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Introduction to Control Systems

Laboratory Experiment Manual

Version 1.2.6

March 2013

Copyright © 2013 Kylowave Inc.

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Copyright © 2013 Kylowave Inc. May not be reproduced without permission from Kylowave Inc.

February 2013, Version 1.2.6 of 31

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Table of Contents

1 Introduction ......................................................................................................................................................................... 6

2 Experiment 1: Introduction to digital control systems ........................................................................................................ 7

2.1 Purpose and Goals ........................................................................................................................................................ 7

2.2 Apparatus required ................................................................................................................................................... 7

2.3 Pre-lab Assignment .................................................................................................................................................. 8

2.4 Procedure ................................................................................................................................................................. 8

2.5 Study Questions ..................................................................................................................................................... 11

3 Experiment 2: Identification of a DC motor system ......................................................................................................... 12

3.1 Purpose and Goals ...................................................................................................................................................... 12

3.2 Apparatus required ................................................................................................................................................. 13

3.3 Pre-lab Assignment ................................................................................................................................................ 13

3.4 Procedure ............................................................................................................................................................... 14

3.5 Study Questions ..................................................................................................................................................... 17

4 Experiment 3: Speed Control of DC motor ...................................................................................................................... 18




4.4 Procedure ............................................................................................................................................................... 20

4.5 Study Questions ..................................................................................................................................................... 22

5 Experiment 4: Position Control of DC motor.................................................................................................................... 23






5.4 Procedure ............................................................................................................................................................... 23

5.5 Study Questions ..................................................................................................................................................... 23

6 Experiment 5: Full State Feedback Control of DC motor ................................................................................................ 24




6.4 Procedure ............................................................................................................................................................... 24

6.5 Study Questions ..................................................................................................................................................... 24

7 APPENDIX 1: PIN Descriptions........................................................................................................................................ 25

7.1 Single-phase and three-phase rectifiers ................................................................................................................. 25

7.2 DCDC Converter ..................................................................................................................................................... 25

7.3 Digital control interface ........................................................................................................................................... 26

7.4 Three-phase inverter .............................................................................................................................................. 27

7.5 Current sensors ...................................................................................................................................................... 27

7.6 Analog sensors ....................................................................................................................................................... 27

8 APPENDIX 2: Additional readings .................................................................................................................................... 28

9 APPENDIX 3: Contact Kylowave ..................................................................................................................................... 29



Revision History

Date Version Description Contributor 03/01/2013 1.0.0 Original Document



1 Introduction

The experiments proposed in this Laboratory Manual are realized using Kylowave K-ECS (Universal

Energy Conversion System) model AM256. K-ECS AM256 includes an Arduino Mega 2560 controller. This

manual includes five experiments that introduce the students to the Arduino Integrated Development

Environment (Arduino IDE), the basic topologies of digital control systems and the principles used to design

these systems.

The experiments are introduced in a progressively increasing order of complexity and such that the

following experiment builds on the knowledge gained during the previous one. Upon completing all the

experiments, the student will understand the differences between each topology, will have learned how to

design and implement controllers using those topologies, and will have developed the knowhow to best

assess the more appropriated technique as a function of the characteristics of the process to be controlled.

For advanced students, the laboratory instructor may choose to propose the use of more advanced control

algorithms such as μ-control, H∞, adaptive control, etc. Therefore, the same training platform can be used

by beginners as well as last year students or even graduate level ones. Throughout the manual, students

will learn all the steps involved in the development flow of modern digital controller, some of the most

important metrics related to the proper functioning of those circuits, and how to use a microcontroller to

implement the required functions.



2 Experiment 1: Introduction to digital control systems

2.1 Purpose and Goals

Digital controllers are found in practically all aspects of modern life such as CD/DVD audio systems, battery

charging systems, automobile assembling robots, hybrid electric vehicles and remotely-operated surgical

medical devices to just name a few. The wide spread of digital controllers compared to the analog

controllers (also called continuous-time controllers) used in the past is due to their improved sensitivity to

signal noise, lower dependency to physical variables (power supply voltage, operating temperature,

manufacturing process, etc.), higher flexibility to be reconfigured and reasonably lower cost. These benefits

come at the expense of relatively lower closed-loop bandwidth compared to the analog controllers.

Figure 2.1 shows the high level architecture of a digital control system. The main objective of this

experiment is to introduce the student to the sampled-data sub-systems available in the K-ECS and explain

how to: i) use them to acquire data from various types of sensors; ii) and show how to use the existing

PWM modulators and low-pass filters to implement DACs which can be used as interface to actuators.

Specifically, the objective of this experiment is to:

Familiarize the student with the Kylowave K-ECS (“Energy Conversion System”), the Arduino and

its free IDE (“Integrated Development Environment”)

Demonstrate techniques to read and generate analog and digital I/Os using the Arduino IDE

libraries.

Introduce the PWM (“Pulse Width Modulation”) technique as a mean to generate analog signals to

control external actuators. Introduce the Arduino bit-banging PWM technique and understand its

advantages and limitations.

Introduce the Kylowave library and understand its performance compared to the standard Arduino

IDE library.

Demonstrate techniques to read and generate analog and digital I/Os using the Kylowave library.

2.2 Apparatus required

K-ECS, Oscilloscope, Multimeter, potentiometer, resistor, and a LED.



