DESIGN AND IMPLEMENTATION OF RAPID CONTROL

DESIGN AND IMPLEMENTATION OF RAPID CONTROL
Informacije MIDEM 41(2011)2, Ljubljana
UDK621.3:(53+54+621+66), ISSN0352-9045
DESIGN AND IMPLEMENTATION OF RAPID CONTROL
PROTOTYPING SYSTEM WITH MATLAB/SIMULINK
Nikolaj Semenič1, Andrej Sarjaš2, Rajko Svečko2, Amor Chowdhury1
1
Margento R&D, Maribor, Slovenia
2
FERI, Maribor, Slovenia
Key words: Rapid control prototyping, Real time workshop, DSP, TMS320F28335, Matlab, Simulink, State space control, inverted pendulum
Abstract: This paper presents the development and implementation of a Rapid Control Prototyping (RCP) System. Key features of RCP are working with
simulink block sets, automation of code generation and automatic downloading of executable code to the target DSP. In such manner, control algorithms
can be rapidly integrated or adapted in no time. Simulink integrated with DSP TMS320F28335 provides a useful development tool for design verification
of control algorithms, suitable for different plants. Through the use of RTW (Real Time Workshop) functionality, different modules on custom made DSP
board are developed, which are needed to create an environment that is suitable for processing execution. Software has been developed with the use
of Simulink block sets. Some of them have been provided from TIC2000 library. More complex blocks have been developed with the use of S-functions
and TLC, target language compiler.
Design and realization of regulation algorithms for stabilization of rotary inverted pendulum are presented.
Načrtovanje in implementacija RCP sistema v
okolju Matlab/Simulink
Kjučne besede: RCP, RTW, DSP, TMS320F28335, Matlab, Simulink, Prostor stanj, inverzno nihalo
Izvleček: V delu predstavljamo razvoj in implementacijo sistema, ki omogoča hitro in zanesljivo integracijo in verifikacijo algoritmov vodenja na realnih
objektih. Ena izmed bistvenih prednosti takšnega sistema je, da ga zgradimo s pomočjo blokovnih objektov v Simulinku. Ti pa se samodejno prevedejo
v ustrezno izvršno datoteko, ki se naloži na DSP. V takšnem smislu sistem omogoča enostavnejšo implementacijo algoritmov in hkrati njihovo lažjo prilagodljivost. Z uporabo Simulinkove knjižnice RTW je moč razviti različne module za podporo različnih funkcionalnosti na digitalnem signalem procesorju.
Sistem smo razvili s pomočjo osnovnih blokov, ki jih najdemo v knjižnici TIC2000. Kompleksnejše funkcionalnosti pa smo zagotovili z razvojem lastnih,
naprednejših blokov, s pomočjo izgradnje S-funkcij in z ustrezno korekcijo prevajalnika TLC.
Predstavljamo razvoj algoritmov vodenja za stabilizacijo rotacijskega inverznega nihala.
1.
Introduction
With the fast development of digital signal processors, they
not only became less expensive but also faster and more
complex. Tools for planning and development of embededsystems are developing in a similar fashion as well. Development of embeded systems is such a complex task that it
demands from an engineer a precise knowledge of the DSP
architecture and the periphery, as well as programing tools
for planning of process systems. The knowledge of suitable
program languages is necessary as well. In spite of the fact
that many manufacturers of developing program equipment invest a lot of energy in the development of efficient
compilers, sometimes it is neccessary to use the assambly
language to optimize specific processes in DSP.,. Even
more with the complex systems, the probability of an error
is high, despite the experience and appropriate expertise
of the developer. Thus, an industrial manufacturing leans
towards a smaller number of errors during the production
as well as to decrease the time needed to develop the
product and all the related costs. With that intent, the rapid
control prototyping (RCP) has started to develop. In that
way, various algorithms can be tested in real time on real
plants through use of the circuit boards, which have been
especially developed for that purpose. That way, there is
122
no need to develop any hardware parts and it is not necessary for the designer to deal with possible mistakes that
would come along. It would be logical that the developer
focuses only on the development of algorithms. A way
of programing is set in a way of blocks that assemble in
complex block models. A way of rapid prototying is offered
through the MathWorks’ Matlab or Simulink. With the built
in real time workshop (RTW) library or precisely TIC2000,
Simulink offers the possibility to develop the embeded
block model system along with blocks that are offered by
other libraries. Through RTW mechanism Simulink block
model is converted to the project in the DSP software
developing environment Code Composer Studio (CCS),
in a form of files (.c and .h), it generates an executable file
(.out) and loads it onto the DSP. TIC2000 library enables
the development of the Texas instruments’ DSPs from
C2000 family. The RTW offers support for custum circuit
boards as well.It si also posible to implement circuit board
with DSPs which are not found in the library. Although this
procedure is a bit more complex.
