Computer Engineering and Mechatronics

Computer Engineering and Mechatronics

 

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IAJ Laboratory exercise 2 Computer Eng & Mechatronics
Rev E 1 27 October 2020
Department of Mechanical, Materials and Manufacturing Engineering
Computer Engineering and Mechatronics MMME3085
Laboratory Exercise 2: Motion Control (preparatory
work)
1 Objectives
The objectives of this exercise are:
• To give some practical experience of how servomotors are used in closed
loop mode in order to achieve accurate motion control
• To give experience of using objects in the form of Arduino libraries
• To give experience of how ramping of step rates can be achieved without
the use of division.
2 The control loop in the context of a servo mechanism
Fundamental to the operation of a servomotor is the concept of closed loop
control – this was covered mathematically in an elementary manner in MM2DYN
(MMME2046), and forms the basis of more advanced study in MM3CAI
(MMME3063).
In brief, the control loop when applied to a servomotor consists of the following:
• Decide on a position we want the motion control system to move to
• Measure the current position
• Compare the position we want with the current position (to give error)
• Decide upon corrective action to bring system closer to its desired position
(this decision process is known as the control algorithm)
• Take the corrective action
This can be represented diagrammatically as follows:
IAJ Laboratory exercise 2 Computer Eng & Mechatronics
Rev E 2 27 October 2020
Within your preparatory work you will be going from “open loop control” (where
you vary the motor signal directly, with no attempt at controlling position) to
“closed loop control”, where you will implement an extremely simple control
algorithm (proportional control) and incorporate a VI implementing a more
sophisticated (PID) algorithm.
You will also be examining the software used to control a stepper motor – unlike
a servo motor, a stepper motor normally operates in open-loop mode as no
feedback is required to achieve a given position.
3 A hint of C++: classes and objects to implement libraries
The programming language taught by Louise Brown in the software engineering
part of the module is ISO C, sometimes known informally as “pure C” to
distinguish it from an enhanced version of C known as C++. The main
difference between the languages is that C++ is designed to be used for objectoriented programming, in which data and functions are no longer separate
concepts but are combined in the form of “objects”, which are instances of userdefined variable types known as classes. A class is essentially a struct with
member functions as well as member data. For instance, the encoder sketch
you used in Lab 1 uses the SPI class. This ad-hoc use of classes in what is
essentially a C program structure is a characteristic of “the Arduino way of
programming” and is not generally regarded as good practice, not least because
pure C simply does not allow this. By contrast, C++ programs are often written
using classes and objects throughout, following an approach known as “object
oriented programming” which is not covered in this module.
4 Preparatory work
This involves creating two separate Arduino sketches which implement
closed loop control: one involves a “home-made” proportional-only control
algorithm; the other makes use of a ready-written “PID” (proportional-integralderivative) library object. You are strongly advised to make an early start
on the preparatory work so you do not run out of time to ask for help if
required
4.1 Exercise 1: Closing the Loop: Proportional Control
1. Download a slightly modified version of the open loop PWM and position
sensing project which you used in Lab 1, now called
MotorControlSkeleton2.ino: this may be downloaded from Moodle in the
Lab and Programming Exercises section. In brief, this drives the motor with
a PWM signal of varying duty cycle and of positive or negative polarity – the
present version differs very slightly from the version used in Lab 1 in that the
state machine and internal counter code has been stripped out and some
variables renamed. If you have an Arduino Mega, try compiling and running
the example, but remember to set the Serial Monitor to 9600 baud rate and
to send “Both NL & CR” on pressing return. If you type a number
IAJ Laboratory exercise 2 Computer Eng & Mechatronics
Rev E 3 27 October 2020
representing the percentage PWM value, you should see the LED glow
brightly or dimly accordingly.
2. You will notice how the printing takes place within a timed loop which cycles
every 1000 milliseconds, and calls the function printLoop(). Just as you did
within the introductory “blink without delay” exercise, create another timed
loop and loop function, called the control loop, with a period of 20 ms. We
suggest you name this function controlLoop().
3. Create a global variable to store the measured position from the encoder.
4. Within this loop, obtain the value of measured position from the encoder (as
counted using the LS7366R counter) just as is done in the print loop, but
store it in the global variable you have just created.
