ABSTRACT

Dc motor has been widely utilized as a part of much mechanical provision for their

exact, basic and nonstop control attributes. We have different controller for control dc motor

speed/position PID, PI and sliding mode using software Matlab and experiment set up. The

brushless dc motor extensively used for control system and industrial application because small

in size, high efficiency and high torque density Design PID controller to get fast step response.

The PID controller gives very good response and the controller further tuned to decrease

overshoot and steady state error. In industries PID controller are better than other controller. PID

controller is not difficult to tune and modest.

This thesis an extensive study to control speed/position of dc motor by Controller like

PID in Matlab simulation as well as experimental Study on dc servo set up. The system

identification technique is used to get the accurate transfer function of dc motor system

identification is the technique where we give some input to the motor and get output

corresponding input and output we get the process model with measured and simulation mode

through is model get the best fit percentage result after find the transfer function of plant we have

design the different controller to control the speed/position of the motor. We have design PID

controller for both speed and position control.

This paper is to design PID controller to supervise and control the speed response of the

DC servo motor and MATLAB program is used for calculation and simulation PID controllers

are widely used in an industrial plants because of their simplicity and robustness. Industrial

processes are subjected to variation in parameters and parameter perturbations. We are choosing

PID parameters and discussed.

INTRODUCTION

Any controller design for any system commonly needs some knowledge about the

system before it will be developed. This involves a mathematical description of the relation

among inputs to the process, its variables and its output, that is called the model of the system.

The model can be represented as a set of transfer functions, which is usually called mathematical

modeling. Modeling for the complex systems can be a very difficult task. For example, in a

complex system such as a multiple inputs and multiple outputs system, the inaccurate models

will cause the systems is unstable or has a bad system performance.

Electrical motor servo systems are indispensable in modern industries. Servomotors

are used in a variety of applications in industrial electronics and robotics that includes precision

positioning as well as speed control Servomotors use feedback controller to control the speed or

the position, or both. The basic continuous feedback controller is PID controller which possesses

good Performance. However is adaptive enough only with flexible tuning. Although many

advanced control techniques such as self-tuning control, model reference Adaptive control,

sliding mode control and fuzzy control have been proposed to improve system performances, the

conventional PI/PID controllers are still dominant in majority of real-world servo systems . To

implement a PID controller the proportional gain KP, the integral gain KI and the derivative gain

KD must be determined carefully. Many approaches have been developed to determine PID

controller parameters for single input single output (SISO) systems.

SERVO MOTOR

This is nothing but a simple electrical motor, controlled with the help of servomechanism. If the motor as controlled device, associated with servomechanism is DC motor, then it is commonly known DC Servo Motor. If the controlled motor is operated by AC, it is called AC Servo Motor.

Servo Motor TheoryThere are some special types of application of electrical motor where rotation of the motor is

required for just a certain angle not continuously for long period of time. For these applications

some special types of motor are required with some special arrangement which makes the motor

to rotate a certain angle for a given electrical input (signal). For this purpose servo motor comes

into picture. This is normally a simple DC motor which is controlled for specific angular rotation

with help of additional servomechanism (a typical closed loop feedback control system). Now

day’s servo system has huge industrial applications. Servo motor applications are also commonly

seen in remote controlled toy cars for controlling direction of motion and it is also very

commonly used as the motor which moves the tray of a CD or DVD player. Beside these there

are other hundreds of servo motor applications we see in our daily life. The main reason behind

using a servo is that it provides angular precision, i.e. it will only rotate as much we want and

then stop and wait for next signal to take further action. This is unlike a normal electrical motor

which starts rotating as and when power is applied to it and the rotation continues until we

switch off the power. We cannot control the rotational progress of electrical motor; but we can

only control the speed of rotation and can turn it ON and OFF.

Servo Motor Working PrincipleBefore understanding the working principle of servo motor we should understand first the basic

of servomechanism.