Analog to Digital

Converter

Microprocessor

Digital to Analog

Converter

CorrectionElement

Process

Sampling TimeClock

Generation

Feedback Sensor System

D D AA

A: Analog

D: Digital

DC-DC

ConverterDC Motor

Optical Encoder

Figure 2.1: Digital control system general architecture

2.3 Pre-lab Assignment

In this Pre-lab the student is required to learn about Arduino.

The student can find very useful information at the Arduino official webpage at www.arduino.cc.

Specifically, the student should study the Blink and the ReadAnalogVoltage examples in the Arduino

Tutorial Webpage (http://arduino.cc/en/Tutorial/HomePage). In addition, get familiarized with the Arduino

programming language at its reference website (http://arduino.cc/en/Reference/HomePage).

Before start working on this experiment pre-lab assignment, we suggest you should study the following

Arduino functions (http://arduino.cc/en/Reference/HomePage): setup(), loop(), pinMode(), digitalWrite(),

digitalRead(), analogRead(), map(), delay() and delayMicroseconds().

For each Arduino sketch example below, look at the respective sketch code available online in the Arduino

webpage and answer the following questions:

1. Blink sketch – This sketch is also available in the Arduino IDE through the following command

sequence: File -> Examples -> 0.1Basics -> Blink. What is the blinking frequency of the original

Blink sketch? How can we make the LED blink at about 10 seconds rate?

2. Fade sketch – This sketch is also available in the Arduino IDE through the following command

sequence: File -> Examples -> 0.1Basics -> Fade. Propose a way to slow down the fading rate to

50% of the original fading rate. Propose a code change to make the maximum LED brightness to

be about 50% of the original maximum brightness.

3. Knob example in the Arduino servo library (File -> Examples - Servo -> Knob). In this example,

explain the maximum possible value that analogRead() can achieve. Explain the purpose of using

the map() function. In the Fade example, if the “val” variable after the map() function assignment is

http://www.arduino.cc/

http://arduino.cc/en/Tutorial/HomePage

http://arduino.cc/en/Reference/HomePage

http://arduino.cc/en/Reference/HomePage



used as the second parameter of analogRead() (instead of brightness), would the LED be able to

achieve its maximum brightness? Explain.

4. Look at steps 6 and 7 of section 2.4 and think how you would realize it. Hint: Consider how the

commands used in the three examples above can help.

5. Complete the four procedure in experiment #1 by writing an Arduino sketch and results.

6. Answer study questions #1 and #2.

Write a pre-lab report (maximum of 3 pages).

2.4 Procedure

The experiment procedure is as follows:

1. Assemble the Analog sensor test circuit as shown in the diagram of Figure 2.3.

2. Set up the potentiometer as shown in Figure 2.3, connect its central connection to K-ECS pin

AnalogIO_0 (ANALOG SENSOR connector, pin #30), and adjust the potentiometer such that the

multimeter reads the following values: 0, 1, 2, 3 and 4. Note: AnalogIO_0 is a 0 to 5V(Max)

analog input pin.

3. Write an Arduino sketch (this is how the Arduino community calls an Arduino program) to read the

voltage value on the K-ECS analog input AnalogIO_0 and print it to the serial monitor. Check that

the printed value matches the value you would expect to see.

4. Using the Arduino map() function, scale the digital value read at step 2 to the range [0, 100] such

that the digital value 0 corresponds to 0V and 100 corresponds to +5 V.

5. Assemble the PWM test circuit as shown in the diagram of Figure 2.4.

6. Using the Arduino PWM bit banging technique, add code to the sketch created in step 3 to

generate a 1 kHz PWM signal on K-ECS pin DacPwm_1 0 (DIGITAL CONTROL connector, pin

#29). The PWM modulation index should be the digital value produced at step 4. Write your code

to ensure that the PWM carrier frequency does not change with changes of the modulation index.

7. For each voltage in step 2, read the PWM signal duty cycle using the oscilloscope. Then, build a

table showing the voltage measured by the Multimeter, duty cycle, the digital number read from pin

#30 (step 3) and the digital number resulting form the map() function (step 4).



2

1

DIGITAL CONTROL

3 5 7

4 6 8 24

23 25 27 29

26 28 30

DG

ND

+5

V

SP

I_S

CL

K

SP

I_S

DO

SP

I_S

S

SP

I_S

DI

PW

MIn

v_

BH

PW

MIn

v_

AH

DA

CP

WM

_0

PW

MIn

v_

BL

PW

MIn

v_A

L

DA

CP

WM

_1

2

1

ANALOG SENSORS

3 5 7

4 6 8 24

23 25 27 29

26 28 30

+3

.3V

DG

ND

AV

DD

AG

ND

+5

V

AG

ND

Res

erv

ed

Sen

sVin

_0

An

alo

gIO

_0

Res

erv

ed

Sen

sVin

_1

An

alo

gIO

_1

Figure 2.2: Lateral View of K-ECS DIGITAL CONTROL and ANALOG SENSORS 30-pin connectors

AVDD

AnalogIO_0

AGND

4704K7

VDC

GND

AN

AL

OG

SE

NS

OR

S

29

28

30

27

26 25

6 5

4 3

2 1

0 – 5V

WARNING: pins #2 and #6 MUST

be connected at all times

5V

Multimeter

Figure 2.3: Analog sensor test circuit



DACPWM_1

DGND

470

DIG

ITA

L C

ON

TR

OL

2

3

1

4

5 6

25 26

27 28

29 30

0 – 5V

LED

Oscilloscope

Figure 2.4: PWM test circuit

2.5 Study Questions

1. Consider the table built in section 2.4. Explain any differences between digital values measured

from pin #30 AnalogIO_0 and the expected values calculated from the DC values measured by the

Multimeter. What is the average ratio value between the number returned by

analogRead(AnalogIO_0) and the respective value measured by the multimeter? Hint: This is the

Arduino A/D converter scaling gain.