In previous work, with the use of Simulink, the researchers
have been involved with rapid prototyping in the control
systems. Some of them have only used the basic blocks,
which are found in the TIC2000 library /1-5/. In part /6/,
N. Semenič, A. Sarjaš, R. Svečko, A. Chowdhury:
Design and Implementation of Rapid Control Prototyping System ...
the development of custom Simulink blocks is discussed
with S-functions in the sense of adding the functionality in
a form of a C language program . In such form there is not
possible to add additional assebly commands or to support
additional hardware moduls. Some of them broadened a
basic block recruitment with the development of additional,
more complex hardware moduls. In this case, a more efficient custom circuit board is used which has been created
independently /7,8/.
Development of rapid prototyping sytem using Simulink
environment and a custom circuit board based on floating
point DSP TMS320F28335 is presented in this work, . To
take into account that we have not used any of the expected
circuit boards from the TIC2000 library, but developed it independently, it has also been necessary to develop specific
blocks that have been more complex than the basic ones.
The more complex modules or drivers have been developed
through use of S-functions and the TLC (Target Language
Compiler). Our rapid prototyping system is more usable
since it has, in comparison to the circuit boards from the
TIC2000 library, some extended hardware peripherals. The
system is tested with the stabilization of the rotary inverted
pendulum in which we use different control algorithms that
are designed with the help of Matlab functions.
System for rapid prototyping designed with Matlab/Simulink
is Presented in the section two. The third section describes,
in detail, a circuit board and the modules that are necessary
to obtain measured quantities. The fourth section describes
the procedures of implementation of simple and more complex blocks. The fifth section offers a detailed description of
the controled plant or the rotary inverted pendulum and the
measured quantitiy. The base and the working of stabilization system of the rotary inverted pendulum is explained
in the sixth section . In the seventh, design of regulators
is summarized. The resaults wich proove the success of
implementation of the system for rapid prototyping with the
Matlab/Simulink are presented at the end.
2.
Informacije MIDEM 41(2011)2, str. 122-131
relationship to the DSP, however in the case of other two,
the default settings are suitable. /9/
Procedure to the executable file is a complex process
(Figure 2.1). Models in the Simulink scheme are translated
into objects (.rtw). The TLC translates these objectcs into
appropriate files (.c and .h) and while at it, adds the system
files. It can add custom files as well. Template makefile
(.tmf), with the generation of the appropriate Makefile (.mk),
links together a file into the executable file (.out) (Figure
2.2). The system of generating a code into the RTW can
Fig. 2.1: Process of creating a code/9/
Rapid Control Prototyping with
Matlab/Simulink
Simulink, with the RTW tool, and the TIC2000 library, that
offers support to all of the DSPs from the C2000 family,
with the development software Code Composer Studio,
presents a basis of rapid prototyping. Before the Simulink is
capable to translate and load the block model onto the DSP
through the use of the CCS, it is necessary to take care of
the DSP‘s fundamental settings. That is done through the
block F28335 eZdsp from the TIC2000 library. Despite
the fact that our circuit board differs from the expected
F28335 eZdsp board, that is not an obstacle in assuring
the basic functionality of the DSP. This block takes care
for an appropriate setting of the memory map and chooses
desired functionalities at the DSP pins. In the RTW system,
it is also necessary to set a suitable System target file, Make
command and a Template makefile. The first one is set in a
Fig. 2.2: Process of creating an exe file /9/
be adapted with the help of the RTW. With an appropriate
adaptation of the TLC, inlined S-functions can be created.
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Informacije MIDEM 41(2011)2, str. 122-131
N. Semenič, A. Sarjaš, R. Svečko, A. Chowdhury:
Design and Implementation of Rapid Control Prototyping System ...
Through use of TLC and wrapper or inlined S-functions we
can add not only the individual functions in the form of C
code, but also the adaptations in the assembly language
or hardware instructions. /9/ In that way, individual drivers
can be implemented to extend the functionality of the circuit
board in the Simulink.
3.
Hardware architecture and
software implementation
considerations
Circuit board, based on DSP TMS320F28335, was developed with the purpose to establish the system for verification of the control algorithms used in various control plants
(Figure 3.1). Individual modules are enabled and executed
on the DSP, which ensure gathering and processing of the
measured quantities as well as signals for driving actuators.
DSP belongs among a 32-bit microcontrollers intended
for applications in real time. DSP TMS320F28335 has a
capacity to operate with the floating point. A good number
of functionalities are built-in, which can be used in different
applications. /10/
-
Up to 88 multiplex GPIO pins with the input filters
In comparison to the circuit board from the TIC2000 library
eZdsp F28335, our circuit board has a number of important
advantages:
- On the circuit board, there is a 22-bit four channel
external AD converter ADS1213,
- external flash 8Mb, M25PE80,
- external 512 kW RAM ISSI IS61LV51216,
- external EEPROM 128 kb, M95128,
- Converter from RS232 to USB for the communication
with the personal computer.