ServomechanismA servo system mainly consists of three basic components - a controlled device, a output sensor,

a feedback system. This is an automatic closed loop control system. Here instead of controlling a

device by applying variable input signal, the device is controlled by a feedback signal generated

by comparing output signal and reference input signal. When reference input signal or command

signal is applied to the system, it is compared with output reference signal of the system

produced by output sensor, and a third signal produced by feedback system. This third signal acts

as input signal of controlled device. This input signal to the device presents as long as there is a

logical difference between reference input signal and output signal of the system. After the

device achieves its desired output, there will be no longer logical difference between reference

input signal and reference output signal of the system. Then, third signal produced by comparing

theses above said signals will not remain enough to operate the device further and to produce

further output of the system until the next reference input signal or command signal is applied to

the system. Hence the primary task of a servomechanism is to maintain the output of a system at

the desired value in the presence of disturbances.

Working Principle of Servo MotorA servo motor is basically a DC motor (in some special cases it is AC motor) along with some

other special purpose components that make a DC motor a servo. In a servo unit, you will find a

small DC motor, a potentiometer, gear arrangement and an intelligent circuitry. The intelligent

circuitry along with the potentiometer makes the servo to rotate according to our wishes.

As we know, a small DC motor will rotate with high speed but the torque generated by its

rotation will not be enough to move even a light load. This is where the gear system inside a

servomechanism comes into picture. The gear mechanism will take high input speed of the motor

(fast) and at the output; we will get a output speed which is slower than original input speed but

more practical and widely applicable.

Say at initial position of servo motor shaft, the position of the potentiometer knob is such that

there is no electrical signal generated at the output port of the potentiometer . This output port of

the potentiometer is connected with one of the input terminals of the error detector amplifier.

Now an electrical signal is given to another input terminal of the error detector amplifier. Now

difference between these two signals, one comes from potentiometer and another comes from

external source, will be amplified in the error detector amplifier and feeds the DC motor. This

amplified error signal acts as the input power of the dc motor and the motor starts rotating in

desired direction. As the motor shaft progresses the potentiometer knob also rotates as it is

coupled with motor shaft with help of gear arrangement. As the position of the potentiometer

knob changes there will be an electrical signal produced at the potentiometer port. As the angular

position of the potentiometer knob progresses the output or feedback signal increases. After

desired angular position of motor shaft the potentiometer knob is reaches at such position the

electrical signal generated in the potentiometer becomes same as of external electrical signal

given to amplifier. At this condition, there will be no output signal from the amplifier to the

motor input as there is no difference between external applied signal and the signal generated at

potentiometer . As the input signal to the motor is nil at that position, the motor stops rotating.

This is how a simple conceptual servo motor works.

Servo Motor ControlFor understanding servo motor control let us consider an example of servomotor that we have

given a signal to rotate by an angle of 45° and then stop and wait for further instruction.

The shaft of the DC motor is coupled with another shaft called output shaft, with help of gear

assembly. This gear assembly is used to step down the high rpm of the motor's shaft to low rpm

at output shaft of the servo system.

The voltage adjusting knob of a potentiometer is so arranged with the output shaft by means of

another gear assembly, that during rotation of the shaft, the knob also rotates and creates an

varying electrical potential according to the principle of potentiometer . This signal i.e. electrical

potential is increased with angular movement of potentiometer knob along with the system shaft

from 0° to 45°. This electrical potential or voltage is taken to the error detector feedback

amplifier along with the input reference commends i.e. input signal voltage.

As the angle of rotation of the shaft increases from 0° to 45° the voltage from potentiometer

increases. At 45° this voltage reaches to a value which is equal to the given input command

voltage to the system. As at this position of the shaft, there is no difference between the signal

voltage coming from the potentiometer and reference input voltage (command signal) to the

system, the output voltage of the amplifier becomes zero.

As per the picture given above the output electrical voltage signal of the amplifier, acts as input

voltage of the DC motor. Hence the motor will stop rotating after the shaft rotates by 45°. The

motor will be at this rest position until another command is given to the system for further

movement of the shaft in desired direction. From this example we can understand the most basic

servo motor theory and how servo motor control is achieved. NB: Although in practical servo

motor control system, instead of using simple potentiometer we use digital or analog position

sensor encoder.