5. Create a global constant called Kp representing the proportional gain, and
initialise it to a value of 0.02.
6. At this stage, check that your sketch compiles correctly and correct any
problems making use of any compile error message. If you have an Arduino
Mega you should still be able to observe how the LED changes in intensity as
you change the entered value between -100 and 100.
7. Now change the way the program behaves as follows. Create a new global
floating-point variable called positionSetPoint and arrange so that this
variable, instead of the variable percentDutyCycle, is set by the user input
from the serial monitor.
8. Within your control loop function, implement the proportional closed loop
control algorithm shown in the diagram below by setting the value of
percentDutyCycle to the proportional gain multiplied by the value of error
(the difference between the position set point and the position measured by
the encoder; make sure you get the difference the right way around as
shown in the diagram).
.
9. Within the control loop function, remember to call the function to update the
motor speed with the updated value of percentDutyCycle.
10.Enhance the contents of printLoop() to print out the setpoint and the error
(which you will need to calculate here again) as well as the measured
position.
11.Try compiling your code; ensure there are no errors. If there are, look at the
error messages and make the necessary connections. If you don’t know
IAJ Laboratory exercise 2 Computer Eng & Mechatronics
Rev E 4 27 October 2020
what’s wrong, please ask for help (so leave enough time for sorting out
problems!).
12.Save your sketch as ProportionalClosedLoopXXX.ino.
13.Save an additional copy of your sketch and call it PIDClosedLoopXXX.ino
ready for the next exercise (so you don’t overwrite your
ProportionalCloseLoopXXX.ino sketch and end up without that work!).
4.2 Exercise 2: Closing the Loop: Proportional-Integral-Derivative
(PID) Control
1. From the Arduino menu bar, look in the Sketch | Include Library submenu to see if the PID library is installed (if it is, it will be in the bottom
section of the sub-menu). If it isn’t, look at the top of the sub-menu for
Library Manager and click on it to start it. You can then search for PID, but
be careful to highlight PID by Brett Beauregard not any of the other PID
libraries (there are several) or the following instructions won’t be applicable.
Install the V1.2 of the PID library.
2. From the Arduino menu bar, load the example sketch from Examples | PID
| Basic (you may need to scroll down to near the bottom of the Examples
sub-menu) and examine the example closely. You will see that:
a. The definition of the PID class is contained within the file PID_v1.h
which is included in the sketch via the directive #include<PID_v1.h>
b. Global variables for the values of proportional, integral and derivative
gain Kp, Ki and Kd are defined and initialised.
c. A global object called myPID, of class PID, is declared, linking the
object to the measured value named here as the input, the control
action named here as the output, and the setpoint. Note that these
values are all passed by address so the PID object has the ability to
change their values. The variables Kp, Ki and Kd are also linked to the
object here. The value DIRECT is not important; it defines that the
positive directions for input and output are the same.
IAJ Laboratory exercise 2 Computer Eng & Mechatronics
Rev E 5 27 October 2020
d. In the function setup() the Setpoint variable is initialised, also the
value of Input is initialised by reading the value of from an analogue
input pin, and the PID controller is made active (set to automatic
control). Two other aspects also need to be set: the PWM duty cycle
can be set from −100% (implying the motor in reverse) to +100%, and
the PID controller needs to be informed of the actual control loop
interval, so you will actually need to include the following three lines of
code within setup(), noting that the percentage limits are (or should
be) already set as constants in your program:
myPID.SetOutputLimits(minPercent, maxPercent);
myPID.SetSampleTime(controlInterval);
myPID.SetMode(AUTOMATIC);
e. Now everything is set up for the PID controller to control the output by
taking decisions on what the input is doing compared with the setpoint.
This takes place in the function loop(), where for each pass through
the loop:
• the value of Input is read from the analogue input
• the PID calculations are calculated by the member function
Compute()
• the value of Output is used to make something happen via an
analogWrite() function call.
3. Now alter your PIDClosedLoopXXX.ino sketch as follows:
• Defining two additional global variables Ki and Kd; at present set these to
zero.
• Define the global PID object so its input is the measured position, the
output is the PWM percentage, and the set point is the position set point
as before.