2. What is the number of bits and maximum values of the Arduino A/D converter? What value would

have to be applied at pin AnalogIO_0 in order to obtain the maximum value for the Arduino A/D

converter?

3. What is the maximum PWM carrier frequency that the Arduino can achieve when using the bit

banging technique? Hint: change the code written in section 2.4 step 6 to experimentally determine

the maximum value.

4. What happens to the LED of Figure 2.4 when the potentiometer is used to change the voltage

value on pin 30: AnalogIO_0? Explain the observed behavior.



3 Experiment 2: Identification of a DC motor system


Identification is defined as the process of determining the transfer function of a system G(s) from a

collection of measured data where neither the form nor the parameters of G(s) are known. If the form of the

transfer function is already known, then problem of identifying the parameters of G(s) is called parameter

identification. In general, model identification is a much more complex problem than parameter estimation.

Especially, if there is noise in the sampled data set.

The objective of this experiment is to identify the parameters of a DC motor of Figure 3.1 including the

motor itself, a load on its shaft and possibly gears. In this experiment, we will identify the parameters of a

first-order and a second-order model. The first-order model is suitable for armature control of DC motors.

The second-order model is normally used for torque and speed control of DC motors.

The objective of the identification experiment is to:

Introduce the DC motor first-order and second-order models.

Introduce the concept of parameter estimation and obtain the first-order model of a DC motor.

Validate the models through Matlab/Simulink simulations against the measured data set.

Introduce MegunoLink as an open source visualization tool:

http://www.blueleafsoftware.com/Resources/EmbeddedSand/MegunoLink.

Load

Va

Ra La

VbT

q

Armature Circuit

VfIa

IfRf

Lf

Field Circuit

VD

C

GN

D

Optical

Encoder

Figure 3.1: DC Motor Electrical Circuit

http://www.blueleafsoftware.com/Resources/EmbeddedSand/MegunoLink




Matlab/Simulink, K-ECS, Oscilloscope, Multimeter and a DC motor kit with load (and possibly gears).


In general and as shown in figure 3.2, the first two steps in the development of a motor control system

consists in identifying the motor parameters, build an equivalent model and simulate it to ensure the model

and identified parameters fit the expected physical results. In this Pre-lab the student is required to do a

theoretical analysis of the DC motor shown in Figure 3.1.

IdentificationModeling

&Simulation

DesignSimulation

&Validation

ImplementationPrototype

Testing

Figure 3.2: DC Motor Controller Development Flow

Let Ra and La be the armature resistance and inductance, J be the total moment of inertia (load, shaft, the

rotor of the motor, etc.), f be the total viscous friction coefficient (bearing and shaft), Kt is the torque

constant such that T(t) = Kt . ia(t), and Kb is the back electromagnetic force such that vb(t) = Kb . d(t)/dt,

then the angular speed transfer function of the armature controlled DC motor is shown in Figure 3.3 and is

mathematically given by:

In many practical applications, the armature inductance is much smaller than the armature resistance.

Thus, we can approximate the previous second-order transfer function by the first-order transfer function

below:

Where

,

and



Kt

Ra + s La

TVa

1

s J + f

1

s

Kb

w=dq/dtq

Second

Order

Km

1 + s tmVa

1

s

w=dq/dtq

First

Order

Figure 3.3: DC Motor Models

Considering the DC motor model of figure 3.1 and the motor parameters previously defined in this section,

answer the following questions:

1. Starting from the DC motor electrical and mechanical equations, derive a continuous-time second

order model for the motor.

2. Assuming the time constant of the motor electrical subsystem (given by Ra and La) is much

smaller than the time constant of the motor mechanical subsystem (given by J and f), derive an

approximated first-order model.

3. Considering the experiment should use a symmetrical PWM controlled Buck DC-DC converter,

explain the need for non overlapping time zone (also called dead zone) in a symmetrical PWM

signal.

4. Explain the difference between a step-down Buck DC-DC converter and a half-bridge DC-DC

converter.

5. Write an Arduino sketch to generate a symmetrical PWM signal on K-ECS DC-DC converter

control signals (PWMDCC_H and PWMDCC_L). The PWM carrier frequency should be set to 2

kHz and the non overlapping to about 10 microseconds (5 microseconds on each edge of the

PWM signal).

Write a pre-lab report (maximum of 5 pages).

3.4 Procedure

Consider the DC motor of Figure 3.1. The procedure below will show how to determine the parameters of

the transfer function of the first-order model. As shown in figure 3.4, the basic idea is to use a V(in) DC

voltage power supply and a PWM controlled Buck DC-DC converter to generate an output V(ou) DC

voltage that is proportional to the PWM duty cycle and the DC voltage source such that: V(out) = D x V(in),



where D in the PWM duty cycle. Because the duty cycle can theoretically vary between 0.0 and 1.0 (0 to

100%), the output voltage can be adjusted to almost any value between 0 and V(in).

