Low-Cost, Flexible Controls Lab Platform using Matlab/Simulink and
Non-Uniform Sampling
John Miller, Ian Gravagne, Scott Koziol
Department of Electrical and Computer Engineering
Baylor University
John Miller1@baylor.edu, Ian Gravagne@baylor.edu, Scott Koziol@baylor.edu
Abstract
There is a movement in undergraduate labs toward smaller, more mobile, more modular equipment for the purposes of engaging students and managing higher enrollments. This paper presents
a relatively low-cost, flexible, modular platform for automatic control system lab experiments. The
hardware consists of a custom circuit board that provides amplification and some signal processing, a National Instruments USB DAQ unit, and one of several peripheral experiment modules
(DC motor, pendulum, thermal tunnel, etc.). The NI DAQ unit can communicate directly to MATLAB/Simulink via the Data Acquisition Toolbox, which allows students to implement closed-loop
control algorithms directly in the ML/SL environment with no concern for the ”target platform”
or code compilation. The control loop sampling rate is randomly distributed with a mean around
40-50 Hz, depending on the host computer’s speed and operating system. While this is too slow
for critical control applications, it is more than sufficient for many basic lab experiments, as will be
shown by experimental results. Furthermore, the authors provide mathematical conditions under
which a non-uniformly sampled system can be controlled. This is supported by experimental data,
which also demonstrates that from the student’s perspective, the system can be expected to behave according to the continuous-time model. This allows the system to be used by undergraduate
students early in their first control systems course, without the need to introduce the concept of
discretization or discrete-time control theory.
Introduction
An effective method of delivering laboratory content is to provide students with equipment they
can operate independently, on their own time, and even in a location of their choosing. Most
commercially availble controls lab experiment platforms are too expensive for this purpose, and a
quick survey of recent articles reveals a number of people trying to address this need by designing
custom systems [1–3].
These systems can be divided into two general catagories: hardware-in-the-loop (HIL) and embedded. HIL systems (see Figure 1) utilize a microcontroller that communicates sensor data to a
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Microcontroller + Hardware
PC/Control
Algorithm
DAC/Amp/
H-bridge
Plant
(e.g. motor)
ADC/Signal
Conditioning
Figure 1: Block diagram of a generic HIL system. The PC performs the control algorithm calculations.
Microcontroller + Hardware
Control
Algorithm
PC
“Hybrid”: Sensor
data back to PC
DAC/Amp/
H-bridge
Plant
(e.g. motor)
ADC/Signal
Conditioning
Figure 2: Block diagram of a generic embedded system. The embedded microcontroller performs
the control algorithm calculations. In ”hybrid” mode, the sensor data is communicated back to the
PC for user visualization.
personal computer (PC), receives control data from the computer, and converts the control values
into the signals that drive the physical plant. An embedded system (see Figure 2) performs the
control algorithm calculations on the microprocessor. [2] provides an additional scenario, termed
”hybrid,” whereby the microcontroller communicates sensor data back to the PC for off-line analysis and visualization, while still performing the control calculations locally.
Each of these systems have their positive and negative characteristics. The HIL system requires a
communications protocol (often RS-232, sometimes converted to USB) between the PC and hardware, but students do not have to program the microcontroller. This can be done for them. The
embedded system requires knowledge of the microcontroller, its programming language, and the
hardware to which it is connected (if any; e.g. H-bridge IC’s or other signal conditioning hardware). It also requires an understanding of digital control algorithms. The benefit is typically a
speed increase for the control loop timing.