External AD converter enables a higher quality gathering of
measurements than the built-in one. Difficulties with lackage
of memory are taken over by large external memories such
as RAM, Flash and EEPROM. Because of high capacity
of memory, the circuit board enables development of very
complex systems as well. A similar circuit board is used in
the mobile payment system /14/.
With the help of the block from the TIC2000 library and
an additional block that extends the basic functionality,
a modul for an encoder support was developed on the
circuit board. Custom made blockfor the support of the
external AD converter was developed independently, with
an additional driver and SPI communication-bus.
3.1. Encoder support modul
Fig. 3.1: Custom made circuit board
Characteristics of the DSP are:
- Highly efficient 32-bit CPU (IEEE-754 Single-Precision
Floating-Point Unit (FPU), 16 x 16 Dual MAC)
- Six channel DMA controller (for ADC, SARAM, …)
- 16-bit or 23-bit external memory interface
- Integrated memory (F28335/F28235: 512KB Flash,
68 KB SARAM, 2 KB OTP ROM)
- Pins from GPIO0 to GPIO63 can be connected to one
of the eight external interrapts
- Up to eight PWM outputs
- Three 32-bit CPU Timers
- Serial ports (up to two CAN modules, up to three SCI
(UART) modules, up to two McBSP modules (set as
SPI), one SPI module, one integrated I2C Bus)
- 12-Bit, 16 channels
- Module for an event count and a modul for encoder
support
124
Encoder support module (eQEP) in the DSP is designed
for linear or rotational incremental encoders for measuring
position, direction of rotation, and speed. The counter
clockwise rotation is defined at the time when QEPA signal
outpasses the QEPB signal (Figure 3.2). A frequency of
QEPA and QEPB signals alters in relationship to the speed
of the motor. That way, the speed is calculated with the
QEPA and QEPB event count or by measuring the time
between two events.
Fig. 3.2: Signals scheme from encoder
The speed can be calculated in two different ways:
/9/
(3.1)
/9/
(3.2)
Equation (3.1) represents a number of pulses that are
perceived by the DSP in a defined period of time. DSP can
be set in a way that it counts positive and negative fronts of
the QEPA and QEPB signals. That way twice the amount
of events is obtained in return.
N. Semenič, A. Sarjaš, R. Svečko, A. Chowdhury:
Design and Implementation of Rapid Control Prototyping System ...
A unit period is set to scan time value , in which the DSP
counts the events. A unit period is set in the QUPRD registry
where the end number, up to which the counter reaches, is
written. The amount of one time quantum is inversely proportional with the frequency of the processor core, which
is 150 MHz. Upon the expiration of the time period, the
register position (QPOSLAT) is copied, with the number of
events, which are perceived by the DSP in the period unit.
This type of measuring and calculating the speed is suitable
for higher speeds, since with the large number of counted
events, the counting error is less noticable.
A more suitable way for lower speeds is offered in the equation (3.2). In that case the time between the two events
is measured. Performed path between the two events
presents an inverse of a maximum number of events in one
turn. In that case the error of the time counter is smaller,
the longer is the time duration between two events. The
timer value, which measures the QCTMR time, is saved
into the QCPRD register when the second event occurs.
Encoder support module was executed with the help of
block from the TIC2000 library. Direction of rotation and
values of registers QPOSLAT and QCPRD were chosen
as output values of the module. To that block, one more
was added, which was developed independetly with the
help of S-function. In that module, both algorithms for
speed measuring were executed. Further the system that
increases the robustness of measurings was added. An
algorithm (3.1) is used to measure higher speeds and an
algorithm (3.2) for lower speeds.
A boundary that defines which speed has a lower error is
defined with the calculation of relative speed errors. That
way, there is a relatively low error in wide range of speed
measuring optaned.
Informacije MIDEM 41(2011)2, str. 122-131
External AD converter ADS1213 is located on the circuit
board and is a 22-bit delta sigma AD converter with the 20bit resolution at 10Hz and a 16-bit resolution at sampling
rate of 1kHz. It has four chanels at the input which are, via
multiplexer, connected onto the diferential input. It also
has an integrated amplifier for small signals and it has a
support for SPI or I2C communication. It is connected to
the DSP through the SPI communication bus and it enables
gathering of data with a frequency of up to 6,25 kHz. The
chip has integrated special callibration mechanisms that
offer a precise set up of the measuring range and of the
initial offset. It also has its own built-in micro controller that
manages instructional, command and data registers as well
as two callibration registers. The way something is written
in these registers is through the SPI bus.
One of the main advantages of this converter is the built-in
digital filter. Its function is decimation of the current measurements that are offered by the delta sigma modulator.
A number of resaults that the filter decimates depends on
the decimation ratio that is set in the command registry.
Turbo mode influences the frequency of the modulator.
