Position Control of Servo Systems using PID Controller Tuning with Soft Computing Optimization Techniques

Position Control of Servo Systems using PID Controller Tuning with Soft Computing Optimization Techniques

P. Ravi Kumar M.Tech (control systems)

Gudlavalleru engineering college Gudlavalleru,Andhra Pradesh,india

V. Naga Babu Assistant Professor

Gudlavalleru engineering college Gudlavalleru,Andhra Pradesh,india

Abstract- In this paper, position control of servo motor using PID controller with soft computing optimization techniques is discussed. PID controllers widely used in the industry. Different methods are available for tuning the PID controller. In this paper conventional tuning method Z-N method and soft computing methods like Genetic algorithm (GA) and Particle swarm optimization (PSO) are used for the position control of the DC servo motor. The results obtained from soft computing methods (GA, PSO) are compared with conventional tuning method (Z-N) found that the soft computing techniques gives better results compared to the conventional PID tuning method.

Key Words: DC servo motor, position control, tuning methods, ZN, GA and PSO methods.

INTROUDUCTION

Now a days PID controllers are widely used in the industry. About 85-90% of the controllers are used in the industry are of PID type. Position control systems are normally unstable when they are implemented in closed loop configuration.PID controllers tuning for positional control systems is a time consuming task , therefore much effort has been given to analyse the servo systems.

The main aim of this paper is to analyse the soft computing methods and enumerate their advantages over conventional PID tuning methodologies. In this paper Position control of a 3rd ordered plant (Servo motor) using Conventional PID tuning and soft computing methods with their comparisons is analysed. Conventional PID tuning method Ziegler-Nichols, soft computing methods like genetic algorithm and PSO is used in this paper for the position control of servo systems.

Except for miner difference in constructional features a dc servo motor is essentially an ordinary dc motor. Physical requirements of DC servo motor are Low inertia and High starting torque. Low inertia is attained with reduced armature diameter with consequent in armature length such that the desired power output is reached.

SYSTEM MODELLING:

In this dc servo motor can be consider as a linear SISO system having 3rd order transfer function. Relation between shaft position and armature voltage is derived from the physical laws.

The air gap flux is given by

k f i f

Torque is proportional to product of Flux and Armature

current

T k1Ia (t)

Or

T k1k f I f (t)Ia (t)

The motor torque when the constant flux established in the

field coil is given by

T Km Ia (t)

Back EMF of the motor is given by

Vb kb

Fig1: separately exited dc motor

By apply Laplace transform to the armature loop

= + + ()

Where () is back EMF voltage proportional to the motor speed. Therefore, we have

= ()

() =

+ +

The armature current is expressed as

()

= ()

+

The closed loop Transfer Function is given by

()

The motor torque is expressed as

= + ()

Here is the load torque

= 2 + ()

The relation between speed and position is given by

() =

The above equations can be represent in a block diagram as

Fig2: equivalent block diagram

From the above block diagram the relation between shaft position and armature obtained as

by assuming the =0,

() =

() + + + ( )

J=0.01kg/ 2 ,B=0.1n.m.s, kb=0.01 v/rad/sec, km=0.01N.m/amp, Ra=1 ohm,L=0.5H

Substitute above values in the above equation,

() = 0.01

() = 1 + () Y(s) =Output response(s) =input, G(s) =plant And =controller

Fig3: Conventional PID controller block diagram

ZN Method:

Ziegler-Nichols (ZN) method is a conventional PID tuning method. This method is widely used for design of various controllers. Ziegler-Nichols presented two methods1.Step response method and 2.Frequency response method. In this Paper frequency response method is discussed for tuning the PID controller

PROCEDURE:

In this method derivative time ( ) is set to zero and integral time ( ) set to infinity. This is used to get the initial PID setting of the systems. The critical gain ( )

()

0.0053 + 0.062 + 0.1001

PID CONTROLLER:

The PID filter is implemented in almost all

and periodic oscillations ( ) are determined by using R-H criteria. Ku is determined by equating the row containing s in R-H row to zero. is determined by equating the row containings^2 in R-H row to zero. Evaluate parameters described by Z-N method. Values

industrial processes because of its well-known

beneficial features. In general, the whole systems performa nce strongly depends on the controllers

Efficiency and hence the tuning process plays a key role in the systems behaviour. Position control of servo systems is normally unstable when they are implemented in closed loop configuration so PID controller is used to improve the dynamic performance and also reduce the steady state error of the systems. The block diagram of PID control is shown below Fig:3

The output of The PID controller (U (t)) is given by

U (t) = + ()+ e (t)

Where , , are proportional, Integral and derivative gains and e (t) =error=set point-output

The PID output in Frequency domain can be represented as

of , are determined using the formulas =0.6* , = / and = .

, , Are calculated using the formulas given in below

table, =2

Table1: ZN PID tuning parameters

The advantage of this method is applying easy rules to simple mathematical models. But the disadvantage of this method does not provide as good results as expected.

PSO

PSO is a robust stochastic optimization technique

GENETIC ALGORITHM:

A genetic algorithm is a powerful searching capabilities and heuristic characteristics. GA has also been used in control tuning applications, being shown to obtain better results than classical techniques. Genetic algorithms are inspired from phenomena found in living organisms (nature).In Genetic algorithms they choose the next generations based on genetic operators like cross over, mutation selection and survival of fittest

The components of GA are

A problem definition as input, and encoding principles (gene, chromosome), initialization procedure followed by cross over, mutation and selection operators for reproduction with the help of an objective function.

Simple Genetic Algorithm:

{

Initialize population; Evaluate population;

While Termination Criteria Not Satisfied

{

Select parents for reproduction; Perform recombination and mutation; Evaluate population;

}

}

GA PARAMETERS:

n this paper the following genetic algorithm parameters are used

Table2: The parameters of the genetic algorithms.

based on the movement and intelligence of swarms. The components of PSO are Swarm Size, Velocity, position components and maximum no of iteration. Here I have consider the following objective function

F= (1-exp (-0.5))*( )) +exp (-0.5)*( )

=peak overshoot =rise time,

=settling time

Algorithm of PSO

1. Create an initial population of particles with random positions and velocities within the solution space.

2. For each particle, calculate the value of the fitness function.

3. Compare the fitness of each particle with local- best. If current solution is better than its local- best, then replace its local best by the current solution.

4. Compare the fitness of all the particles with global best. If the fitness of any particle is better than global- best, then replace global-best.

5. Update the velocity and positions of all particles using velocity update equations.

6. Repeat steps (2)-(5) until a stopping criterion is met.

   FLOW CHART OF PSO

   Block Diagram Of Dc Servo Motor With Pid Controllr :

   Fig4: Block diagram of servo motor

   STEP RESPONSE OF Z-N METHOD:

   Fig5: Step response of Z-N method

   STEP RESPONSE OF GA

   FIG 6: STEP RESPONSE OF GA

   STEP RESPONSE OF PSO

   FIG 7: STEP RESPONSE OF PSO

   COMPARISONS OF ALL WAVE FORMS:

   parameters	ZN	GA	PSO
   Settling time(sec)	5.0139	1.6	0.56
   Rise time(Sec)	0.2901	0.25	0.35
   Peak over shoot (%)	61.74	30	3
   Fitness fun value	17.57	0.7225	0.4668

   Fig8: Comparisons of all Wave form Comparisons of all methods

   Table3: comparison of all methods

   CONCLUSION:

   In this paper conventional and soft computing methods for position control of DC servo motor is used. Soft computing techniques to the optimum tuning of PID controllers led to a satisfactory close loop response. By comparing the all methods PSO gives better response in terms of performance indices. The draw backs associated with GAs may have a tendency to converge towards local optima or even arbitrary points rather than the global optimum of the problem is over come in PSO .This work may be extending by using advanced genetic algorithm and also using evolutionary algorithms.

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