a four quadrant dc motor closed-loop speed control based on a … · 2019-07-13 · control...

Vol. 10(35), Jan. 2020, PP. 4471-4482

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Article History: Received Date: Apr. 14, 2019 Accepted Date: Jun. 06, 2019 Available Online: Jan. 01, 2020

A Four Quadrant DC motor Closed-Loop Speed Control Based on a

Patterned-Disk Optical F/V Feedback Sensor system

Ignatius I. Uzoeto1.* and Emenike C. Ejiogu2 1, 2 Department of Electrical Engineering University of Nigeria Nsukka, Nsukka, Nigeria

Phone Number: +234-08039401810

*Corresponding Author's E-mail: [email protected]

Abstract

his paper is aimed at designing and implementing an optical feedback control system for a PWM

four quadrant chopper driven conventional DC motor. Motor speed control is achieved from an

efficient feedback measuring accuracy. In the implementation of the feedback path, an optical

sensor and a patterned disk are the transducer for converting the output speed of the motor to voltage.

The results obtained shows the interaction of the speed and voltage, and the PWM signal generated for

the four quadrant chopper switches. And the feedback system provides an effective response to any

change in the system’s output and the practicable advantage of the high efficiency brands it an optimal

control.

Keywords: DC Motor, Patterned-disk, Optical Sensor, feedback path, four quadrant chopper, F/V

1. Introduction

As technology advances in the aspect of system operations, so also is improvement in the use of

control laws and mechatronics configuration in system design and control. Practical system dynamics

are subject to non-linearity which could be due to sudden internal and or external change of condition

and disturbances [1]. Automatic control operation is to ensure that certain system parameters; such as

system temperature, pressure, voltage and speed (as in our case) follow the preset control laws applied

in the design and to bring these parameters to certain pre-defined values (set-points) and to maintain

them against any possible disturbing influence [1], [2], [3]. Different control technique can be adopted

for a close loop control system it can be modern or classical control technique and in any case requires

a form of sensor and feedback path. The accuracy and efficiency of the control action of the entire

system rest on the feedback path and the implicit functions of its individual subsystem. Different control

techniques and research works are been developed and used in the control of a conventional DC motor

based on the configuration of its fields and armature windings as to separately-excited DC motor. Some

of these techniques includes those of [4], [5], [6], [7], [8] and numerous others who presented and

proposed a speed controller for DC motor by a way of comparing classical control “PI” and modern

control “Sliding Mode control” strategies and drawing conclusion on the optimal control strategy. Also

considering the works of [9], [10] and others who carried out analysis on estimating the speed of a DC

motor and presented the possibility of controlling a DC motor speed explicitly sensor-less. In both cases:

with sensor and sensor-less the output variable is measured or estimated so the efficiency and critical

analysis of the measuring unit or sensor control still remain important.

1.1 DC Motor Model

DC motor speed control and it transient response in industrial applications has made it relevant

despite its size to power ratio and the dominance of the induction motor. And it control system

development is an interesting area to explore [6]. The system used in this paper is a fixed voltage field

T

mailto:[email protected]

Ignatius I. Uzoeto et al. / Vol. 10(35), Jan. 2020, PP. 4471-4482

4472

International Journal of Mechatronics, Electrical and Computer Technology (IJMEC)

Universal Scientific Organization, www.aeuso.org PISSN: 2411-6173, EISSN: 2305-0543

that is armature controlled and operated in the constant flux region. Figure (1) describes both the

electrical and mechanical variables, by applying the subsequent circuit and motion laws we develop

Equations (1), (2) and (3).