This means that those two factors indirectly influence the
calculation speed and the delivery of data into the data
register./11/
The speed of output data is determined by the following
relation:
Where:
fpodatki - frequency of output data
fXIN - frequency of the input oscilator is 2 MHz
(3.3)
Because we want an even more precise measurings, that
way we want an even higher decimation ration. That can
be reached with the highest setting of the turbo mode.
It is necessary to enter Turbo Mode, Decimation Ration
and many other parameters in appropriate addreses in the
command registry. The measuring range of the input signl
is from -5 to +5 V, with the selection of inside amplification.
Fig. 3.3: Algorithm errors
As it is seen, (3.2) algorithm has lower error for the speeds
up to 240 turns per minute. For higher speeds (3.1) algorithm is more accurate.
3.2. External AD conversion through the
SPI bus
Conversion from the notebook or an analog world to a discret or digital world is one of the frequent procedures that
are part of the everyday, when it comes to control systems.
The communication between the AD converter and the DSP
was realized through the SPI, serial peripheral interface.
The type of communication is in a form of master to slave,
in which the DSP is the master and the AD converter is a
slave. This means that the AD converter only responses to
a demand of the DSP. Communication is functions in a way
that it is necessary to send the content of the instructional
registry to the AD converter first, with which AD receives
the name of the appropriate registry and the information if
DSP will write out of it or read from it. Since DSP manages
the SPI clock, there is a need to detect when the data is
ready to be received from the AD converter. AD reports
that through an external pin. External pin triggers external
interrupt in which DSP processes received information.
The external AD converter is used because of the higher
quality of measurements in the system. As we have seen,
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Informacije MIDEM 41(2011)2, str. 122-131
N. Semenič, A. Sarjaš, R. Svečko, A. Chowdhury:
Design and Implementation of Rapid Control Prototyping System ...
it has a built-in digital filter that averages in our case 2499
measurements. One more advantage is that the AD converter is completelly autonomous and works independently
from the DSP. Therefore a good amount of processing time
is saved for the DSP.
Modul that enables gathering of measurements from the
external AD converter was developed in Simulink, independently, in a form of a block. Due to the complexity, the
communication system was not able to be built with the
basic blocks from the TIC2000 library.
3.3. Connection to the computer
Serial Communication Interface (SCI), also known as UART,
is a two-wire asynchronous bus that is used for communication with other DSPs or devices. It is made out of seperate
units for sending and receiving which enables half-duplex
or full-duplex transfer of data.
parison with the previous versions of Matlab, this library is
wealthier. Modules are more comprehensive and enable
more precise registery settings. For example, a comparison between an encoder modul for TMS320F2812 and
TMS320F28335 is noticable. (Figure 4.1 and Figure 4.2).
As it can be seen, the difference is considerable. We are
very limited with the older version. In the mean time, with
the newer version, we can reach for more demanding settings of the DSP hardware modul, which enables a more
demanding and more universal use of the modules. Matlab
7.4, in comparison to its previous versions is reacher for
newer platforms. A functionality to control interrupt routines
in a form of Hardware interrupt and Software interrupt
blocks was added.
UART is used for the communication with personal computers. In such way the measurements are received from the
DSP. The reverse communication, from personal computer
to the DSP, was also realized.
Communication of data was realized according to the idleline,, because there are not more than two participants in
the communication. Measuring resaults are sent in the core
of the main programe without disturbing time-deterministic
programe interrupts.
That model was also developed on our part. In such way it
was simpler to realize the measuring of time necessary to
send the data to the personal computer. The time duration
of programe routines were measured with CPU-timer by its
activation at the beginning of selected programe routine and
its determination at the end of programe routine.
Fig. 4.1: Block for encoder support in Matlab 7.1
3.4. Pulse width modulation
The DSP supports six PWM modules that enable, on each
of the external pins, two different pulse width modulated
signals. Every modul enables an optional selection of the
most different properties at the exit of the generated signal.
PWM signals have a wide use in the telecommunication, to
manage different elektromechanical sections, as well as to
supply systems in the alternative circuit.
The necessary moduls have been enabled with the help of
blocks from the Simulink library.
4.
Implementation of program units into the Matlab/Simulink
Individual programe units on the circuit board were developed with the Simulink programe, real time workshop
(RTW) tool. Matlab 7.4, respectively, the Simulnk TIC2000
library with the DSP support TMS320F28335 was used
for the implementation of modules. The library supports
all basic models that are provided by the DSP. In com126
Fig. 4.2: Block for encoder support in Matlab 7.4
4.1. Set of Moduls in TIC2000
In the TIC2000 library, which is designed for hardware
support of the texas‘ DSPs, the following blocks can be
found; block for AD converter support, digital inputs and
outputs, PWM block, encoder block, block for an event
count, Watchdog, support for SCI, SPI, CAN, I2C communication, idle task block as well as a support block for
N. Semenič, A. Sarjaš, R. Svečko, A. Chowdhury:
Design and Implementation of Rapid Control Prototyping System ...
hardware interrupts and software interrupts. In the library,
next to those, are also blocks To RTDX and From RTDX.