From this basic working principle of servo motor it can be concluded. The shaft of the servo is

connected to a potentiometer . The circuitry inside the servo, to which the potentiometer is

connected, knows the position of the servo. The current position will be compared with the

desired position continuously with the help of an Error Detection Amplifier. If a mismatch is

found, then an error signal is provided at the output of the error amplifier and the shaft will rotate

to go the exact location required. Once the desired location is reached, it stops and waits.

Continuous Rotation Servo Motors

Continuous rotation servo motors are actually a modified version of what the

servos are actually meant to do, that is, control the shaft position. The 360° rotation servos are

actually made by changing certain mechanical connections inside the servo. However, certain

manufacturer like parallax sells these servos as well. With the continuous rotation servo you can

only control the direction and speed of the servo, but not the position. Two of the most popular

Servo motor manufacturers are FUTABA and HITEC.

CONTROLLER

The combination of proportional, integral and derivative control action is called PID

control action. PID controllers are commonly used to regulate the time-domain behavior of many

different types of dynamic plants. These controllers are extremely popular because they can

usually provide good closed-loop response characteristics. Consider the feedback system

architecture that is shown in Fig. 1 where it can be assumed that the plant is a DC motor whose

speed must be accurately regulated.

The PID controller is placed in the forward path, so that its output becomes the voltage

applied to the motor's armature the feedback signal is a velocity, measured by a tachometer .the

output velocity signal C (t) is summed with a reference or command signal R (t) to form the error

signal e (t). Finally, the error signal is the input to the PID controller.

PROPORTIONAL CONTROL:

The proportional part of PID examines the magnitude of the error and it reacts

proportionally. A large error receives a large response. For example, if there is a large

temperature error, the fuel valve would be opened a lot. On the other hand, a small error receives

a small response. In mathematical term, the proportional term (Pout) is expressed as:

Pout = Kp*e

Where:

Pout: Proportional portion of controller output

Kp : Proportional gain

e: Error signal,

e = Set-point – Process Variable

The following figure illustrates a proportional control and shows that there is always

a steady state error in proportional control. The error will decrease with increasing gain, but the

tendency towards oscillation will also increase

There are issues with proportional control only. One of them is that proportional

control cannot compensate very small errors (these errors are also known as offset.) Another

issue is that it cannot adjust its output based on the rate of change in the measured variable.

Proportional controllers only respond to the magnitude of the error, not to its rate of change.

INTEGRAL CONTROL:

To address the first issue with the proportional control, integral control attempts

to correct small error (offset). Integral examines the error over time and increases the importance

of even a small error over time. Integral is equal to error multiplied by the time the error has

persisted. A small error at time zero has zero importance. A small error at time 10 has an

importance of 10 times error. In this manner, integral increases the response of the system to a

given error over time until it is corrected.

Integral can also be adjusted and the adjustment is called the reset rate. Reset rate

is a time factor. The shorter the reset rate the quicker the correction of an error. However, too

short a reset rate can cause erratic performance. In hardware-based systems, the adjustment can

be done by a potentiometer changing the time constant of a RC circuit. Most of today’s

applications use software based control such as PLC module in which the engineer changes the

parameter of reset rate. The mathematical expression of an integral-only controller (Iout) is:

Where:

Iout: Integral portion of controller output

Ti: Integral time, or reset time

Ki: Integral gain

e: Error signal, e = Set-point – Process Variable

DERIVATIVE CONTROL:

The derivative part of the control output attempts to look at the rate of change in the

error signal. Derivative will cause a greater system response to a rapid rate of change than to a

small rate of change. In other words, if a system’s error continues to rise, the controller must not

be responding with sufficient correction. Derivative senses this rate of change in the error and

provides a greater response. Derivative is adjusted as a time factor and therefore is also called

rate time. It is essential that too much derivative should not be applied or it can cause overshoot

or erratic control. In mathematical term, the derivative term (Dout) is expressed as:

Where:

Dout: Derivative portion of controller output

Td: Derivative time

Kd: Derivative gain

e : Error signal, e = Set-point – Process Variable

The Proportional-Integral Controller (PI):

A PI Controller is where Derivative control is not used in the controller. The absence of

derivative control makes the system more stable in the steady state region, In the presence of

noise. This is due to the derivative control is sensitive to higher Frequency terms in the inputs.

