pg. 1

Feedback and Stability Lab Report

Arnold Mukuvare

Demonstrator: S. Adhami

SMOR: N. Rockliff

Work carried out: 19 February 2013

Report completed: 3 March 2013

Abstract:

DC motors are commonly used in operations where speed control is essential. The objective

of this experiment was to show the differences between an open and closed-loop system, in a

control system. An analogue control unit and a mechanical unit (PMDC) motor were used to

show this phenomenon, concepts of feedback positive and negative were compared against

each other and advantages summed up as a result. Initial motor conditions were replicated by

starting with the same speed (ω) for both the systems. The open-loop system was set up and

load applied, results were recorded and the relation between the speed and current was

tabulated as a graph. The same process was repeated for the closed loop system. Comparisons

of the two graphs (open-loop and the closed-loop) were plotted on the same plane and from

the data it showed the closed loop system to be more stable meaning less prone to

disturbances. Positive and negative feedback were compared to each other and it showed that

the negative feedback had a self-correcting factor hence more preferable.

pg. 2

Contents

Introduction ………………………………………………………………………….. 2

Theory ……………………………………………………………………………….. 3

Procedures and Equipment …………………………………………………………... 5

Results ……………………………………………………………………………….. 6

Discussion …………………………………………………………………………… 7

Conclusions ………………………………………………………………………….. 8

References ………………………………………………………………………….... 9

Appendix

Introduction The concept of control is one that has been around even before civilisation. As engineers

control plays a vital role in instrumentation and key manufacturing processes. One system

that invariably relies on this is the DC motor, and modern day DC motors could be used in

Hydroelectricity to even small things as hand fans. The DC motor follows the basic physics

concepts that a current-carrying wire (conductor) experiences a force when it cuts a magnetic

field. For a constant magnetic field a permanent magnet (PMDC motor) is more preferable

unlike induction field generated motors.

At a constant voltage, a PMDC will produce a linear torque/speed characteristic and as a

result this is the motor which will be used in the experiment. The PMDC motor will be

arranged in either an Open-loop system or a Closed-loop system. In an open loop system,

there is an absence of a closed signal path so the output does not influence the input

(Franklin, Powell and Emami-Naeini 2010). For the PMDC the input was electricity and the

output rotation; a direct proportionality relationship between the input and the output (see

fig.2). Open-loop systems are not desirable for they do not record give the actual response but

give a response plus disturbances.

The closed loop system is different from the open loop due to the availability of a feedback

loop. The feedback path links the output back to the input and it could either be added or

subtracted. The feedback path helps in minimising the possible effect or disturbances (noise),

the control strategy will compare the desired output from the actual output and this

sometimes would result in an error which is just the difference between the desired and the

actual output. It is however, important to note that there are two forms of feedback (i)

Positive feedback and (ii) Negative feedback. Where the positive feedback would continue to

increase the output even adding the phenomenon of noise resulting I more noise and negative

feedback maintains steady system by subtracting output from input to obtain an error signal.

pg. 3

Theory In designing any form of a system the major specification that one should try to meet is the

issue of stability. Stability has mainly to with the response time a system has until it becomes

steady.

A current carrying conductor has a magnetic field around it, as explained in the introduction.

Concepts of magnetic flux, torque and voltage, for the DC motor are the ground works for the

experiment. Our DC motor will be assumed to be idealised meaning that when a supply

voltage is applied, Vs is applied to the rotor winding current will flow around the circuit,

since the conductor has a current this will cut the field of the permanent magnet and the

motor will start to rotate. At the same time a back EMF, Eg which is proportional to the

speed, ω will be generated.

(1)

(2)

From Eqn (2), assuming that the armature resistance (Ra) is kept constant and the armature

current equalled zero (Ia=0), but it is important to note that the motor is not ideal hence

(Ia≠0).For mathematical reasons assuming that (Ia=0) would mean the cancellation of the

(Ia*Ra) term which establishes a direct proportionality between the motor speed and the

supply voltage.

