A Comparative study between DC speed controller techniques

 

Astha Sharma¹ and S.P. Dubey²

¹ME Student, Rungta College of Engineering and Technology, Bhilai, Chhattisgarh

² Head of Dept., Dept. of Electrical Engineering, Rungta College of Engineering and Technology, Bhilai, Chhattisgarh

*Corresponding Author E-mail: astha_gec@yahoo.com, spd1020@yahoo.com

ABSTRACT:

DC motor is the most common choice if wide range of adjustable speed drive operation is  specified. Of the three kinds of DC motors – series, shunt and separately excited DC motors, separately excited DC motors are most often used. Different speed can be  obtained by changing the armature voltage and the field voltage A common actuator in control systems is the DC motor[2]. It directly provides the rotary motion and, coupled with wheels or drums and cables, can provide transitional motion[1].  Today variant applications require more and more features such as speed applications to  multipurpose accessories, user friendly interfaces, and security features. Such new requirements can be achieved through a fuzzy logic approach. Nowadays, most of fuzzy logic based controls are only limited to a complicated ranking management of user interfaces, sensors and actuators, corresponding to a slow software speed operation. Fuzzy Logic motor control is a promising technique for extracting maximum performance from modern motors. More efficient motors can significantly reduce energy consumption and help mitigate environmental problems such as acid rain and global warming. Today improved motor control has reached a point requiring either highly accurate simulation of the complex, non-linear system or an alternate mechanism for predicting and optimizing controlled motor system behavior. Fuzzy logic has been chosen here to fill the latter role.

 

 

INTRODUCTION:

The Proportional, or, “P”, controller is the most basic controller. The control law is simple: control is directly proportional to error.  Proportional control is the easiest feedback control to implement, and simple proportional control is probably the most 18 common kind of control loop[4]. A proportional controller is just the error signal multiplied by a constant and fed out to the drive[5]. The chief shortcoming of the P-control law is that it allows DC offset error; it droops in the presence of fixed disturbances. Such disturbances are ubiquitous in controls: Ambient temperature drains heat, power supply loads draw DC current, and friction slows motion. DC offset error cannot be tolerated in many systems, but where it can, the modest P controller can suffice [6  8].

 

B)  Proportional Integral Controller

With PI control, the P gain provides similar operation to that in the ‘P’ controller, and the ‘I’ gain provides DC stiffness. Larger ‘I’ gain provides more stiffness but also more overshoot.

 

The primary shortcoming of the P controller, tolerance of DC error, is readily corrected by adding an integral gain to the control law. Because the integral will grow ever larger with even small DC offset error, any integral gain (other than zero) will eliminate DC offset droop. Integral control is used to add long-term precision to a control loop [5]. The main drawback is that the PI controllers are more complicated to implement.  Also, the saturation becomes more complicated. The PI controller lacks a windup function to control the integral value during saturation [6].

 

C)  Proportional Derivative Controller

The P controller is augmented with a ‘D’ term to allow the higher proportional gain. The ‘D’ gain advances the phase of the loop by virtue of the 90 degree phase lead of a derivative. Using the ‘D’ gain will usually allow the system responsiveness to increase [9].  The differential term is the last value of the position minus the current value of the 19 position. This gives a rough estimate of these velocity (delta position/sample time), which predicts where the position will be in a while. The ‘PD’ controller is fast, powerful but more susceptible to stability problems, sampling irregularities, noise, and high frequency oscillations. Derivatives have high gain at high frequencies. So while some ‘D’ does help the phase margin, it affects the gain margin by adding gain at the phase crossover, typically at high frequency [3]. Also, the derivative gain is sensitive to noise. In case of a differential element, the output is proportional to the position change divided by the sample time. If the position is changing at a constant rate but the sample time varies from sample to sample, noise will be observed. Since the differential gain is usually high, this noise will be amplified a great deal. Differential control suffers from noise problems because noise is usually spread relatively evenly across the frequency spectrum. Control commands and plant outputs, however, usually have most of their content at lower frequencies. Proportional control passes noise[10]. Integral control averages its input signal, which tends to eliminate noise [1]. Differential control enhances high frequency signals, so it enhances noise. The ‘D’ gain needs to be followed by a low pass filter to reduce the noise content. 

 

D) Proportional Integral Derivative Controller

The PID controller adds differential gain to the PI controller. A PID controller is a two zone controller. The ‘I’ gain forms the low- frequency zone. The benefit of the ‘D’ gain is that it allows the ‘P’ gain to be set higher than it could be otherwise. The ‘P’ and ‘D’ gains together form the high-frequency zone. PID stands for "proportional, integral, derivative." These three terms describe the basic elements of a PID controller. Each of 20 these elements perform a different task and have a different effect on the functioning of a system. In a typical PID controller these elements are driven by a combination of the system command and the feedback signal from the object that is being controlled (usually referred to as the "plant"). Their outputs are added together to form the system output A PID controller provides faster response than a PI controller but is usually harder to control and more sensitive to changes in the plant model. 