K-ECS includes a DC-DC converter module can be configured to implement various DC-DC converter

topologies. The connection mapping of table 3.1 shows how to configure it to implement the step-down

converter shown in figure 3.4. This converter can be operated in step-down Buck mode by driving logic “0”

to DIGITAL CONTROL pin PwmDCC_L and driving a PWM signal to PwmDCC_H. The converter can also

be operated in half-bridge mode by simultaneously driving a symmetrical PWM signal to pins PwmDCC_H

and PwmDCC_L.

The input power (positive of the DC power supply V(in)) should be connected to pin DCDC_In. The scaled

output voltage V(out) (V(out) = D x V(in)) comes out on pin DCDC_Out. DGND is the common ground and

should be connected to the negative terminal of the DC power supply and the DCDC_Ref pin.

Configuration Pins I/O Pins

DCDC_S1 DCDC_In

DCDC_S2 DCDC_Ref

DCDC_S3 DCDC_Out

Table 3.1: K-ECS DC-DC Converter Buck Connection Mapping

Load

Tq

Optical

Encoder

PWMDCC_H

PWMDCC_L

V(in)

DGND

DCDC_Out

DCDC_InStep-Down DC-DC Converter

DCDC_Ref

Figure 3.4: DC Motor Controlled by a Half Bridge DC-DC Converter



The experiment procedure is as follows:

1. Talk to your TA to obtain the motor kit specification and fill up table 3.2.

2. Assemble the test circuit as shown in the diagram of Figure 3.5. WARNING: connect the system

ground to just ONE point and connect the single point ground to DGND pin of the DCDC

CONVERTER connector as shown in figure 3.4. This centralized ground connection is a best

practice that should be adopted in all power electrics applications. It prevents creating circulating

currents that can flow through ground loops which can couple noise to various parts of the circuit

and in many cases can prevent the circuit to work or even worse permanently damage the circuit

and the equipment involved. NOTE: The power supply should be set to a voltage level smaller than

or equal to the motor maximum terminal voltage (ask your TA for the voltage level to be used).

3. Write a sketch to drive a symmetrical PWM signal to K-ECS DC-DC converter pins PWMDCC_L

and PWMDCC_H (DIGITAL CONTROL connector, pins #21 and #22) to operate K-ECS DC-DC

converter in half-bridge mode.

4. Add code to the previous sketch to measure the motor shaft angular speed in rad/s. Note: See

appendix 8.

5. Choose a reasonable duty cycle to apply a voltage of known magnitude Va and measure the final

shaft speed and the time from applying the voltage up to 50% of the final shaft speed.. Suggestion:

choose duty cycle such that the average voltage Va is about 50% of the motor nominal speed. Set

up the duty cycle such that the average voltage Va is 25% and 75% of the motor nominal voltage,

and redo the measurements.

6. Develop the expression for the gain constant of the first-order model as a function of the final shaft

speed and the armature voltage Va. Using this expression, calculate the estimated value of the

gain constant.

7. Develop the expression for the first-order time constant as a function of the final shaft speed, the

shaft speed at time t0 (In our case, the time measured in step 3) and time t0 itself. Using this

expression, calculate the estimated value of the first-order time constant.

8. Using the parameters identified in step 7, build a Matlab/Simulink model, apply a step input to the

model and record the simulated output speed. Simulate the model to the following scenarios: Va

values of step 5. Note: the step input signal should have a value equal to the averaged Va signal

value.

Parameter Specification Unit

Nominal Voltage V

Nominal Current A

Gear Rateio

Nominal Speed Rad/s

Maximum SPeed Rad/s

Table 3.2: DC Motor Kit Specification



3-PHASE RECTIFIER

1 2 3 4 5 6

DCDC CONVERTER

1 2 3 4 5 6

DC

DC

_S1

DC

DC

_In

Optical

Encoder

Tq

DC Power Supply

DC Motor

Note: The voltage of the DC power

supply should be set to a voltage level

smaller than or equal to the motor

maximum terminal voltage

To PWMDCC_H

Current

Measurement

DC

DC

_S2

DC

DC

_Ou

t

DC

DC

_Ref

DG

ND

DC

DC

_S3

Ground

Input

Output

+

-

DIGITAL CONTROL

1 2

21 22

29 30

PWMDCC_HPWMDCC_L

19 20 DIGITAL_0DIGITAL_1To DIGITAL_0

Figure 3.5: DC Motor Parameter Estimation Test Circuit

3.5 Study Questions

1. If the moment of inertia of the load and the viscous friction coefficient were doubled, what would be

the new transfer function? Do the time and gain constants equal half of those of the first transfer

function?

2. Write the first-order transfer function from the applied voltage Va(t) to the angular displacement

(t)? What is its unit-step response? What is (∞)? What does it mean physically?

3. Compare the measured results of steps 4 and 5 to simulated results of step 8. Explain any

differences.

4. Explain the coupling mechanism responsible for the ground loop circulating current effect. In power

electronics applications, which parasitic effects contribute the most to increase its effects? Parasitic

resistance, capacitance, or inductance? Explain.