• Initialise the set point to zero in setup()
• Remember to make the PID controller active. Two other aspects also need
to be set: the PWM duty cycle can be set from −100% (implying the motor
in reverse) to +100%, and the PID controller needs to be informed of the
actual control loop interval, so you will actually need to include the
following three lines of code within setup()noting that the percentage
limits are (or should be) already set as constants in your program:
myPID.SetOutputLimits(minPercent, maxPercent);
myPID.SetSampleTime(controlInterval);
myPID.SetMode(AUTOMATIC);
• Replace the proportional action in the control loop with the PID action in
the same way as in the PID example.
IAJ Laboratory exercise 2 Computer Eng & Mechatronics
Rev E 6 27 October 2020
4. Save PIDClosedLoopXXX.ino and try compiling. If there are problems,
please seek help, allowing enough time to do so.
4.3 One step at a time
4.3.1 Overview of stepper motors and ramping
Part of the laboratory exercise involves controlling a stepper motor. These
devices are motors which operate under (usually) open-loop control and
produce a fixed angle of rotation for each increment (step) of their
movement. The basics of stepper motors were covered in Electromechancial
Devices and should be revised before the laboratory.
In the present case, the stepper motor controller is a combination of a timer
and various input-output lines rather than a separate device. Stepper
motors are driven by circuitry (translator and driver –covered in the
Electronics in Mechanical Engineering laboratory as an example of digital
logic) which normally take in signals on two lines:
• Step signal: each complete pulse on the step line corresponds to a
single increment of angular rotation
• Direction signal: if the signal is TRUE, the step takes place in one
direction e.g. clockwise, if it is FALSE, the step is in the opposite
direction
In practice it is usual to make a movement by ramping up the motor from a
low speed (which may be zero) up to full running speed and back towards
rest via a “profile” of uniform acceleration, constant speed and uniform
deceleration. This smooth profile is needed so that there are no sudden
changes in speed or very rapid accelerations or decelerations, in order to
avoid “desynchronising” the rotor of the motor from the magnetic field which
is stepping around the stator.
This profile involves generating trains of pulses which are initially widely
spaced in time, then gradually become more closely spaced as the motor is
IAJ Laboratory exercise 2 Computer Eng & Mechatronics
Rev E 7 27 October 2020
accelerated, and eventually become more widely spaced again and cease
altogether as the motor slows down to a halt.
The generation of these pulses under computer control is simple in principle
but in practice is non-trivial, not least because it is desirable to avoid
computationally intensive calculations (such as division operations and
mathematical functions) which will take longer to complete that the time
available for each step. Some ingenious approaches are therefore used to
perform the calculations using only addition and multiplication operations,
for example by making a Taylor series expansion of the “difficult” functions.
The pulses are typically timed using an interrupt service routine which is
repeatedly called at intervals determined by a timer counter. For simplicity
however simple timed loops are used for the initial version of the sketch. It
could be naively assumed that incrementally changing the timer counter
intervals (so that the ramp down linearly from long intervals to short
intervals and back up again) would provide the required acceleration and
deceleration profile, and your starting point is a sketch which implements
this. However, as you will see, this results in a poor profile, which starts very
slowly then builds up to an unrealistically large acceleration as the desired
speed is approached.
The approach you will use is the “Leib Ramp Algorithm” as presented by
Eiderman1, one of several approximate methods available for performing a
good approximation to the desired uniform acceleration/deceleration profile.
4.3.2 Existing program – a simplistic approach that nearly works
The scenario for your exercise is that an Arduino sketch has been written by
a competent programmer to implement a ramping profile. Let’s assume that
the writer had a basic understanding of stepper motors but assumed that the
generation of a ramping profile is a trivial exercise (which of course it isn’t)
1 Aryeh Eiderman, “Real Time Stepper Motor Linear Ramping Just by Addition and Multiplication”.
http://hwml.com/LeibRamp.pdf
IAJ Laboratory exercise 2 Computer Eng & Mechatronics
Rev E 8 27 October 2020
and has implemented a ramping profile which works, but not very
effectively.
The starting point for your sketch is SimplisticRampStepper.ino which you
can download from Moodle; however, as debugging an Arduino program is
difficult, you will develop your code first within a specially-provided C test
program which also acts as a simulation of the real sketch behaviour.
(Health warning: so that the functions in the C program are largely the same
as those in the Arduino sketch, the C program uses several global variables.