Figure 1: DC Motor Equivalent circuit

𝑣𝑎(𝑡) = 𝑅𝑎 ∗ 𝑖𝑎(𝑡) + 𝐿𝑎 ∗𝑑𝑖𝑎

𝑑𝑡+ 𝑒𝑏(𝑡) (1)

𝑒𝑏(𝑡) =𝑃∗𝜙∗𝑍

2𝜋∗ 𝜔𝑚(𝑡) = 𝑘𝑏 ∗ 𝜔𝑚(𝑡) (2)

𝑇𝑚(𝑡) = 𝑘𝑏 ∗ 𝑖𝑎(𝑡) = 𝐽𝑚 ∗𝑑𝜔𝑚

𝑑𝑡+ 𝑏𝑚 ∗ 𝜔𝑚(𝑡) (3)

Where;

𝑣𝑎 and 𝑖𝑎 = Armature voltage and Current

𝑅𝑎and 𝐿𝑎 =Armature Resistance and Inductance

While

𝑣𝑓 , 𝑖𝑓 , 𝑅𝑓 and 𝐿𝑓 = Are the field equivalent

𝑒𝑏 , 𝑇𝑚 and 𝜔𝑚 = The back EMF, motor torque and speed respectively

𝐽𝑚 and 𝑏𝑚 = Inertia and damping coefficient

Applying the Laplace transform we get the transfer function of the above equation that relates the motor

speed to the armature voltage considering load torque 𝑇𝐿 as zero and as input;

𝐺Ω(𝑠) =Ω(𝑠)

𝑉(𝑠)|

𝑇𝑙(𝑠)=0=

𝐾𝑚

(𝐿𝑎𝑠+𝑅𝑎)(𝐽𝑚𝑠+𝐵𝑚)+𝐾𝑚2 (4)

𝐺L(𝑠) =Ω(𝑠)

𝑇𝐿|

𝑉(𝑠)=0= −

𝐿𝑎𝑠+𝑅𝑎

(𝐿𝑎𝑠+𝑅𝑎)(𝐽𝑚𝑠+𝐵𝑚)+𝐾𝑚2 (5)

And the state space representation is

= 𝐴𝑥 + 𝐵𝑢 = [−

𝑏𝑚

𝐽𝑚

𝐾𝑚

𝐽𝑚

−𝐾𝑚

𝐿𝑎−

𝑅𝑎

𝐿𝑎

] 𝑥 + [−

1

𝐽𝑚0

01

𝐿𝑎

] 𝑢 (6)

+

−

𝑉𝑓

𝑇𝑚, 𝜔𝑚

𝑏𝑚 𝐽𝑚 𝐸𝑏

𝐿𝑎

𝐿𝑓

𝑅𝑓 𝑖𝑓

𝑅𝑎 𝑖𝑎

𝑉𝑎

+

−

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𝑥 Is a two dimensional vector 𝑥 = [𝑥1 𝑥2]𝑇 where 𝑥1 and 𝑥2 are angular velocity of the shaft and

armature current respectively represents differentials of 𝑥. 𝑢 = [𝑇𝐿 𝑉𝑎]𝑇

1.2 Closed-loop path

An optical interrupter sensor senses the speed of the DC motor, thereby generating a pulse train

of high and zero amplitude when light is blanked and allowed to pass through the patterned disc. This

light and dark interval of the slot sensor gives a pulse signal with a frequency proportional to motor

speed, the frequency of this waveform is given by [11]

𝑓𝑚 =𝑁∗𝑟𝑝𝑚

60 (7)

Where;

𝑓𝑚 = Frequency of the output waveform

𝑟𝑝𝑚 = Speed in revolution per minute

𝑁 = Number of white or black strips on the disc

The frequency is then converted to a voltage signal and sent to a comparator with control set-point to

produce an error signal for the system compensator.

1.3 Dc drive

With the advent of DC-DC chopper variable speed of DC motors became a reality. Choppers are

static switch used to convert fixed DC to variable DC [12]. There are five types of this DC choppers

[12]. The proposed project implementation is done with the four quadrant chopper type. The chopper

utilizes the full bridge H switch topology. The four quadrant operation enables us to drive the DC motor

in all four quadrant of motor drive of forward, reverse, forward-braking and reverse-braking operation.

Figure 2 gives a description of the chopper.

Figure 2: Full bridge four quadrant chopper

2 Design outline and procedure

The design was implemented in as different modules to simplify circuit design, building and

assembling as shown in Figure 3.