This paper provides an alternate HIL system, replacing the microcontroller with an off-the-shelf
(OTS) data acqusition (DAQ) unit, which is intended to be:
• Relatively low cost: much less expensive than commercial units, but more than the examples
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referenced above
• Flexible: able to perform multiple types of experiments
• Transparent: very little is hidden from students
• Target-free: does not require compiling code or an external microcontroller
The last item is the key factor that differentiates this design from others. All algorithms are run
within MATLAB/Simulink (hereafter abbreviated ML/SL), which communicates sensor and control data with the DAQ unit via USB. This avoids the need for a) writing code in another language
or b) writing ML code, compiling it, and downloading it to a target processor, which often requires
multiple software applications (ML, compilers, drivers, etc.) to operate together and appropriate
programming hardware. It also avoids custom communication protocols and embedded processor
timing issues. Another advantage of OTS hardware and software is that it is likely to be wellsupported for an extended period of time. (For example, NI just released an updated set of USB600x DAQ’s that are compatible with the previous versions.) The downside is that the sampling
rate is relatively slow, averaging around 40-50 Hz, depending on the host computer. This issue is
discussed in depth below.
System Design
The system can be divided into four main parts, as shown in Figure 3:
• ML/SL software - functions as both the user interface and control algorithm computation
engine
• National Instruments (NI) USB-600x DAQ unit - analog and digital signal interface
• A custom PCB - provides output signal amplification, sensors, and some sensor signal processing
• A peripheral (system) to be controlled - the present use is for DC motor control, but addiitional peripherals are discussed in the Future Development section
Hardware
A picture of the hardware (custom PCB and DAQ) and a corresponding block diagram are shown
in Figures 4 and 5.
The NI USB-6008 DAQ unit was chosen for its low cost, simplicity, appropriate I/O channels, and
direct connectivity to ML (via the Data Acquisition Toolbox). NI sells an ”OEM” version, without
the standard casing, which allows it to easily mount to the custom PCB. (Note: The new USB6000/1/2/3 series is pin and connector compatible with the 6008/9 versions. Only mount spacings
will have to change.) The current version of the hardware uses the following DAQ I/O channels:
• Two analog outputs for driving the amplifiers, which in turn drive the motor (or other load).
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Custom PCB
MATLAB/
Simulink
USB-600x
DAQ
Amplifiers
Plant
(e.g. motor)
Sensor Signal
Conditioning
Figure 3: Block diagram of the system showing the four main components.
• One analog input for measuring output (motor) voltage.
• Two analog inputs for measuring output (motor) current. Future revisions will have only one
curent sensor.
• One digital counter input for measuring motor speed by counting pulses from the encoderto-counter decoder.
• One analog input for determining motor direction. (This function could be performed by a
digital pin, if available.)
• Twelve digital inputs driven by a set of hardware binary counters for determining motor
position.
• One analog input for measuring temperature, which is not currently being used.
The two analog outputs from the DAQ unit are the inputs to two independent amplifiers. Both
amplfiers are powered from a single 15 V dc power supply. Their outputs can be used either as
one differential output or as two single-ended outputs. As a differential output, they can produce
a ±12 V signal (but not a 24 V differential signal because neither amplifier can be less than 0 V),
which allows for bidirectional motor control. This control scheme is used primarily because of the
presence of analog outputs and lack of digital pulse-width modulated (PWM) outputs on the DAQ
unit. (The digital I/O channels can produce a PWM signal, but they are timed in software, meaning
the modulation frequency would be far too slow.)
An optical rotary encoder is mounted on the motor and is connected to a quadrature clock converter
IC that converts the quadrature encoder signal pair into two seperate signals—a pulse train that can
drive a standard binary counter and a direction bit. These signals actually drive two different counters.
One is onboard the DAQ unit and is used to determine motor speed. The onboard counter simply counts the number of pulses, regardless of whether the motor is turning clockwise or counter
clockwise. The direction signal is also input to the DAQ and can be used to determine the direction
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Thermocouple solder point
and IC (not present)
Current
sensors
NI USB
DAQ
Motor
output
Position
reset
Encoder
input
Hardware counters
(position)
Amplifiers
Quadrature clock
converter IC
Figure 4: Custom PCB and associated hardware components.
