Servo Motor

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 Theory There 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 Principle Before understanding the working principle of servo motor we should understand first the basic of servomechanism.

Servomechanism A 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 Motor A 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 Control For 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+ 1�₁� + 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 ( �₁) 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 P PI PID

Kp T/L 0.9*(T/L) 1.2*(T/L)

Ki Infinite L/0.3 2L

Kd 0 0 0.5L

The table shows Ziegler Nichols Tuning Rules Based on step response of plant The transfer function may for

approximated by first order system with a transport lag as

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 (��) 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 (Kcr) and periodic oscillations (�cr) are determined by using R-H criteria. Kcr is determined by equating the row containing ‘s’ in R-H row to zero. �cr is determined by equating the row containing‘s^2’ in R-H row to zero. Evaluate parameters described by Z-N method. Values of �p, �� ��� �� are determined by using the formulas given in below.

Control type P PI PID

Kp 0.5Kcr 0.45Kcr 0.6Kcr

Ki infinite (1/0.2)Pcr 0.5Pcr

Kd 0 0 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 fieldcontrolled 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 �= 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/�. 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/�, 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

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Study on the Servo Motor Study on the PID Controller Mathematical Modelling of the Dc Servo Motor Simulation Using MATLAB

Design of Hardware Verify the performance of the working model with Simulink model Documentation

Methodology:

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