However, without the implementation of the derivation Parameter, a PI- controller system

response will be less stable and tends to overshoot compared to a well-tuned PID system.

The Proportional-Integral controller is to improve the system gain and steady state error.

It has the integral of (Ki/s) which will cause the system to have a decaying exponential response.

When this response reached value of zero, the system Will only left with the forced response.

Therefore, the output will reach to the same Level as the input eventually. This controller has

element of Kp whereby to improve the system gain.

The Proportional-Derivative Controller (PD):

The Proportional-Derivative controller is able to improve the system gain and Transient

response but will not improve on the steady state error. This derivative Element is Kds and is

proportional element, Kp. This exponential response will determine the transient response of the

system. Figure 2.6 shows the basic structure of PD controller.

The Proportional-Integral Derivative Controller (PID):

The Proportional-Integral Derivative (PID) controller behavior can be interpreted as the sum of

the three terms actions for (P) terms gives a rapid control Response and a possible steady state

error, the (I) term eliminates the steady state Error and the (D) term improves the behavior of the

control system during transients.

Figure shows the block diagram of the PID controller. The parameters for the controllers

are Kp, Ki and Kd. The process of determining the most suitable value of these parameters is

known as controller tuning method. There are a few methods that can be used to tune these

parameters value such as Ziegler-Nichols method, Cohen-coon method, Fuzzy-logic method and

trial and error method.

Transfer function for PID is:

C(s) =Kp (1+ 1𝑇 𝑠₁ + Td s)

The proportional control (Kp) is used so that the control signal u(t) responds to the

error immediately. But the error is never reduced to zero and an o offset error is inherently

present. To remove the offset error the integral control action (𝑻₁) is used. The Derivative

control (Td) is used to damped out oscillations in the process response. By tuning the gains of

the PID controller and producing the optimum response using trial and error method.

TUNNING OF PID:

The second part of setting a PID is to tune or choose the numerical value of the PID

parameters. PID controllers are tuned in terms of P, I and D. Tuning the control gains may result

in the following improvement of response:

Proportional gain (Kp): Larger proportional gain typically means faster response, since the

larger the error, the larger the proportional term compensation. However, an excessively large

proportional gain may result in process instability and oscillation.

Integral gain (Ki): Larger integral gain implies steady-state errors are eliminated faster.

However, the tradeoff may be a larger overshoot, since any negative error integrated during

transient response must be integrated away by positive error before steady state can be reached.

Derivative gain (Kd): Larger derivative gain decreases overshoot but slow down transient

response and may lead to instability due to signal noise amplification in the differentiation of the

error.

The following table lists some common tuning methods and their advantages and disadvantages.

The choice of method will mostly depend on whether or not the loop can be taken offline for

tuning, and the response time of the system. If the system can be taken offline, the best tuning

method often involve s subjecting the system to a step change in input, measuring the output as a

function of time, and using this response to determine the control parameters. Manual tuning

methods can be quite inefficient, especially if the loops have response times on the order of

minutes or longer.

Ziegler-Nichols (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 methods.

Step response method

Frequency response method.

In this Paper frequency response method is discussed for tuning the PID controller.

FIRST METHOD (RECTION CURVE METHOD):

In this method, we obtain experimentally the response of the plant to a step input as shown in fig.

This method applied if the response to a step input exhibits an s-shaped curve. Such a step

response curves may be generated experimentally or

Form dynamic simulation of the plant.

The S-shaped curves may be characterized by two constant delay time ‘L’ and time constant

‘T’the delay time and time constant are determined by drawing a tangent line at the inflection

point of the S-shaped curved and determining the intersection of the tangent with the time axis

and line C(t) = K as shown in figure.

The table gives the value of Kp, Ki and Kd for step response plant.