Those blocks are used to reestablish the connection between CCS and Matlab programe, which enables transfer
of data in real time.
Out of those blocks, folowing blocks were used; for the
actuator PWM block drive, encoder support block, block
for hardware interrupt as well as the idle task block. The
hardware interrupt block enables control over triggering hardware interrupt service routines for external AD
converter and encoder. The idle task block was used for
independent functioning of communication system with
the personal computer in a way that it does not distrub
carrying out of time deterministic interrupt routines (Figure
5.1). Blocks To and From RTDX were used to reestablish
the connection between CCS and Matlab software. That
way, the executable file can be downloaded and run onto
the DSP out of Matlab‘s workspace. This tool is also suitable for exchange of optional variables between the DSP
and Matlab‘s workspace. In spite of the fact that we were
able to establish a connection through a single channel
and to qualify the transfer of one variable, we noticed large
irregularities by the transfer of more variables through more
channels. That kind of working could be expected due to
a poor J-Tag equipment. By the work J-Tag XDS510 was
used. Better J-Tags (XDS560) promise more robust transfer
of data and higher data rates (up to 2 MB/s) through the use
of the Hi Speed RTDX functionality. Because of unespacted
functioning of RTDX, the transfer of data was conducted
via serial bus SCI, respectively UART.
The basic framework programe, built by the Simulink in
the CCS tool programe, is built in the form of a CpuTimer0
timer interrupt routine in a way that the blocks in the basic
Simulink scheme are carryed out with a specified sampling
time. Therefore we have to be careful by choosing the sampling time. In order to assure a time deterministic system,
the sampling time has to be longer than the carrying out
of a system in the preemption. In case we want a certain
part of the system to be carryed out in the background, so
it does not disturb high priority interrupts, an idle task has
to be used. In idle task block can be specified whether the
preemption is preemptible or non-preemptible.
4.2. Development of additional blocks with S-function
S-function is a tool that enables integration of custom functionality in the form of a program language C or Matlab‘s
script language. That way a custom block, with a specific
functionality, can be created. There are three different ways
to integrate program codes in Simulink, Noninlined S-functions, Wrapper S-functions and Fully Inlined S-functions.
Noninlined S-function does not require any of the additional
tasks such as code adaptation in TLC. They can be created
with tools that enable an automatic creation of S-functions
or they can be written individually. In the last case, we have
to be deeply engaged in the building of a function as well as
Informacije MIDEM 41(2011)2, str. 122-131
to master the syntax. Taking into an account that the syntax
of S-functions is unique, this work, specialy with complex
functions, may take a good amount of our valuable time.
That type of building of S-functions does not prove to be
the best in the case when we want to integrate a code into
Simulink. For example, in the program language C, which
is a widespread way of programming especially among
embeded systems programers. The integration of the code
can be done with the Wrapper S-function. In that case it is
not necessary to integrate an entire code manually in the
S-function, but only a call to the assigned routine can be
added. Ony the basic model of S-function can be used,
therefore we do not have to occupy ourselves with the
in-depth knowledge of S-functions. The above mentioned
procedures are only suitable for the integration of a C programe language and that way they are not suitable for the
development of drives, that require hardware instructions
syntax for access to registers and the assignment of their
evaluations. Fully Inlined S-function means that the algorithm is integrated with the TLC functionality. In that case, a
more precise knowledge of TLC syntax is necessary. This
case of S-function is suitable for development of drivers,
since an optional code, or hardware instructions, can be
added into the TLC file. Or appropriate instructions can
be added to the TLC, which can add suitable hardware
instruction files (.c or .h) to the CCS project.
Matlab 7.4 version is reacher for quite appliable tool, Code
Legacy Tool /9/, which provides automated creation of
Wrapper or Fully Inlined S-functions. Matlab 7.1 does not
support that tool. That way, an integration of the programe
code written in the C language is now faster and a lot
simpler. A code that we want to implement in the form of
S-function has to be written in the form of a function based
on C language. It is needed to remodel input and output
function variables. With mentioned tool, we were able to
develop custom blocks in the C language. Also, through
this procedure an outline for development of drives was
also developed.
4.3. Increase of encoder robustness
A block for encoder support, from the TIC2000 library is
used to gather position and rotation speed measurements.
The block is adjusted to the appropriate settings. On the
output of the block, an information on the rotation direction and the value on the event count in sampling time and
the number of time quantums between two events can
be obtained. With this information, the position and the
rotation speed in every sampling time can be determined.
During testing of functionality of the modul, was found that
in specific situations it came to an irregular calculation of
values. A block or S-function, which eliminates the occured difficulties, was added to increase the robustness
of operating of the modul.