Don’t do this in other C programs!) Before starting work on the updated
algorithm first take a look at the SimplisticRampStepper.c program. As
set up, this uses a timed loop (like the one in the “Blink Without Delay”
example, but working in microseconds not milliseconds) to time the steps.
However, the code includes some “hidden” options for using interrupts – you
may safely ignore these for the present time, but don’t be confused by (or
try to delete) lines such #ifdef HARDWARETIMING as you will use these in the
lab.
Firstly, try running SimplisticRampStepper.c and see that it displays (in real
time) a table simulating the individual steps, the time relative to starting for
each step, the speed and acceleration at each step, the duration of each step
etc. You can specify a position (in steps, relative to the initial starting
position) for the motor to move to, so you can see the effects of running the
motor short distances involving only acceleration and deceleration, or longer
distances involving a period of running at constant speed.
At this, run the program for the case of starting at position 0 and running to
position 50. Use the default values of minimum and maximum speed and
maximum acceleration (1 step/s, 20 steps/s and 10 steps/s2 respectively).
Cut and paste the text from the command prompt window into a text file
(call it “SimplisticProfile.csv”) and import it into Excel. Plot a graph of
velocity vs. time and save your Excel file as “SimplisticProfile.xlsx”. It is
desirable for the velocity profile to involve constant acceleration and
deceleration and (if required) a period of constant velocity. Is this achieved?
If not, how badly does it deviate from the ideal?
The current version of the program (and Arduino sketch) uses a crude and
simplistic ramping algorithm which increments or decrements the loop
interval by a fixed value calculated as:
p p max min
p
S
 = (1)
where S is the number of steps over which acceleration takes place, so that
for each step the new step interval pnew is given in terms of the previous step
interval pold as follows:
new old new old
new old
(during acceleration), (during deceleration),
(during constant speed phase)
p p p p p p
p p
= −  = + 
=
(2)
IAJ Laboratory exercise 2 Computer Eng & Mechatronics
Rev E 9 27 October 2020
Note that in the code the new value of p simply overwrites the old one –
there is no need for two separate variables.
4.3.3 Replacing the simplistic approach with one that works much better
Now use the LeibRampSkeleton.c program to develop the new algorithm.
This is very similar to the SimplisticRampStepper.c program but has the
simple algorithm stripped out and comments to indicate where the changes
outlined below should be inserted.
The minimum stepping speed of the motor, the maximum permissible speed
maxPermisSpeed and the acceleration maxAccel are already defined as global
constants so you don’t need to redefine these. The number of steps for the
acceleration phase accelSteps is also specified; this is no longer going to be
constant so is not defined as a constant.
The number of steps still to move Stg is obtained from the function
getStepsToGo() and we will call the initial value of this distance Stot.
However, to replace the simplistic approach above with the approach
described by Eiderman you will need to make some changes. Note that all
your arithmetic, constants and variables must be floating point, and only at
the final point of use (when it is used for timing the loop or as the register
value for a timer) should your step interval p be converted to a long integer.
Starting with the changes to be made in function main() forming the section
labelled “Pre-computation code” (the comments STEP 1 etc in the skeleton
program correspond to the numbering of the points below):
1. The number of steps S (variable name accelSteps) over which acceleration
is to take place must be calculated: this is calculated from equation 4 in the
paper:
2 2
0
2
v v
S
a

= (3)
where v is initially assumed to be the maximum permissible speed (termed
“slew speed” in the paper), and v0 is the minimum stepping speed.
2. If twice this value of S exceeds the total number of steps to move Stot then:
a) The maximum speed v needs to be re-calculated using the following
equation (a slight variant of equation 5 from the paper, noting that the
total distance Stot is twice the acceleration distance S):
𝑣 = √(𝑣0 2 + 𝑎𝑆𝑡𝑜𝑡) (4)
b) The number of steps for acceleration is now re-calculated as the integer
part of half the value of Stot:
int tot
2
S
S =    
  (5)
(convert to long rather than int to avoid overflow)
IAJ Laboratory exercise 2 Computer Eng & Mechatronics
Rev E 10 27 October 2020
3. After the end of the if-block mentioned above, the initial step interval (in
microseconds) is calculated as p1 from equation 17 in the paper and should
be made a global variable so it can be accessed elsewhere:
1
2 0
2
F
p
v a
=
+
(6)
where F is the number of time measurements or “ticks” per second. In the C
program we will be using milliseconds so F is defined for you as 103; the
Arduino sketch however uses microseconds (when using a timed loop) or
system clock ticks (which occur at 16 MHz, for use with the interrupts and
timer counters) so in those cases F is 106 or 1.6×107 respectively.