Controller Kp Ki Kd P T/L Infinite 0 PI 0.9*(T/L) L/0.3 0 PID 1.2*(T/L) 2L 0.5L

The table shows Ziegler Nichols Tuning Rules Based on step response of plant

The transfer function may approximated by first order system with a transport lag as

for

Ziegler and Nichols suggested to set the value of Kp, Ki and Kd according to the formula shown

in table. The PID control tuned by the Ziegler –Nichols rules gives

In this paper thee Second method of Zeigler-Nichols method of tuning of PID, also

called the Continuous cycling method or Closed loop method, is used

SECOND METHOD:

In this method derivative time (𝑇𝑑) is set to zero and integral time (𝑇𝑖) set to

infinity. This is used to get the initial PID setting of the systems. The critical gain (Kcr) and

periodic oscillations (𝑃cr) are determined by using R-H criteria. Kcr is determined by equating

the row containing ‘s’ in R-H row to zero. 𝑃cr is determined by equating the row

containing‘s^2’ in R-H row to zero. Evaluate parameters described by Z-N method. Values of 𝐾p, 𝐾𝑖 𝑎𝑛𝑑 𝐾𝑑 are determined by using the formulas given in below.

Control type Kp Ki Kd P 0.5Kcr infinite 0 PI 0.45Kcr (1/0.2)Pcr 0 PID 0.6Kcr 0.5Pcr 0.125Pcr

The table shows Ziegler-Nichols Tuning Rules based on critical Gain Kcr and critical Pcr

The PID controlled tuned by the continuous cycling method of Ziegler-Nichols method gives.

Thus the PID controller has a pole at the origin and double zeros at s =

Block Diagram Description

The block diagram consists of

Comparator

Driver

Power circuit

Motor setup

Position feedback loop

Speed feedback loop

Comparator

A comparator is a circuit which compares two signals and determines which one is greater. The

result of this comparison is indicated by the output voltage. In our module a comparator

compares the carrier signal with position feedback loop signal or speed feedback Signal. The

output of comparator is given as input to the delay circuit. Delay circuit is used to avoid the short

circuit problems when the two MOSFETs operate at the same time.

Driver

Delay circuit output is given to the driver circuit. The driver circuit amplifies this signal and

converts it into the desired output level. The driver circuit output is in the form of PWM pulses.

These pulses are given to the gate of the power circuit MOSFET devices.

Power Circuit

The power circuit consists of MOSFET based Four quadrant bipolar chopper circuit. The PWM

pulses are obtained from the firing circuit. The output of power circuit is connected to motor

load.

Motor setup

Motor setup consists of PMDC motor, Position sensor and Tacho generator. The position sensor

senses the motor position and the tacho generator sense the motor speed. This position and speed

values are given to position feedback loop and speed feedback loop for motor control.

Position Feedback Loop

Position Feedback Loop consists of error detector, P and I gain control knobs. The output

position and the input position of the motor is given to error detector provided in the position

feed back loop. The error detector compares these two signals and produces the error signal. The

error signal will be a weak signal and so it has to be amplified and integrated or differentiated to

produce a control signal using P and I controller. The output of the position feedback loop is

given to the comparator.

Speed Feedback Loop

Speed Feedback Loop consists of error detector and P gain control knobs. The output speed and

the input speed of the motor is given to error detector provided on the speed feedback loop. The

error detector compares these two signals and produces the error signal. The error signal will be

a weak signal and so it has to be amplified and differentiated to produce a control signal using P

controller. The output of the speed feedback loop is given to the comparator.

Position Control with Speed Feedback

In the above figure, the angular position of the output shaft is intended to follow

the reference voltage but it should be clear that if the motor drives a toothed belt linear outputs

can also be obtained. The potentiometer is mounted on the output shaft. The voltage from this

potentiometer must be a linear function of angle, and must not vary with temperature; otherwise

the accuracy of the system will be in doubt.

The feedback voltage (representing the actual angle of the shaft) is subtracted from

the reference voltage (representing the desired position) and the resulting position error signal is

amplified and used to drive the motor so as to rotate the output shaft in the desired direction.