4 Experiment 3: Speed Control of DC motor


Some of the objectives of feedback control is to reduce the effect of disturbances on a system, make the

system more insensitive to parameter variations and create a well defined input-output relationship.

Nevertheless, careful design of the feedback controller is required as the feedback can unintentionally

make a stable open-loop system to become unstable in closed-loop operation.

Initially, most feedback controllers were implemented using analog electronics such operation amplifiers.

Presently, the vast majority of feedback controllers are implemented using a digital processor

(microcontroller, DSP, FPGA, etc.). Analog controllers are used almost exclusively in applications that

require a high closed-loop bandwidth that can not attained by digital controllers. During the last three

decades, many different topologies of feedback controllers have been developed, but the popular PI

(Proportional-Integral) and PID (Proportional-Integral-Derivative) structures are still used in most industrial

applications. This is due to the of their analysis and design process, reduced resource utilization, and

reasonable performance to many important industrial applications. In general, PID controllers produce

higher performance than PI controller. However, the additional derivative action makes the controller more

sensitive to noise or fast transients in the feedback control loop. Usually, PI controllers are used on speed

control applications because of the potential noisy signal related to the motor shaft speed measurement.

The integral relationship between the position and the speed of the motor shaft causes the position sensor

signal to be much smoother than the speed measurement signal. Thus, PID controllers are often used for

position control systems.

The objective of this experiment is to develop a digital feedback PI controller for the DC motor of Figure 3.1.

The student will design a PI (Proportinal-Integral) controller to regulate the speed of the group motor-gear-

disc. During the experiment, the student will:

Design a PI controller to meet the given specification.

Simulate the system dynamics (PI controller and DC motor group).

Investigate the effect of integral windup in the system performance.

Implement the PI controller in an Arduino to control the actual system

IdentificationModeling

&Simulation

DesignSimulation

&Validation

ImplementationPrototype

Testing

Figure 4.1: DC Motor Controller Development Flow




Matlab/Simulink, K-ECS, Oscilloscope, Multimeter and a DC motor kit with load (and possibly gears).


In this Pre-lab the student is required to do a theoretical analysis of the speed controller of Figure 4.2. The

plant is the DC motor shown in Figure 3.1 and identified in the previous section. The student is required to

design the controller “by hand”. You must use a simulation tool such as Matlab/Simulink to interactively

tune the parameters Kp and Ki to achieve the requirements of table 4.1.

Use Figure 3.3b to create a first-order DC motor model in Matlab/Simulink, and use the Km and values

identified in the previous experiment. Using the diagram of Figure 4.2, design a continuous-time PI

controller to meet the specification of Table 4.1. Afterwards, discretize the continuous-time PI controller to

produce a discrete-time controller that meets all the requirements of Table 4.1, implement it in

Matlab/Simulink using the discrete-time transfer function block. Re-simulate the speed control system with

discrete-time controller and compare the results against the continuous-time controller. Hint: Look for the

attachInterrupt() function in the Arduino webpage and understand how it works. Consider using this

interrupt mechanism to implement an accurate sampling time step for the PI controller control loop.

w=dq/dtq

Km

1 + s tm

1

sKi

s

Kp

wrefVcontVerr

Kv

1 + s tv

Low-Pass Filter

DC Motor Model

PI Controller+

+

+

-

Vcont= (Kp + Ki/s) * Verr

Figure 4.2: DC Motor Speed Controller



Parameter Specification

Overshoot Minimal overshoot of 5% or less

Rise Time Rise time greater than 2s but less than 2.5s.

Settling Time Settling time greater than 4s but less than 4.5s.

Reference Signal The reference signal should be a square wave with amplitude 50 RPM and 100 RPM. And a period of 10 seconds. This will

Saturation Saturate the PI controller output with a Simulink saturation block so that the PWM duty cycle stays in the 20% to 80% range.

Discretization Method

Backward Euler

Sampling Frequency

To be chosen by the student such that the difference between the continuous-time and discrete-time closed loop overshoot is less than 1% (it must be bigger than 100 Hz).

Table 4.1: Requirements of the DC Motor Speed Controller

4.4 Procedure

Consider the DC motor group of Figure 3.1 and the speed controller of Figure 4.2. The speed controller

design process can be summarized as follows:

Design a continuous-time controller using one of the design techniques such as ad-hoc, optimal

controller, robust controller, full state and full observer, etc. We suggest you should use the

interactive ad-hoc tuning method. Start with a large value for Kp that do not cause the system to

become unstable. Then, increase the Ki gain to reduce the overshoot. Iterate tuning the Kp and Ki

gains until you meet all the requirements. Quiz: reference 8.7 (available online at

http://eprints.gla.ac.uk/3817/1/IEEE3.pdf), explain the independent effect of each PID gain in the

controller closed loop response.

Add sampled-data system elements such as analog to digital converters (SFCs), digital to analog

converters (DACs), pulse width modulators (PWMs), antialiasing filter, etc.

Choose an appropriated sample period. As a rule of thumb, the sampling period should be at least

10 times the closed loop frequency such that Ts = 1 / (10 * fB), where Ts is the smapling period and

fB is the closed-loop frequency (fB = B / (2 * π), B is the closed loop bandwidth).

