in Fig 5. A new functional block called the Error Interpreter is added to the basic system of Fig 2.The function of the block is to sense the error, identify its ranges. And determine the location of the singletons. In this method, the error and error rate are used to change the supporters in the motor voltage singletons. The defuzzified output of controller is given by
Where PL, PS, NS. And NL is the inference membership values and PLVC, PSVC, NSVC, and NLVC are the corresponding supports of change in the motor voltage singletons. In the new method, the error signal is fed to an interface that changes the value of the supports. The magnitude of output error is divided into ranges covering (100 – 40 ),(40 - 20), (20 - 5), and (5 - 0) percent of the maximum output. Each time the error is sampled the specified range is determined and the location of the singleton corresponding to that range is obtained. A scale factor ‘a’ is used for changing the location of the singletons which in turn changes the value of the supports. For a lower range of error, the supports are multiplied by a coefficient less than unity (around set point) and for higher ranges, the supports are multiplied by a coefficient greater than unity. The following method is suggested for controlling the time – response parameters:
Range 1: (100 – 40). This range is used to effectively control the rise time and to obtain maximum overshoot. If the coefficient of supports is increased, the rise time is decreased and vice versa.
Range 2: (40 - 20). The variation of the coefficient during this range will affect the maximum overshoot by about 80% and the variation in each of ranges 1 and 3 will affect by about 10%.
Range 3 and 4: (20 – 5) (5 – 0). The coefficient of this range has the maximum effect on the steady state oscillations. If the coefficients are larger, the oscillations will persist for a longer time and thus the setting time will be more.
Fig 5: Block diagram of system with proposed FLC
The steps in designing the controller are :
1. Identify the variables (inputs, states and outputs of the) of the plant.
2. Partition the universe of discourse or the internal spanned by each variable into a number of fuzzy subsets, assigning each a linguistic label.
3. Assign or determine a membership function for each fuzzy subset.
4. Assign the fuzzy relationship between the inputs or states, fuzzy subsets on the one hand and the outputs fuzzy subsets on the other hand, thus forming the rule base.
5. Choose appropriate sealing factors for the input and output variables in order to normalize the variables to the [0,1] or [-1,1] interval.
6. Fuzzify the inputs to the controller.
7. Use fuzzy approximate reasoning to infer the output contributed from each rule.
8. Aggregate the fuzzy outputs recommended by each rule.
9. Apply defuzzification to form a crisp output.
Thus based upon these rules fuzzy logic controller is designed and can be suitable for any kind of control applications.
SIMULINK ROOT BLOCK DIAGRAM:
PARAMETERS: Source type: DC
Amplitude: 220V
Rated speed: 1500 rpm
Signal generator Amplitude: 1; Frequency: 1
Gain=9.8
OUTPUT:
CONCLUSIONS:
The proposed fuzzy logic controller is suitable for speed control of a DC motor. The personal computer provides the necessary flexibility in setting any speed profile with the use of fuzzy packages. The proposed fuzzy controller gives better response compared to the basic fuzzy controller. The step response parameters can be closely controlled with the help of simple operations within the controller.
REFERENCES:
[1] C.C.Lee, Fuzzy logic in control systems: Fuzzy logic control part-1&2, IEEE
Trans nsystems Man & Cybernatics.
[2] Mattavelli, General purpose Fuzzy Control for DC to DC converter.IEEE Trans
Power Electronics.
[3] Fuzzy Logic Control of a Switched reluctance motor drive.
Bolognani, s.; Zigliotto, M;
Industry Applications, IEEE transactions on volume 32, issue 5, Sept-Oct 1996
Pages: 1063-1068.
[4] W So .C Tse & Y Lee development of Fuzzy Logic Control for DC to DC converter design, computer simulation & experimental evaluation IEEE trans on Power Electronics