When the encoder modul counts a full event, it means that
the encoder modul measured the change of the position
exactly for one turn. The encoder modul is designed in a
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Informacije MIDEM 41(2011)2, str. 122-131
N. Semenič, A. Sarjaš, R. Svečko, A. Chowdhury:
Design and Implementation of Rapid Control Prototyping System ...
way that when it counts a full event, the encoder counter
is set to 0. In case of the opposite rotation, when it counts
to 0-th events, the values are set to the maximum number
of events in one turn. Most of the time, the difficulties with
the measuring had occured exactly at the turn of 0., the
maximum number of events and when the rotation direction
suddenly had changed. Difficulties had appeared when the
position had to be determined and with the calculation of
speed through an algorithm for higher speeds (Equation
3.1). From an equation 3.1, it follows that the position and
the rotation speed are usually measured with the difference
between the current number of events and the number of
previous events. Scheme on how the position and speed
are determined is presented in Figure 4.3. The beginning
of the arrow represents the number of previous events,
the end of the arrow the number of current events. Arrows
are designed to schematically illustrate posible occasions
of two successive events and they do not proportionaly
represent events of real values. In a real example, the proportions among values of previous and current events are
diminishing, they depend on the rotation speed.
In example A, the difference between the number of current
and previous number of events is higher than the half of
the maximum number of events (Half-event). A difference
upon which the new position and speed can be calculated
is defined with:
difference = -(full-event - (current_eve -previous_eve));
abs_position += difference; where the position is
reduced with an actual difference, which is negative
In the example B, difference is defined with:
difference = current_eve - previous_eve;
abs _position += difference; where the position is
increased for an actual difference.
In the example C, difference is defined with:
difference = (full-event + current_eve - previous_eve);
abs _position += difference; where the position is
increased for an actual difference
In the example D, difference is defined with:
difference= current_eve - previous_eve;
abs _position += difference; where the position is
decreased for an actual difference
Fig. 4.3: Scheme of the encoder events and the
principle calculation of speed and position
128
A suggested algorithm is suitable for both directions of rotation, since it considers actual shifts, regardless of direction
of rotation. It also fixes incorrect calculations that occur
around 0-th or full event. Operating of the module improves
and the measurements robustness increases.
4.4. Realization of drivers in the Simulink
As it has been already mentioned, the Code Legacy Tool
enables an automated procedure of code integration written
in C. In this way, an outline of more complex blocks were
created, which also include manipulations with registers
and hardware instructions. A custom block was developed
to receive values from the external AD converter through
the SPI communication bus and a block for communication with the personal computer. For the development of
complex blocks, that also contain drivers, we used the
following algorithms:
- A compiler with the command mex(‚-setup‘) is set in
Matlab
- In the custom C function, input and output values
are appropriately adapted just like Code Legacy Tool
requires. Input and output function values represent
inputs and outputs of the block. The function can also
contain instructions. It can also contain calls of other
functions from other files as well as macroes or lists.
- In the custom C function it is necessary to coment all
calls to other functions, macroes, hardware instructions, registry manipulations. The purpose of the
Code Legacy Tool is only the development of C-MEX
S-function, which can be integrated as Simulink‘s Sfunction block.
- C-MEX S-function and the TLC file is created with the
use of Code Legacy Tool.
- To the TLC file, required source or header files (.c
or .h) containing hardware instructions are added.
Source files (.c) can be added with the instruction
%<LibAddToModelSources(„SPI“)>, header files (.h)
can be added with the instruction %<LibAddToCom
monIncludes(„Device.h“)>. Instructions have to be
added in the core of BlockTypeSetup function in TLC
file. Calls to initialization routines of hardware moduls
can be added to the function start. In the function
outputs, function call to the custom C function can be
noticed, which is a result of previous C-MEX S-function
generation.
- The model is loaded in Simulink. A project with source
and header files in CCS is generated. We look for a
custom C function file in the project and uncomment
the commented parts of code.
- Added part of the code can be debuged as well and in
that way the success of operation of the added module
can be prooved in the CCS
After the mentioned algorithm, a modul that receives values
from an external AD converter and a modul for communication with a personal computer were added. Modul for AD
conversion was developed, since that kind of system was
N. Semenič, A. Sarjaš, R. Svečko, A. Chowdhury:
Design and Implementation of Rapid Control Prototyping System ...
not possible to realize with basic blocks, mainly because
of the complexity of communication through the SPI bus.
Modul for communication with a personal computer enables
an easier supervision over the sent and received data, since
a duration time needed for the execution of the specific
part of code can be exactly measured with the CPU timer
in the DSP.
5.
Example of test plant control
Informacije MIDEM 41(2011)2, str. 122-131
among each other by 90 ° (Figure 3.1). Encoder has 1000
lines. Taking that in consideration, due the possibility to
register positive and negative fronts, it can be registered
4000 events in one turn.