(2a)

Multiplying equation (2) by Ia would result in obtaining electrical power

(3)

Eqn (3), shows that (TL = Tm) when the speed (ω) reaches a steady speed. Which are torque

load (TL) and the stall load (Tm). Under ideal conditions the armature current (Ia) would be

proportional to the motor torque under ideal conditions (Henslee E., and Ward S., 2013).

(4)

Equation (4); is a general equation that relates the speed and the load relationship for an ideal

permanent magnet. ( ) is the speed when the load is zero, and the armature voltage and b

are the constants of a motor.

Constructing equation (4)

Substitute Eqn (2a) into the above equation [ ]

From Eqn (3) make Ia the subject of the formula with respect to the stall load such that

Eqn(2a) would become:

This would mean:

(5)

pg. 4

Eqn (5) is the same as Eqn (4), and the constants being (

) and (

)

It is essential in control to have Block diagrams these have great mathematical connotations

and makes it easy to be able to see the relationship between inputs and outputs.

Figure 2: Block diagram of an open loop system (Celcelja F., 2013)

In the Open loop system above it is worth knowing that the system does not measure the

output (y(t)) as indicated in Figure 2. In Figure 2 instead of having an input coming into the

motor (plant) the manipulated variable is the input to the system after being amplified. How

accurate the system is depends on its calibration.

The introduction has already stated the differences between the open-loop system and the

closed loop control systems. Closed loop systems imply mainly the use of a feedback in order

to reduce error. Figure 3 shows the closed loop control system.

Figure 3: Block diagram of a closed loop system (Celcelja F., 2013)

In closed loop system summing points determine whether the error would be additive

(positive feedback) or subtractive (negative feedback), Figure 4, shows the summing points

and the effect of the error into the amplifier.

Figure 4: (a) Summing point with a negative feedback

(b) Summing point with a positive feedback

Summing amplifier

A summing amplifier or inverting amplifier can be used to establish closed loop feedback

system. From Figure 4 resistors RA=RB=RC=R1 on the Analogue unit R1=100Ω, using

Kirchhoff’s law that current meeting at a junction sum up and Ohm’s law as the relationship

between voltage resistance and current.

pg. 5

[6]

[7]

Figure 5: Summing (Inverting) Amplifier (Hughes M., 2012)

Procedures and Equipment Equipment:

33-110 Analogue unit

33-100 Mechanical unit

Multi-meter (measure voltage)

1mm wire connections

Procedures:

Before conducting the experiment one should be well acquainted with the equipment in this

practical. The power supply should be switched off; wire connections pulled from the

analogue unit and have to be switched off whenever one is going to touch the Analogue unit

33-100.

Open-Loop

Figure 5 in the Appendix shows the Analogue unit, for the open loop system. Connections

were made using the wire connections, the knob P3 is a potentiometer and is used to regulate

the speed on the mechanical unit to 40rpm. Before moving the load on the mechanical unit

current was measured by altering the RPM/DVM switch to DVM so as to obtain the current

readings and the same procedure was repeated after each brake step applied. At the same time

the RPM/DVM was switched between the two options to obtain the speed (ω) and the current

(I).

Closed-Loop

The output of P3 is connected to the tacho-generator which is on the top left of the unit. By

connecting the 1MΩ resistor on the summing amplifier ensures that there is a closed-loop

system. P3 switch was turned to zero and on the motor unit no brake was applied before the

switching the power supply and tuning P3 switch unit the RPM display unit reads 40rpm.

Using the voltmeter the reference voltage was measured with respect to the ground, including

pg. 6

the voltage across the tacho-generator signal and error amplifier. The results from this

procedure are in Table 3 in the appendix.

By connecting the gain output was connected to the positive terminal on the tacho-generator,

while P3 is zero and the power supply switched off. This means that the feedback is now

positive. If the load is returned to zero/the uppermost position and the switched turned on,

then gradually turning P3 until 40rpm is achieved on the RPM display on the Mechanical

unit. It can be seen that the motor will rotate clockwise. This procedure could be carried out

again to eliminate location errors.

Repeating the same procedure but by changing from the positive terminal to the negative

terminal on the tacho-generator means that the feedback is now negative. This time it can be

seen that the motor rotates in an ant-clockwise direction, this was due to the magnetic field

passing current in an opposite direction so the motor will rotate in an opposite direction.