−

𝑇1

𝑇3 𝑇4

𝑇2 𝐷2

𝐷4 𝐷3

𝐷1

+ 𝑉𝑎 C + −

𝑉𝑜

𝑖𝑎

𝑖𝑜

𝐸𝑏 + −



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Figure 3: Proposed system Block Diagram

The source voltage to the system is certainly of the DC nature, of which can be sourced directly from

a DC source or from a rectified and filtered AC source of which the latter is in our case.

The feedback path consist of an Opto-interrupter which is a non-contact sensor for detecting the

rotational speed/frequency of the motor, a patterned disk for interrupting the light wave of the sensor, a

signal conditioner which converts this train of pulses. The sensor consist of an optical emitter of an

infrared LED, and an optical detector which is an infrared phototransistor.

In the design of the four quadrant chopper the pulse width modulation (PWM) technique is employed

for the periodic switching of the chopper switch pair (𝑇1, 𝑇4) and (𝑇2, 𝑇3). This logic control consist of a

triangular wave circuit a comparator and a dc reference signal input from the feedback controller (be it

PI or Sliding Mode Control).

3 Design implementation

The design implementation is according to that of Figure 4, this paper focuses on the feedback path

and as that the circuits of the PWM and controller (PI and SMC) and the control analysis on equations

(4), (5) and (6) is not elaborated here in this paper.

Figure 4: Circuit Module diagram of the closed-loop system

The output of the opto-interrupter is a binary high or low based on whether light from the emitter is

received by the detector.

𝑉𝑟𝑒𝑓

𝑉𝑠

DC-DC Converter

Signal

Conditioner

𝑉𝑚

Feedback and PWM

controller

Optical sensor

𝑓𝑚 𝑓𝑠

PWM Signal Frequency proportional

to shaft speed Voltage corresponding

speed

Equally spaced Disk

𝜔𝑚

DC Motor

Controller circuit. Comparator

−

𝑇1

𝑇3 𝑇4

𝑇2 𝐷2

𝐷4 𝐷3

𝐷1 +

𝑉𝑎 𝑉0 M 𝐿𝑜𝑎𝑑

Opto-interrupter

circuit F-V converter

𝜔∗ 𝜔

PWM control logic circuitry.

𝑇1 𝑇2 𝑇3 𝑇4

𝑉𝑓

𝐿𝑓𝑖𝑙𝑡𝑒𝑟

+

−

𝑖𝑎

𝑖𝑓



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Figure 5: Opto-interrupter module and circuit

A H42B6 model opto-interrupter. The 4.7KΩ act as a pull-up resistor for the output transistor

designed based on the electro-optical characteristics. The basic circuit requires a limiting resistor R, with

the information from the data sheet [13]. With respect to voltage drop on the LED 𝑉𝑓𝑖, feed current 𝑖𝑓𝑖

and the module bias Voltage 𝑉𝑐𝑐, R becomes

𝑅 =𝑉𝑐𝑐−𝑉𝑓𝑖

𝑖𝑓𝑖=

5𝑉−1.2𝑉

20𝑚𝐴= 190Ω ≈ 220Ω (8)

Other resistors are selected according to the bias voltage between the base and emitter of the

transistor Q which act as an amplifier of the signal of the phototransistor. The speed sensed is a pulse

train of a square wave form, the duty-cycle is constant but the frequency varies linearly with respect to

the motor’s rotation.

Figure 6: Opto-interrupter signal pulse train

The patterned disk is the direct contact to the motor armature shaft, its design is such that it

bears a pattern of light and dark sides configured and spaced from each other at a particular angle; for

this design 7.50 was used. These pattern of sides, cuts the signal transfer of the opto-interrupter to create

pulses of frequency as expressed in equation (7).