When the output shaft reaches the target position, the position error becomes zero, no voltage is

applied to the motor, and the output shaft remains at rest. Any attempt to physically move the

output shaft from its target position immediately creates a position error and a restoring torque is

applied by the motor.

The dynamic performance of a simple scheme described above is very

unsatisfactory as it stands In order to achieve a fast response and to minimize position errors

caused by static friction, the gain of the amplifier needs to be high, but this in turn leads to a high

oscillatory response which is usually unacceptable. For some fixed - load applications, matters

can be improved by adding a compensating network at the input to the amplifier, but the best

solution is to use 'tacho' (speed)feedback (shown as dotted in the above Figure) in addition to the

main position. Tacho feedback has no effect on the static behavior, but has the effect of

increasing the damping of the transient response. The gain of the amplifier can therefore be made

high in order to give a fast response, and the degree of tacho feedback can then be adjusted to

provide the required damping. Many servo motors have an integral tacho generator for this

purpose.

The example provided above deals with an analog scheme in the interest of simplicity,

but digital position control schemes are now gradually taking precedence, especially when

brushless motors are used. Complete 'Controllers on a card' are available as off-the-shelf items,

and these offer case of interface to othersystems as well as providing improved flexibility in

shaping the dynamic response.

DC Servo Motor Response

The response of the DC servo motor can be considered as a second order system. A

second order system will have a natural frequency ω, a damping factor ς. The general response of

a second order system with a step input is shown in Figure 3. From the response of the second

order system we can get some of the characteristics of the system, and the design criteria can be

implemented using these characteristics.

Different parameters can be used to evaluate the response of the dc motor; by

adjusting the value of these parameters we can reach our design goal. Mp is the overshoot value,

ts is the settling time and β is the allowable error tolerance. These three parameters can define the

design criterion and output response of any second order system response.

The ideal system response will have a zero overshoot, zero settling time and zero

tolerance, but in real life achieving the ideal response will be hard and will have a high cost of

implementation. So, the solution can be found by defining an accepted range for the values of the

three parameters mentioned before to achieve a good system response for a specific application.

In many practical cases the desired performance characteristics of control system are

specified in terms of time domain quantities. Frequently, the performance characteristics of a

control system is specified in terms of the transient response to a unit-step input since it is easy to

generate and is sufficiently drastic. In specifying the transient characteristics of a control system

to a unit-step input, it is common to specify the following.

Delay time, td 2. Rise time, tr 3. Peak time, tp 4. Maximum overshoot, Mp 5. Settling time, ts

Delay time, t d

The delay time is the time required for the response to reach half the final value, for the very first

time.

Rise time, t r

The rise time is the time required for the response to rise from 10% to 90%, 5% to 95%, or 0% to

100% of its final value. For under damped second order systems, the 0% to 100% rise time is

normally used. For over damped systems, the 10% to 90% rise time is commonly used.

Peak time, t p

The peak time is the time required for the response to reach the first peak of the overshoot.

Maximum overshoot, M p

The maximum overshoot is the maximum peak value of the response curve measured from unity.

If the final steady - state value of the response differs from unity, then it is common to use the

maximum percent overshoot. The amount of the maximum (Percent) overshoot directly indicates

the relative stability of the system.

Settling time, t s

The settling time is the time required for the response curve to reach and stay with in a range

about the final value of size specified by absolute percentage of the final value (usually 2% or

5%). The settling time is related to the largest time constant of the control system.

Chopper Circuit

Static DC to DC converters, called as choppers, achieve a similar function transformers but in

DC. Choppers are widely used for traction motor control in electric automobiles, trolley cars,

marine hoists, fork lift trucks, and mine haulers. They provide smooth acceleration control High

efficiency, and fast dynamic response. Choppers are also used in DC voltage regulators.

Four Quadrant Chopper

In four quadrant operation the output current as well as output voltage can take positive or

negative values. The circuit diagram for MOSFET based chopper is shown below.

In the first quadrant the power flows from the source to the load and is assumed to be

(+) ve. In the second quadrant the voltage is still positive but the current is negative. The power

is there- fore negative. In this case power flows from the load to the source and this can happen if

the load is inductive or back emf source such as a DC motor. In the third quadrant both the

voltage and current are negative, but the power is positive, and the power flows from the source

to the load. In the fourth quadrant voltage is negative but the current is positive. The power is

therefore negative.