Results After carrying out the setup process as illustrated above. Two experiments are to be carried

out to obtain (i) the open-loop experiment and (ii) closed loop systems and results recorded in

Table 1 and Table 2.

To calculate the averages for the speed () and current (I) equation 8 was used.

Table 1. Speed (ω) and current (I) results from the Open-Loop control system, for the various

armature positions

Brake SET 1 SET 2 SET

3

AVERAGE

ω (rpm) I (A) ω (rpm) I (A) ω (rpm) I (A) ω (rpm)

I (A)

0 41.7 -0.22 41.7 -0.19 39.8 -0.19 41.06667 -0.2

1 40 -0.24 40.3 -0.23 38.5 -0.22 39.6 -0.23

2 38 -0.28 38.3 -0.28 38.2 -0.22 38.16667 -0.26

3 38.6 -0.27 37.2 -0.3 37.9 -0.23 37.9 -0.26667

4 33.6 -0.4 33 -0.42 34.1 -0.33 33.56667 -0.38333

5 31 -0.47 29.4 -0.51 29.2 -0.46 29.86667 -0.48

6 26.2 -0.6 26.2 -0.58 25.9 -0.55 26.1 -0.57667

pg. 7

Table 2. Speed (ω) and current (I) results from the Closed-Loop system at various armature

positions

Brake SET 1 SET 2

AVERAGE

ω (rpm) I (A) ω (rpm) I (A) ω (rpm) I(A)

0 40 -0.19 40 -0.19 40 -0.19

1 40 -0.2 40 -0.2 40 -0.2

2 40 -0.24 40 -0.23 40 -0.235

3 39.8 -0.27 39.8 -0.28 39.8 -0.275

4 38.7 -0.4 39.4 -0.4 39.05 -0.4

5 38.2 -0.67 38.7 -0.55 38.45 -0.61

6 37.7 -0.82 37.7 -0.82 37.7 -0.82

The following voltages were recorded when measured according to the ground. This is done

so as to prove that equation (7) is true. Input voltages were put across RA and RB. This means

that there is no current passing through Rc, in diagram 5.

Input voltage across RA: 3.84V

Input voltage across RB: -3.47V

Error voltage/output Vo: -3.80V (Experimental)

Theoretical calculation to find output voltage:

Substitute the voltages above into equation 5.

(Va=3.84V, Vb=-3.47V, R2= 100KΩ and R1=1MΩ)

This will give us a theoretical value of the output voltage which is: Vout= -3.7V

The above value shows that there is a difference between the actual value of the output

voltage and the theoretical/calculated value.

(10)

Therefore the error = 2.702%

The discussion will include ideas on why this error is probable and acceptable.

Discussion

In every experiment there is the unavoidable Human error, to prevent this however people

were tasked to stick to the same duty until the end of the experiment this increases accuracy.

In digital system we trust that the calibration of the instruments is accurate and the only errors

that are to be considered are those due to calibration error. In this lab this is the major error

and can be dealt with by repeating the experiment a number of times and taking an average.

With respect to the open-loop system the slope is steeper (greater gradient) than that of the

closed-loop system. This shows that with an increase in the current the speed also changes,

pg. 8

this raises concerns for the open-loop system that there is a continuous increase in output and

no regulation because of the failure of interaction or communication between the ouput and

the input. As a result the open-loop system is very prone to disturbances.

In case for the closed-loop system, earlier results on application of load shows no change in

the speed (ω), and the gradient was far small and close to producing a horizontal graph. On

setting the initial speed to 40rpm, it was fairly easy in comparison to the open-loop system;

this is because the closed-loop system has a feedback network system and the time response

to self-correct is system is small. An increase in the current would mean that a restoring

torque is generated and the speed is kept constant.

Fluctuations were observed when voltage measurements were taken for the open-loop system

unlike the closed-loop system. Feedback is a desirable effect that helps eliminate errors.

In the results section there was a 2.702% error, this could have been likely due to the

hysteresis error and background noise. Given that the experiment includes resistors, they are

suspect to change of resistance with a change in the temperature.