+5𝑣 𝑉𝑐𝑐

Output

Ground

𝑅

4.7𝑘Ω

200Ω

10𝑘Ω

𝑄



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Figure 7: Patterned Disk

A frequency to voltage (F/V) converter come in as a signal conditioner which convert’s the

frequency to voltage that is then sent to the controller. An LM331 IC is used to achieve this goal. Supply

voltage, ground, timing resistor and current set resistors are all connected as in Figure 8

Figure 8: F/V Converter circuit [14]

As expressed in [14], we can relate the functions of the individual components

For our construction the maximum frequency of operation as measured with the help of the patterned

disk which makes a total of 24 ON pulse and 24 OFF pulse, we get using equation 7.

𝑓𝑚 =24 𝑝𝑢𝑙𝑠𝑒

𝑟𝑒𝑣×

3000 𝑟𝑒𝑣

𝑚𝑖𝑛×

1 𝑚𝑖𝑛

60 𝑠 = 1200𝐻𝑧

The output of the converter can be manipulated from equation (9)

𝑉𝑂𝑢𝑡 = 𝐹𝐼𝑁 × (𝑅𝐿

𝑅𝑠⁄ ) × (1.9𝑣) × (1.1𝑅𝑡𝐶𝑡) (9)

𝑅𝐿 Is the filter/load resistor and 𝑅𝑠 is the current-set resistor. Component selection as 𝑅𝐿 = 100𝑘Ω

and 𝑅𝑠 = 12𝑘Ω with a 5𝑘Ω potentiometer. 𝑅𝑡 Is the timing resistor while 𝐶𝑡 the timing capacitor

picked as 68𝑘Ω and 0.01𝜇𝐹 respectively for a 10𝑉 full-scale output.

The rotating disk, opto-sensor and the F-V converter make up the transducer circuitry. The

dynamic performance specification as regards the accuracy, repeatability, linearity, resolution as well

as the response rate of the transducer is compiled as related to each components in the circuitry. The

opto-interrupter’s rise and fall time is 15 μseconds, which determines how fast it responds it’s a change

in its input. For our module apply equation (10)

𝑓 =1

𝑇=

1

15×10−6 = 66.66𝐾𝐻𝑧 (10)

From equation 11 it can be seen that the frequency range of the module convers the maximum

speed capability of the patterned disk. The patterned disk is divided as much as possible so as to ensure

better accuracy transmitted to the opto-interrupter and also to reduce sluggish response of the module.

1uF

+12𝑉𝑐𝑐

10kΩ

18kΩ 100kΩ

0.01uF

68kΩ

LM331

8 7 5

6

3

1

4 2

470pF

68kΩ 10kΩ

Frequency

signal Voltage

output



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Just as the module handles response, the disk handles the resolution of the transducer while the F-V

converter handles the repeatability, accuracy and linearity of the sensor

Figure 9: Signal output as seen in pin 6

4 Hardware and result 4.1 Setup

A laboratory prototype test bench was developed and built as shown in Figure 10 with a 250W 63-111 model Feedback DC machine. The operation of the control method has been found to be 95% stable.

It is designed with four IRFP460 MOSFETS mounted on heat sinks with each switch having a 0.1μF 600V capacitor and 5W, 5.6Ω resistor connect as a snubber to protect the switches. The AC voltage through a Variac is rectified and filtered using a 10A full bridge rectifier and two 470μF/450V capacitors. And the switching pulses are generated from analog ICs using TL084 op-amp IC to generate the triangular wave whose frequency we fixed at 3𝐾𝐻𝑧 and compared with a DC value from the controller and thus

Spiked Signal

Figure 10: Experimental setup

PSU

Patterned Disk Feedback Path

Logic circuit

Rectifier and Filter

Oscilloscope

DC motor

H-Bridge

Varactor



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produce the triggering pulses passed through a dead-band circuit and switch drivers. The system was tested and measured with a Tektronix TBS1052B digital Oscilloscope.

4.2 Experimental Result

Figure 11 and 12 shows the pulse signal as interpreted from the patterned disk at various speed levels particularly at high and low speed and the corresponding changes in amplitude of the voltage input to the controller.