4. The minimum step interval ps is given by equation 18 in the paper and is a
global variable so it can be accessed elsewhere:
s
F
p
v
= (7)
5. The constant multiplier R is calculated from equation 19 in the paper:
2
a
R
F
= (8)
All of the above pre-computation tasks involve operations which are
mathematically tedious such as division, calculation of square roots etc., as
well as less onerous tasks such as multiplication and addition. Think why we
are not worried about the time taken by these.
6. It is now time to change the calculations of the step rate at each step within
the section labelled “On-the-fly step calculation code”. The update of the
step interval p for each step (in computeNewSpeed()) can now be changed
from equation (2) above to the “best approximation” theory contained in the
paper:
a) Define a temporary variable m. If in the acceleration phase :
m R = − (9)
Or if the deceleration phase:
m R = (10)
Or if the constant speed phase:
m = 0 (11)
(see definition following equation 20 in the paper; noting that the three
situations are already correctly identified in computeNewSpeed()but
you will need to add your code to them).
b) Define temporary variable q:
q m p p =   old old (12)
(definition following equation 22 in paper; note that pold is simply the
existing value of p in computeNewSpeed())
c) Now update p as follows (equation 22 in paper)
p p q q q oew old = + +   (1 1.5 ) (13)
IAJ Laboratory exercise 2 Computer Eng & Mechatronics
Rev E 11 27 October 2020
Note that this will be represented in your program as a good example
of “replace existing value of p with a new value calculated from old
value of p” – as before, you don’t need separate variables for pold and
pnew, they are the old and new values of p.
d) Finally, if p is greater than p1, set it equal to p1.
7. Save your code as LeibRampStepperXXX.c. Compile your code and check
for issues such as undefined variables.
8. Now try running your program with the same parameters as previously, and
similarly plot the graph of velocity and acceleration vs. time in Excel. You
should find that it gives a reasonable approximation to a linear acceleration
and deceleration profile. As a check, the first four values of step time (p)
should be 218.218, 188.528 and 157.245 ticks (here representing
milliseconds).
9. Once you are happy that your code is working correctly, you should be able
to incorporate your changes into the Arduino sketch LeibRampStepper.ino.
Simply replace the pre-computation section of the Arduino sketch with the
pre-computation section of the C program, and similarly replace the on-thefly calculation section of the Arduino sketch with that from the C program.
Save it as LeibRampStepperXXX.ino then compile and run it.
10.If you run your code on an Arduino Mega, you should see the LED flash at a
steadily increasing speed, then at constant speed, then at steadily reducing
speed. If you are not able to get your code to work, please ask for help (in
good time!). Note that the code will only work on an Arduino Uno if
USEINTERRUPTS is not defined as we use more timers than are available on
the Uno.
11.Finally, it has been noted that the current version of the program only causes
the stepper motor to run in one direction, even though the rest of the
program satisfactorily takes account of the direction of movement of the
motor via the variable direction (which is true, denoted FWDS, for running
forwards and false, denoted BWDS for running backwards). In fact, the
stepper driver module will run the motor forwards when the line connected to
pin dirPin is high, and backwards when it is low. Add two lines of code to
the function moveOneStep() to implement this. (Indeed, you can do it in one
just line of code if you really want!).
12.When you are satisfied that it is correct, save it.
IAJ Laboratory exercise 2 Computer Eng & Mechatronics
Rev E 12 27 October 2020
5 Submission
You will need to submit your preparatory work online. Zip up
ProportionalClosedLoopXXX.ino, PIDClosedLoopXXX.ino and
LeibRampStepperXXX.c and LeibRampStepperXXX.ino along with the
spreadsheet with graphs of step rate vs. time, and submit this to the appropriate
Moodle submission box no later than 18:00 on 12th November 2020.
You will need to bring your programs to the laboratory
L. P. Brown
Revised 27 October 2020
I. A. Jones
5 November 2019

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