The four quadrant chopper is widely used in reversible DC motor drives. The

reversible DC motor drive system requires, power flow in either direction, in order to achieve

fast dynamic response. By employing four quadrant chopper it is possible to implement

regeneration and dynamic braking by means of which fast dynamic response is achieved.

Mathematical Modeling of Armature Controlled DC Servo

Motor

DC Servo Motor

The motors which are utilized as DC servo motors generally have separate DC source for field

winding and armature winding. The control can be archived either by controlling the field

current or armature current. Field control has some specific advantages over armature control

and on the other hand armature control has also some specific advantages over field control.

Which type of control should be applied to the DC servo motor, is being decided depending upon

its specific applications.

The motor is paired with some type of encoder to provide position and speed feedback. In the

simplest case, only the position is measured. The measured position of the output is compared to

the command position, the external input to the controller. If the output position differs from that

required, an error signal is generated which then causes the motor to rotate in either direction, as

needed to bring the output shaft to the appropriate position. As the positions approach, the error

signal reduces to zero and the motor stops.

MODELING

A DC servo motor is used in a control system where an appreciable amount of shaft

power is required. The DC servo motors are either armature-controlled with fixed field, or field-

controlled with fixed armature current.

DC servo motors used in instrument employ a fixed permanent-magnet field, and the

control signal is applied to the armature terminals.

Ra = armature-winding resistance, ohms

La = armature-winding inductance, henrys

Ia = armature-winding current, amperes

If = field current, amperes

Ea = applied armature voltage, volts

Eb = back emf, volts 𝜃= angular displacement of the motor shaft, radians

T = torque delivered by the motor, lb-ft

J = moment of inertia of the motor and load referred to the motor shaft, slug-ft2.

f = viscous-friction coefficient of the motor and load referred to the motor shaft, lb-ft/rad/sec

Flux produce is directly proportional to filed current

Torque produced is proportional to product of flux and armature current

Back emf is directly proportional to shaft velocity (wn) as flux is constant∅

Apply KVL to armature circuit

Taking a lapalas transfer function

NOW

Here shaft torque Tm is used for driving load against the inertia and frictional Torque.

Taking lapalas transfer function

Equating equation (5&7)of Tm

Since If is neglected

Where motor time constant

Armature time constant

The transfer function of the output angular speed is derived using Laplace transform using the

second order system equation:

The resulting Transfer function:

From Equation the relationship between the angular position and the speed can be found by multiplying the angular position by1/𝑠. Our major Concern on this research is the proper control of the angular speed of the motor; since the angular speed is the part that suffers the most from the non-linear ties. The angular non-linear effect on the angular position tends to be less due to the term used to derive it1/𝑠, which adds an integral effect or filter effect to this part. Figure shows the block diagram which represents the servomotor system using MATLAB SIMULINK.

DC Servomotor parameter values.

Parameter Value

Moment of Inertia(J) 0.001 Nms²/rad

Damping Coefficient(B) 0.1 Nms/rad

Torque constant (Kt) 0.01 Nm/A

Electromotive force constant (Ke) 0.01 Vs/rad

Electrical Resistance (R) 1 Ohms

Electrical Inductance(L) 0.5 Henry

Calculation of Kcr and Pcr:

As we know that the transfer function of dc servo motor

Put the value of (La, Ra, Km, Kb, Bm, Jm)

By using Ziegler-Nichols second method and we get,

Kcr = 13.2

Pcr = 0.4236807355

And find Kp, Ti and Td

Kp Ti Td

7.92 0.2118403678 0.05296009194

Project Scheduled Chart:-

Weekly Activity 2015-2016

July August September December January1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Study on the Servo Motor

Study on the PID Controller

MathematicalModelling of the Dc Servo Motor

Simulation Using MATLAB

Design of Hardware

Verify the performance of

the working model with

Simulink model

Documentation

Methodology: Start