Figure 11: Frequency scope at High speed and voltage scope at high speed

Figure 12: Frequency scope at Low speed and voltage scope at Low speed

V=10.6V F=1198Hz

F=120.7Hz V=1.20V



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Figure 13 – 15 shows the Triangular wave, the DC reference signal, the PWM waveform and the firing

signal across the bridge.

Figure 13: DC signal and Triangular wave signal

Figure 14: Pulse Width Modulated Signal

Figure 15: Gating Signals for switches T1 and T3

𝑇1

𝑇3

Triangular wave DC Reference signal



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Figure 16: Firing Signal across the H-Bridge

Table 1 is used to show the test for accuracy of the F/V converter.

Table 1: F/V converter test of Accuracy

Frequency (Hz) True Output

Calculated

(V)

Actual Voltage

Measured

(V)

Error (V) % FSO

0 0 0.008 -0.008 -0.067

120.8 1.21 1.2 0.01 0.0833

279.3 2.79 2.8 -0.01 -0.083

483 4.83 5.0 -0.17 -1.42

606.8 6.07 6.4 -0.33 -3.75

735 7.35 7.8 -0.45 -2.75

935 9.35 9.4 -0.05 -0.42

1197 11.97 10.6 1.37 11.42

Figure 17: Graph output voltage against input frequency



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Equation 11 [14] is used to form the last column of table 1 𝑉𝑓𝑢𝑙𝑙 𝑠𝑐𝑎𝑙𝑒 = 12𝑣 and 𝐼𝑛𝑝𝑢𝑡𝑓𝑢𝑙𝑙𝑠𝑐𝑎𝑙𝑒 =

1.2𝑘𝐻𝑧. The accuracy is gotten as a percentage of full scale output (FSO) and the largest deviation

recorded is 11.42% which place the efficiency of the converter at about 90%

𝑉𝑡𝑟𝑢𝑒 =𝑉𝑓𝑢𝑙𝑙 𝑠𝑐𝑎𝑙𝑒

𝑖𝑛𝑝𝑢𝑡𝑓𝑢𝑙𝑙𝑠𝑐𝑎𝑙𝑒× 𝑖𝑛𝑝𝑢𝑡 (11)

The transducers efficiency with little approximation could thus be calculated as.

𝜂𝑇𝑟𝑎𝑛𝑠𝑑𝑢𝑐𝑒𝑟 = 𝜂𝑑𝑖𝑠𝑘 × 𝜂𝑜𝑝𝑡𝑜 × 𝜂𝑓−𝑣 (12)

𝜂𝑇𝑟𝑎𝑛𝑠𝑑𝑢𝑐𝑒𝑟 = 0.98 × 0.98 × 0.90

𝜂𝑇𝑟𝑎𝑛𝑠𝑑𝑢𝑐𝑒𝑟 = 0.864 ≈ 86%

The gain 𝐾𝑠𝑔 of the feedback path can be represented as the accuracy of the transducer as shown in

Figure 18

Figure 18: Feedback gain of the Close-loop system

Conclusion

In this work, an approach is used to develop a closed-loop system control for a DC motor to obtain

optimum feedback path control. The suggested method basically uses a patterned-disk optical F/V

feedback sensor system which helps effectively to close the system loop. With the results obtained the

accurate record of the speed is converted with little or no loss in the entire feedback system

configuration.

Reference

[1] M. Schlelcher and F. Blasinger, Control Engineering : A guide for Beginners, Fulda Germany: Jumo GmbH and Co.

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[2] F. Golnaraghi and B. C. Kuo, Automatic Control Systems 9th Edition, New Jersey USA: John Wiley and Sons, Inc.,

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[3] R. S. Burns, Advanced Control Engineering, Jordan Hill, Oxford: Butterworth-Heinemann, 2001.

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[8] T. Hanamoto, Y. Tenaka, T. Mochizuki Z. Xu and T. Ogawa, "Speed Control Method of DC Motor Drive System with

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a four quadrant dc motor closed-loop speed control based on a … · 2019-07-13 · control...

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