Digitize the continuous-time control law using an appropriated discretization rule such as: backward

Euler, Tustin, fisrt-order hold, second-order hold, zero-pole placement, etc.

Verify the digital controller performance using discrete-time model simulation (ex.: Matlab/Simulink)

If the performance does not meet the requirements, fine tune the digital controller as necessary,

until the requirements are met.

http://eprints.gla.ac.uk/3817/1/IEEE3.pdf



The procedure below will show how to design, implement and test a PI controller to implement a DC motor

speed control system.

1. Assemble the test circuit as shown in the diagram of Figure 4.3

2. Choose the number of bits and appropriate sampling frequency to implement your controller.

Notice that the Arduino is a 8-bit microcontroller running at a master clock frequency of 16 MHz.

3. Discretize your PI controller using the Backward Euler discretization rule and the chosen sampling

frequency. Quantize the PI controller constants to minimize the additional error introduced by

quantization compared to the continuous-time controller.

4. Write an Arduino sketch to implement the PI controller. We suggest that you try to complete the

sketch before your lab period so that you will have more time to test the PI controller on the actual

motor.

Read the angular speed reference value.

Read the optical encoder position on the DIGITAL CONTROL pin #8 and calculate the

estimated shaft angular speed. Attach an interrupt to this pin such that the code does not

need to consume CPU time to monitor the pin.

Filter out the calculated speed using a low-pass digital filter and write the filtered value to

DACPWM_1 pin.

In the code, create a loop that steps the shaft speed from 50 RPM to 100 RPM and back,

within a period of 10s.

Use the filtered speed value to calculate the error signal to be used by the PI controller.

Calculate the control signal value and use it to drive the DC-DC PWM control inputs.

Measure the control effort. Send the duty cycle value between the PI controller output and

the DC-DC converter control signal to DACPWM_0 and observe the signal coming out at

DacFlt_0.

Sample the estimated raw speed, the filtered speed and the control signal at the output of

the PI controller. Store these values in an internal memory array.

5. After the controller is correctly working, store the DC motor speed response in open-loop and in

closed-loop for the following scenarios: i) speed step signal applied to the reference input; ii) motor

shaft is running at steady state speed than it is locked; iii) motor shaft is released.

6. Send the stored values to MegunoLink to be plotted. Report the measured results in your Lab

report.

7. Compare the steady state and transient responses for the open-loop and closed-loop test

scenarios.



3-PHASE RECTIFIER

1 2 3 4 5 6

DCDC CONVERTER

1 2 3 4 5 6

DG

ND

DC

DC

_RefD

CD

C_S

1

DC

DC

_In

DC

DC

_S2

DC

DC

_S3

DC

DC

_Ou

t

AGND (6)

Optical Encoder

DIGITAL CONTROL

(MAX: 5.5V)

2

3

1

4

5 6

25 26

27 28

29 30

Tq

DacFlt_0 (10)

DCDC_In (28)

ANALOG SENSORS

29

28

30

27

26 25

6 5

4 3

2 1

(27) DCDC_Out

(30) Control SignalEstimated Speed (29)

(9) DacFlt_1(8) Optical Encoder

Figure 4.3: DC Motor Speed Controller Test Circuit

4.5 Study Questions

1. Using the data acquired during the experiment, plot the data acquired in section 4.4 item ___.

Upload the data to Matlab and compare it against the simulated results.

2. Explain the problem caused by the optical encoder rollover. How can it be corrected?

3. Explain the issue of integral windup. How can it be solved?

4. Explain the advantages and inefficiencies of a purely proportional or purely integral digital controller

5. Explain the methodology used to choose the sampling frequency. What would happen if the

sampling frequency was five times smaller or five times bigger than the chosen value?

6. BONUS question 1: Additional bonus points will be granted to implementations that avoid complex

mathematical operations such as floating point, multiplication, division, etc. These operation cause

the controller algorithm to run at a much smaller sampling frequency.

7. BONUS question 2: Keeping the same integral gain and DC motor group, what is the maximum

proportional gain where the closed-loop system is still marginally stable?



5 Experiment 4: Position Control of DC motor


NOTE: ask to design a PID to control the DC motor. Ask to compare the results with the Ziegler-Nichols

and the Robust design method proposed in the Lecture 8 and Lecture 6 (Optimum Control).

.

The objective of the ________ experiment is to:

.


.


Using integration in the Laplace domain, derive the transfer function for motor position from the

velocity transfer function obtained in Experiments 2 and 4.

.

Verify the design with the instructor, then:

1. .

5.4 Procedure

1. .

5.5 Study Questions

1.



6 Experiment 5: Full State Feedback Control of DC motor


NOTE: use full state feedback in series with full state observer. Compare results with experiment 4. Use

method presented in Lecture 6.

.

The objective of the _________ experiment is to:

.


.


.

1.

.

Verify the design with the instructor, then:

1. .

6.4 Procedure

.

1. .

6.5 Study Questions

1.