An electrical circuit is located on the external circuit board,
which adapts levels of voltage supply between the processor and the motor as well as between the processor and
the sensores.
A test plant consists of a mechanical framework, pendulum,
electrical motor, feeder and a processor with the adapted
electrical circuit.
On the ecternal circuit board, there is a H-bridge that
provides up to 6 A of current for the motor. H-bridge is
controled by the processor by the principle of pulse width
modulation (PWM).
The concept of stabilization of an invert pendulum presents
a mounted arm on an electrical motor, where at the end,
on the bearings, a pendulum is mounted. With a suitable
control of the electrical motor, we can affect the position
of the arm and indirectly so, the position of the pendulum.
6.
State space controller have been designed to achieve
stabilization. That way we need the information on all of
the internal states od the system. These are the speed and
angle of the pendulum and the speed and position of the
arm. The speed of pendulum is calculated on the basis of
pendulum angle change. Position and speed of the arm is
measured with the encoder.
Potentiometer is set behind the bearing of the pendulum
and it is supplied by voltage of 5 V. The signal in the frame
of 0-5 V presents the position of the pendulum 0-360 °.
Due to the nonlinearity of the potentiometer, it is possible
to measure in a range of 0-340 ° with ± 3 ° of tolerance.
Encoder modul enables measuring of the position and the
speed of the arm with event signals received from encoder.
Event represents every positive or negative front of the
encoder output QEPA or QEPB signals, that are dislocated
Design of the core program for stabilization of the inverted pendulum
A row of hardware interrupts were realized in the DSP.
Every interrupt has its own specific time deterministic
task. In the center portion of the program core, which is
presented by an infinite while loop, functions are carryed
out that take care of sending the measuring resaults to the
personal computer.
Synchronization of the external AD converter with the DSP,
is carryed out through an external interrupt. When AD has
the current measured data available in the memory data
registry, the external pin DRDY falls to 0. This happens
exactly evey 0,01 s, which is the sampling time. This event
triggers the hardware interrupt in which, through the SPI
bus, value of the data register of AD converter is obtained.
In that interrupt, the value of the register QUTMR of encoder
module is adapted as well. That is the encoder modul timer
which is responsible for triggering of the encoder interrupt,. that is also triggered every 0,01 s, respectively the
sampling time. With the adaptation of the encoder timer,
the synchronization of the encoder interrupt routine with the
interrupt of the AD converter is reached. In the interrupt of
the AD converter, with the appropriate setting of CpuTimer0
value, the synchronization with the system interrupt is also
performed. Through the proper synchronization encoder
interrupt occures just before the interrupt of AD converter.
System interrupt of Simulink follows both interrupts. The
position and the speed of the arm is obtained during the
interrupt of the encoder. In the interrupt of the AD converter,
the information on the position of a pendulum is obtained,
the speed of the pendulum is calculated on the basis of the
change of the pendulum position. In the system interrupt,
the chosen regulator is calculated and an adequate PWM
exit is set (Figure 5.1)
The system is designed so that the interrupt of AD converter
has a priority over the encoder interrupt.
Fig. 5.1: RCP for inverse rotation pendulum
129
Informacije MIDEM 41(2011)2, str. 122-131
7.
N. Semenič, A. Sarjaš, R. Svečko, A. Chowdhury:
Design and Implementation of Rapid Control Prototyping System ...
Designing the state space controllers
For the control system, inverted pendulum two type of state
space controllers were designed. The first type of state
space controller was designed through pole placement
technique (PPT) and the second type with optimization of
the quadratic continuous-time cost functional ( LQR). A
mathematical model of third and fourth order was used for
design of controllers. Model was adapted from work /12/.
Pole placement controller was designed with the closedloop poles assignment and Matlab command »acker«. LQR
controller was designed with the expression »lqr« and the
appropriate weightening (Q and R) matrices.
Fig. 8.2: Controller with the setpoint-crossbar position
Taking into consideration that the controllers were designed
for a linear system and tested on a nonlinear model in
Simulink, where was checked whether the solutions suit
the stability criteria. With the simulations, we could also
test until which point the system was stable, if pendulum
had deviated.
8.
Resaults
During the design of PPT controllers, a third order model
was used, since the control upon the position of the arm is
not significant for the stabilization of the pendulum. During
the realization of the controller with the setpoint, a fourth
order model and the position of the arm was used as a
reference signal. LQR controller was designed with the
systems of third and fourth order.
Fig. 8.3: Third order LQR controller
As results show, the best designed controllers are those,
which are designed with the third order system. That is
to say, the controllers do not demand the stabilization of
pendulum in exact defined point of the position of the arm.
If we compare these two controllers to the controller with
the setpoint, it is established that in the maximal deviation
of angle of the pendulm, it swings almost twice the amount.