These observations were in accordance to many text, showing that the a closed-loop system

has improved accuracy, improved dynamic response and stable (Sen P.C., 1997, pg 195)

Conclusion

From the experiment the following conclusion where made about the open loop system,

disturbances affect the output and that slower response time made for there to be high

fluctuations between the valves of the armature current and the motor speed.

Where as in a closed loop system the motor became steadier as a result of the feedback path

and disturbances did not affect the output due to the cancellations hence the system is stable.

On testing negative feedback the system corrects itself and obtains stability (motor speed

ω=0). Whereas positive feedback the diles continue to rotate failing to reach stability.

Negative feedback has a corrective system/mechanism that eventually brings systems to

stability. Phase lag that exceeds 180˚ leads to unstable systems due to the rise in the positive

feedback.

pg. 9

References

[1] Franklin F. Gene, Powell J. David and Emami-Naeini Abbas, 2010. Feedback Control of

Dynamic Systems, Sixth Edition, Pearson

[2] Hughes Austin, 2006, Electric Motors and Drives, Third Edition, Elsevier

[3] Nise S. Norman, 2011, Control Systems Engineering international student version, Sixth

Edition, John Wiley and Sons

[5] Sen P.C., 1997, Principle of Electric Machines and Power Electronics, Second Edition,

John Wiley and Sons

[6] Celcelja F., 2013, Concept of Control, Lecture notes, Surrey University

[7] Henslee E., and Ward S., 2013, Numerical and Experimental Methods, Background

Documents and Methods

[8] Hughes M., 2012, Amplifiers, Electronic Instrumentation, Surrey University

pg. 10

Appendix

Table 1. Speed (ω) and current (I) results from the Open-Loop control system, for the various

armature positions

Brake SET 1 SET 2 SET

3

AVERAGE

ω (rpm) I (A) ω (rpm) I (A) ω (rpm) I (A) ω ±0.005

(rpm)

I ±0.02

(A)

0 41.7 -0.22 41.7 -0.19 39.8 -0.19 41.07 -0.2

1 40 -0.24 40.3 -0.23 38.5 -0.22 39.6 -0.23

2 38 -0.28 38.3 -0.28 38.2 -0.22 38.17 -0.26

3 38.6 -0.27 37.2 -0.3 37.9 -0.23 37.9 -0.27

4 33.6 -0.4 33 -0.42 34.1 -0.33 33.57 -0.38

5 31 -0.47 29.4 -0.51 29.2 -0.46 29.87 -0.48

6 26.2 -0.6 26.2 -0.58 25.9 -0.55 26.1 -0.58

Table 2. Speed (ω) and current (I) results from the Closed-Loop system at various armature

positions

Brake SET 1 SET 2 AVERAGE

ω (rpm) I (A) ω (rpm) I (A) ω

±0.005

(rpm)

I

±0.02(A)

0 40 -0.19 40 -0.19 40 -0.19

1 40 -0.2 40 -0.2 40 -0.2

2 40 -0.24 40 -0.23 40 -0.24

3 39.8 -0.27 39.8 -0.28 39.8 -0.28

4 38.7 -0.4 39.4 -0.4 39.05 -0.4

Important diagram excluded from the text:

pg. 11

Figure 1: Ideal model of PMDC motor and the torque/speed characteristics. (Henslee E., and

Ward S., 2013)

Figure 5: Image capture 33-110 analogue unit (Henslee E., and Ward S., 2013)

pg. 12

Figure 6: 33-100 Mechanical unit (Henslee E., and Ward S., 2013)

Figure 7: The plot of the speed/current graphs from table(1)&(2) with standard error bars

Vital equations used in this report:

(1)

pg. 13

(2)

(2a)

(3)

(4)

(5)

Equation (6) is the Kirchorff’s current rule being applied. Combination of the equation and

the Ohm’s law would give equation (7)

(6)

Ohm’s law states:

Applying this to Equation (6) would mean:

(6a)

If resistor A,B,C are all equal then we can factorise to get:

(6b)

Rearranging would give equation (7) which is the gain of a summing amplifier.

(7)

Calculating the average and the error:

Where: m = the average/ mean

n = number of samples

xi = motor speed or current

(8)

Standard deviation: √

∑

(9)

(10)