7 APPENDIX 1: PIN Descriptions

7.1 Single-phase and three-phase rectifiers

K-ECS External Connector

PIN K-ECS Signal Detailed Description

1-PHASE RECTIFIER connector

1-Phase Rectifier 1 Rect1Ph Single-phase rectifier input AC phase voltage

1-Phase Rectifier 2 RectRef1Ph Single-phase rectifier input AC reference voltage

1-Phase Rectifier 3 DC1Ph+ Single-phase rectifier positive output DC voltage

1-Phase Rectifier 4 DC1Ph- Single-phase rectifier negative output DC voltage

1-Phase Rectifier 5 DC3Ph+ Three-phase rectifier positive output DC voltage

1-Phase Rectifier 6 DC3Ph- Three-phase rectifier input output DC voltage


3-Phase Rectifier 1 Rect3Ph_A Three-phase rectifier phase A input AC voltage

3-Phase Rectifier 2 Rect3Ph_B Three-phase rectifier phase B input AC voltage

3-Phase Rectifier 3 Rect3Ph_C Three-phase rectifier phase C input AC voltage

3-Phase Rectifier 4 RectRef3Ph Three-phase rectifier input AC reference voltage

3-Phase Rectifier 5 DCDC_S4 DC-DC converter 5: DCDC_S4 signal


7.2 DCDC Converter






DCDC CONVERTER connector

DC-DC Converter 1 DCDC_S1 DC-DC converter 2: DCDC_S1 signal

DC-DC Converter 2 DCDC_S2 DC-DC converter 2: DCDC_S2 signal

DC-DC Converter 3 DCDC_In DC-DC converter positive output DC voltage

DC-DC Converter 4 DCDC_Out DC-DC converter negative output DC voltage

DC-DC Converter 5 DCDC_Ref DC-DC converter reference voltage

DC-DC Converter 6 DGND Power ground and Digital Ground



7.3 Digital control interface



DIGITAL CONTROL connector

Digital Control 1 DGND Digital Ground

Digital Control 2 +5V +5V DC Power Supply

Digital Control 3 SPI_SS General Purpose Digital Signals + 3: SPI_SS (Slave Select) – used by Ethernet card

Digital Control 4 SPI_SCLK General Purpose Digital Signals + 4: SPI_SCLK (Serial Clock) – used by Ethernet card

Digital Control 5 SPI_SDI General Purpose Digital Signals + 5: SPI_SDI (Master Out Slave In) – used by Ethernet card

Digital Control 6 SPI_SDO General Purpose Digital Signals + 6: SPI_SDO (Master In Slave Out) – used by Ethernet card

Digital Control 7 Reserved not connected

Digital Control 8 Reserved not connected

Digital Control 9 Digital_11

Digital Control 10 Digital_10

Digital Control 11 Digital_9 General purpose I/O digital signal










Digital Control 21 PWMDCC_L DC-DC converter PWM input high

Digital Control 22 PWMDCC_H DC-DC converter PWM input low

Digital Control 23 PWMInv_CL Three-phase inverter phase C PWM input high

Digital Control 24 PWMInv_CH Three-phase inverter phase C PWM input low

Digital Control 25 PWMInv_BL Three-phase inverter phase B PWM input high

Digital Control 26 PWMInv_BH Three-phase inverter phase B PWM input low

Digital Control 27 PWMInv_AL Three-phase inverter phase A PWM input high

Digital Control 28 PWMInv_AH Three-phase inverter phase A PWM input low

Digital Control 29 DACPWM_1 PWM input to a second order Sallen-Key low pass filter with output at 10: DACFlt_0 of analog connector

Digital Control 30 DACPWM_0 PWM input to a second order Sallen-Key low pass filter with output at 9: DACFlt_1 of analog connector



7.4 Three-phase inverter



3-PHASE INVERTER connector

3-Phase Inverter 6 DGND Digital Ground

3-Phase Inverter 5 Inv3Ph_DC- DC power supply negative voltage terminal

3-Phase Inverter 4 Inv3Ph_DC+ DC power supply positive voltage terminal

3-Phase Inverter 3 Inv3Ph_C Phase C AC signal

3-Phase Inverter 2 Inv3Ph_B Phase B AC signal

3-Phase Inverter 1 Inv3Ph_A Phase A AC signal

7.5 Current sensors



CURRENT SENSORS connector

Current Sensors 6 Inp0+ General purpose current sensor #0 input current

Current Sensors 5 Inp0- General purpose current sensor #0 output current

Current Sensors 4 Inp1+ General purpose current sensor #1 input current

Current Sensors 3 Inp1- General purpose current sensor #1 output current

Current Sensors 2 Reserved not connected

Current Sensors 1 VSupply Main DC power supply from power connector

7.6 Analog sensors



ANALOG SENSORS

Analog Sensors 30 AnalogIO_0 General Purpose analog input to Arduino (0 to 5V)

Analog Sensors 29 AnalogIO_1 General Purpose analog input to Arduino (0 to 5V)

Analog Sensors 28 SensVIn_0 General purpose analog input to the voltage sensor (0 to 48V)

Analog Sensors 27 SensVIn_1 General purpose analog input to the voltage sensor (0 to 48V)

Analog Sensors 26 Reserved not connected







ANALOG SENSORS


Analog Sensors 22 SensVOut_C Analog output from three-phase inverter phase C voltage sensor (22: SensVOut_C = 3: Inv3Ph_C / 10)

Analog Sensors 21 SensVOut_D Analog output from three-phase inverter phase D voltage sensor (21: SensVOut_D = 4: Inv3Ph_DC+/ 10)

Analog Sensors 20 SensVOut_A Analog output from three-phase inverter phase A voltage sensor (20: SensVOut_A = 1: Inv3Ph_A / 10)