 

E) Fuzzy Logic Controller

Fuzzy logic, unlike the crispy logic in Boolean theory, deals with uncertain or imprecise situations. A variable in fuzzy logic has sets of values which are characterized by linguistic expressions, such as SMALL, MEDIUM, LARGE, etc. These linguistic expressions are represented numerically by fuzzy sets (sometimes referred to as fuzzy subsets). Every fuzzy set is characterized by a membership function, which varies from 0 to 1 (unlike 0 and 1 of a Boolean set). A fuzzy set has a distinct feature of allowing partial membership. In fact, a given element can be a member of a fuzzy set, with degree of membership varying from 0 (non-member) to 1 (full member), in contrast to a “crisp”  or conventional set, where an element can either be or not be part of the set. Although fuzzy theory deals with imprecise information, it is based on sound quantitative mathematical theory. A fuzzy control algorithm for a process control system embeds the intuition and experience of an operator, designer and researcher. The control does not need accurate mathematical model of a plant, and therefore, it suits well to a process   where the model is unknown or ill-defined. Fuzzy control algorithm can be refined by adaptation based on learning and fuzzy model of the plant. The fuzzy control also works 21 well for complex nonlinear multi-dimensional system, system with parameter variation problem, or where the sensor signals are not precise.  The fuzzy logic speed controller has the internal structure of a knowledge based expert system. It requires a set of heuristic rules based upon the experience gained in the design of a conventional controller. The rules are expressed in terms of linguistic variables. The design of a fuzzy logic speed controller is based upon the error, and change in error. The internal structure of the fuzzy logic speed controller comprises of three functional blocks namely – the fuzzifier, the decision–maker and the defuzzifier [7]. The fuzzifier converts crisp data into linguistic format. The decision maker decides in linguistic format with the help of logical linguistic rules supplied by the rule base and relevant data supplied by the data base. The output of the decision maker passes through the defuzzifier wherein the linguistic format signal is converted back into the numeric form or crisp form [3]. The inputs are categorized as various linguistics variables with their corresponding membership values. Triangular membership distribution is used in the analysis and defuzzification is carried out by center of gravity method [9]. The data flow in a fuzzy logic based system 

 

Fuzzy Logic Controller:

 

(i) Fuzzification:

Fuzzification means converting the crisp data to information represented by linguistic variables. The normalized error and change in error are fuzzified to overlapping fuzzy sets represented by linguistic variables in their respective universe of discourse. The change in control action is also fuzzified in its universe of discourse. The number of fuzzy sets, the membership functions, and the degree of overlapping depends on desired accuracy, response of the system, ease of implementation, upgradeability etc.

 

(ii) Rule – Base Evaluation

The knowledge base of a fuzzy logic based system contains a set of rules to define the response of the controller to various values of the input variables. Normally, the number of rules is equal to the product of the number of fuzzy sets in the input variables. The rules have the form of “IF – THEN” statements. The “IF” side of the rules contains one or more conditions called “antecedents” and the “ THEN” side of rules contains on ormore actions called “consequences” [10]. The response of the controller to input conditions is determined by processing the rule base module. The antecedents of a rule correspond directly to the degree of membership calculated during the fuzzification process. The strength of a rule is computed based on antecedent’s values and then assigned to the rule’s fuzzy action part. Normally minimum function is used. As a result , the value of the least true antecedent is assigned as the strength of the rule. When more than one rule is applied to the same action, the common practice is to use the highest strength rule.

 

(iii) Deffuzification

The response of the controller should be non fuzzy in nature. This module defuzzifies the response after the evaluation of the rule base module[7]. Normally, the weighted average method is used for defuzzification.

 

In fuzzy logic (FL) concept, the processing takes place as follows:

(i) Calculation of the nth instant values of the two input signals namely, speed error and rate of change in speed error.

(ii) Scaling of the two input signals namely, speed error and the change in speed error.

(iii) The scaled input signals are fed to the fuzzy logic controller.

(iv) The scaled crisp data is converted into linguistic format in accordance with the defines fuzzy sets [9].

(v) In accordance to the linguistic rules, value of the output signal is determined. The required rules and data are supplied by the rule base and the data base [8].

(vi) The Linguistic output data is converted back into crisp output data by application of the method of defuzzification as follows: Given a combination of two inputs , the membership of the corresponding output is taken as minimum membership value of the two respective inputs.

Mathematically [10].

 

Where, μ refers to the membership value, the output membership is stored in α and (pm) refers to location of peak of membership function.

 

The crisp value obtained is re scaled back to get the controller output. The input membership functions are defined by taking into account the speed and the acceleration of the motor. The motor speed range is well covered with the seven membership functions – NB (Negative Big),NM(Negative Medium),NS(Negative Small), ZE(Zero),PS(Positive Small), PM(Positive Medium), PB(Positive Big).

 

Fuzzy Controller rules:

 

Matlab Simulink of Fuzzy Logic Controller:

 

The two inputs namely, speed error and change in speed error are properly scaled and fed to the MATLAB fuzzy logic controller. The re-scaled defuzzified output of the fuzzy logic block after limiting forms the output of the controller block.

 

Comparative Study of  Various Controller:

 

CONCLUSION:

This paper gives a comparative study between various controller used to control the speed of DC Motor  like proportional controller , Proportional derivative controller, Fuzzy controller, Hybrid Fuzzy controller, etc. Fuzzy controller gives more accurate result as compare to proportional controller / derivative controller.

 

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