It is comprehensive that by the setpoint controller considerations not only about the angle of the pendulum but also
the position of the arm like setpoint is taken into account.
Fig. 8.4: Fourth order LQR controller
Two linear quadratic controllers were calculated. A third
order system was used to design the first one. With the
second one, a fourth order system and the position of the
arm as a reference position were used. If we compare the
measurements with previously mentioned controllers, it is
visible at first sight that both positions of the pendulum were
steadier. If we compare the strenghtening of both regulators
with the ones before, it is stated that they are much more
sensitive to the position of the pendulum.
Fig. 8.1: Pole placement controller
130
N. Semenič, A. Sarjaš, R. Svečko, A. Chowdhury:
Design and Implementation of Rapid Control Prototyping System ...
9.
Conclusion
Informacije MIDEM 41(2011)2, str. 122-131
/5/
S.H. Seo, S.W. Lee, S.H. Hwang, J.W. Jeon, Development of
Platform for Rapid Control Prototyping Technique, SICE-ICASE
International Joint Conference, October 18-21, Busan, 2006.
/6/
K.H. Hong, W.S. Gan, Y.K. Chong, K.K. Chew, C.M. Lee, T.Y.
Koh, An Integrated environment for rapid prototyping of DSP
Algorithms using MATLAB and Texas instruments‘ TMS320C30,
Microprocessors and Microsystems 24, 349-363, 2000.
/7/
Z. Fang, Y. Qi, Q. Zhang, T. Chai, Design and Implementation
of a Low Cost DSP Based Rapid Control Prototyping System,
Industrial Electronics and Applications, ICIEA 2009.
/8/
Z. Fang, N. Song, L. Wang, Design and Implementation of a
Novel Fuzzy Controller with DSP for Rotary Inverted Pendulum,
Control and Decision Conference, 2009.
/9/
Real-Time Workshop, User‘s Guide Version 7.4, 2009.
/10/
Texas Instruments, Incorporated, Reference Guide, TMS320x2833x, 2823x Enhanced Quadrature Encoder Pusle
(eQEP) Module, SPRUG05A, avgust 2008.
/11/
Texas Instrumets, Incorporated, Data Manual, TMS320F28335,
TMS320F28334, TMS320F28332, TMS320F28235,
TMS320F28234, TMS320F28232, Digital Signal Controllers
(DSCs), SPRS439F, junij 2007.
10. Acknowledgment
/12/
Burr Brown Corporation, ADS1212, ADS1213, 22Bit analog to
digital converter, USA, april 1998.
Operation part financed by the European Union, European
Social Fund.
/13/
Tan Kok Chye, Teo Chun Sang, Rotary inverted pendulum,
Scool of electrical and electronic engineering, 1999.
/14/ Zdenko Mezgec, Andrej Medved, Amor Chowdhury, Rajko
Svečko,. Mobile payments - design of new terminal = Mobilno
plačevanje - razvoj sodobnega terminala. Inf. MIDEM, mar. 2008,
letn. 38, št. 1(125), str. 53-60.
The goal of our work was to carry out the system for
rapid prototyping in the Matlab/Simulink environment. It
is confirmed that the newer version of Matlab has numerous advantages with the development of Code Legacy
Tool modules and the expanded set of TIC2000 library.
Individual basic moduls in the library are more complex
and enable more precise hardware settings, that are very
welcomed since they enable improved functionality. With
that, an in-depth knowledge of hardware DSP moduls is
neccessary. The system of rapid prototyping, with rich
library collection in Simulink, presents a simpler and faster
way of adaptation of algorithms that are in the form of block
models and a simplified algorithm testing on real plants. The
system of rapid prototyping was successfully tested with
the stabilization of the rotary inverted pendulum.
References
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DC/DC Converter for Fuel Cell Electric Vehicles, Power and
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R. Duma, P. Dobra, M. Abrudean, M.Dobra, Rapid Prototyping
of Control Systems using Embedded Target for TI C2000 DSP,
Mediterranean Conference on Control and Automation, July
27-29, 2007, Athens.
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W.S. Gan, Y.K. Chong, W. Gong, W.T. Tan, Rapid Prototyping
System for Teaching Real-Time Digital Signal Processing, IEEE
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/4/
A. Rubaai, M.J. Castro-Sitiriche, A.R. Ofoli, Design and Implementation of Parallel Fuzzy PID Controller for High-Performance
Brushless Motor Drives: An Integrated Environment for Rapid
Control Prototyping, IEEE transactions on industry applications,
vol.44, no.4, July/August, 2008.
Nikolaj Semenič1, Andrej Sarjaš2, Rajko Svečko2,
Amor Chowdhury1
1
Margento R&D, Gosposvetska c. 84, 2000 Maribor
2
FERI, Smetanova ul. 17, 2000 Maribor
E-pošta: [email protected]
Prispelo: 01.07.2010
Sprejeto: 24.06.2011
131
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