Analog Sensors 19 SensVOut_B Analog output from three-phase inverter phase B voltage sensor (19: SensVOut_B= 2: Inv3Ph_B / 10)

Analog Sensors 18 SensVOut_GP0 Analog output from the general purpose voltage sensor (18: SensVOut_GP0 = 28: SensVIn_0 / 10)

Analog Sensors 17 SensVOut_GP1 Analog output from the general purpose voltage sensor (SenseV1 = 27: SensVIn_1 / 10)

Analog Sensors 16 SensIOut_C Analog output from three-phase inverter phase C current sensor (16: SensIOut_C = 1.65V + 0.175 * IPhaseC) (3)

Analog Sensors 15 SensIOut_D Analog output from three-phase inverter phase D current sensor (15: SensIOut_D = 1.65V + 0.175 * Isupply)

Analog Sensors 14 SensIOut_A Analog output from three-phase inverter phase A current sensor (14: SensIOut_A = 1.65V + 0.175 * IPhaseA) (3)

Analog Sensors 13 SensIOut_B Analog output from three-phase inverter phase B current sensor (13: SensIOut_B = 1.65V + 0.175 * IPhaseB) (3)

Analog Sensors 12 SensIOut_GP0 Analog output from the general purpose current sensor (12: SensIOut_GP0 = 1.65V + 0.175 * 6: Inp0+)

Analog Sensors 11 SensIOut_GP1 Analog output from the general purpose current sensor (11: SensIOut_GP1 = 1.65V + 0.175 *4: Inp1+)

Analog Sensors 10 DACFlt_0 Analog output of the second order Sallen-Key filter 30: DACPWM_0

Analog Sensors 9 DACFlt_1 Analog output of the second order Sallen-Key filter 29: DACPWM1

Analog Sensors 8 Reserved spacing

Analog Sensors 7 Reserved spacing

Analog Sensors 6 AGND Analog ground

Analog Sensors 5 AGND Analog ground

Analog Sensors 4 AVDD Analog VDD (can be set up to +5V or +3.3V)

Analog Sensors 3 +5V +5V DC Power Supply

Analog Sensors 2 DGND Digital Ground

Analog Sensors 1 +3.3 V +3.3V DC power supply



8 APPENDIX 2: Useful Formulae

8.1 Position and Speed Conversion Formulae

(8.1)

(8.2)

(8.3)

8.2 Position and Speed Calculation Formulae

The optical disk shown in the figure can be used to convert the circular

motion into a sequence of digital pulses that can be processed by a digital

controller. Digital pulses are produced every time a radial line in each

track interrupts the beam between a photo emitter-detector pair. By

counting these pulses the information can be converted to a relative or

absolute angular position or angular speed.

Consider an optical disk with N radial lines. The angular displacement of each radial line can be calculated

by equation (8.4). If the digital controller counts n pulses, than the motor shaft connected to the optical

encoder disk would have turned an angular distance given by equation (8.5).

(8.4)

(8.5)

As shown in equation (8.6), the angular speed can be measure by counting the number of pulses p

produced by the optical encoder, multiplying this number by the angular displacement of one radial line

and dividing by the time in seconds passed between the first and last pulses ( . This

method is easier to implement and can produce very accurate measurements if the number of pulses is

large enough. However, in case the motor shaft is turning at low speed it may take a long period of time to

measure the angular speed. The uncertainty in one measurement is given by ξ(%) = 100 / p, where p is the

number of pulses.



(8.6)

Another method that produces faster measurements (generally at the expense of lower accuracy) consists

in using a high frequency clock f(clk) and counting the number of this high frequency pulses P between the

beginning and the end of one optical encoder pulse (or a few pulses). The angular speed can be calculated

by equation (8.7). Note that the uncertainty now depends on the frequency of the fast clock signal and the

ability to synchronize the measurements to the edge of the optical encoder pulses.

(8.7)

9 APPENDIX 3: Additional readings

1. Nise, Norman S., Control Systems Engineering, 6th Edition, Wiley & Sons, 2011.

2. Dorf, Richard C. and Bishop, Robert H., Modern Control Systems, 11th Edition, Prentice Hall, 2008.

3. Chen, Chi-Tsong, Analog and Digital Control System Design: Transfer-function, State-Space and

Algebraic Methods, Oxford University Press, 2006.

4. Franklin, Gene F., Powell, J. David and Emami-Naeni, Abbas, Feedback Control of Dynamic

Systems, 6th Edition, Prentice Hall, 2009.

5. Batarseh, Issa, Power Electronic Circuits, 2004.

6. Kazimierczuck, Marian K., Pulse-Width Modulated DC-DC Power Rashid, Muhammad H., Power

Electronics: Circuits, Devices and Applications, 3rd ed., 2004.

7. Ang, K. H. and Chong, G. and Li, Y., “PID Control System Analysis, Design, and Technology,”

IEEE Trans. On Control Systems, Vol. 13, No. 4, July 2005.

10 APPENDIX 4: Contact Kylowave

Kylowave Inc (613) 454-1437 www.kylowave.com K-ECS Technical Support

http://www.kylowave.com/



[email protected]

K-ECS Order Information

[email protected]

mailto:[email protected]

mailto:[email protected]

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