12-25 VDC
input
Op-amp
1
USB-600x DAQ
Current
sensor(s)
Op-amp
2
Motor
output
(USB bus-powered, provides
+5V to other components)
Count and
direction
Position binary
counters (x3)
Quadrature clock
converter IC
Encoder
input
Position counter
reset button
Note: only some connections are shown
Figure 5: Block diagram of custom PCB and hardware components.
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the motor is turning. However, if the motor changes direction too quickly and/or frequently, it is
possible for the software to miss these changes and not account for them. (Recall that the sampling rate is approximately 40-50 Hz.) This is not a significant issue as long as there is a reasonable
load (moment of inertia) on the motor shaft and speed is the variable of interest (i.e. speed control).
Where it becomes a problem is trying to accurately position the motor (i.e. position control). For
this application, a set of three four-bit binary counters (for a total of twelve bits) is added. The
binary counter IC’s have inputs for both the pulse signal and the direction signal. Thus, they track
the bidirectional movement of the motor (unlike the onboard counter).
Software
Since the hardware is based on an NI DAQ, a natural choice for the software would be NI’s Labview. While this would certainly work, the authors chose to use ML/SL because it was already in
use by the control systems courses at the university and they felt that being able to integrate the lab
platform with the mathematical analysis already being done in ML/SL would be beneficial.
The Data Acquisition Toolbox (DAQ Toolbox) contains functions for setting up the DAQ unit
(specifying which I/O channels are being used and their properties), reading input values, and
writing output values. The DAQ Toolbox includes two interfaces for communicating with hardware: ”legacy” and ”session-based.” The older USB-6008/9 units supported both interfaces, but
the newly-released USB-600x (0,1,2,3) series only supports the session-based interface. It is also
worth noting that the legacy interface has to operate under the 32-bit version of ML. For all of
these reasons, the current platform uses the session-based interface. The reader is referred to the
Mathworks website for more information[4].
The reading and writing functions access all of the configured inputs and outputs together. Thus,
for example, the more input channels that are configured, the longer the read operation takes. Listing 1 shows a simple setup and single read operation for the DAQ unit.
Listing 1: Basic USB DAQ session
% Create DAQ session object
s = daq . createSession ( ’ ni ’ );
% Add input channel & set as " single ended " ( ref to ground )
s . addA n a l o g I n p u t C h a n n e l ( ’ Dev2 ’ ,0 , ’ Voltage ’ );
set ( s . Channels (1) , ’ TerminalConfig ’ , ’ SingleEnded ’ , ’ Range ’ ,[ -10 10])
% Read ( measure voltage )
s . inputSingleScan
The session-based interface does not have native SL commands (blocks); however, the ML commands can be called from ”MATLAB Function” blocks within SL. There are some potential limProceedings of the 2015 ASEE Gulf-Southwest Annual Conference
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itations (e.g. SL cannot generate code for these functions; they have to be handled as ”extrinsic”
functions), but since the intent is to operate within the ML/SL environment (and not compile to
another target), these do not present a real problem. It is expected that these issues will be hidden
from the students and that the students will be provided SL blocks/ML functions that they can use
to interface with the DAQ unit.
The session-based read and write commands are single, blocking operations. Thus, all of the
communication with the DAQ unit is initiated within ML/SL, and the timing of these operations
depends on ML, the operating system, the USB connection, and the DAQ’s embedded processor.
Non-uniform Sampling
Closing a feedback loop with a non-deterministic digital controller naturally raises two issues. The
first has to do with how much timing variance (sometimes known as ”jitter”) the closed-loop system can accept while still yielding acceptable performance. The second is whether a controller
ought, in some way, to be designed to ameliorate or at least better tolerate the negative effects of
timing variance. Fortunately, recent theoretical advances using a field of mathematics known as
dynamic equations on time scales can shed some light on these questions.
Figure 6 illustrates a typical timing histogram of a closed-loop controller executed in ML running
on a non-real time operating system. The histogram approximates the timing statistics for a controller running as fast as possible, where timing is not regulated by the use of timers or interrupt
routines. From it, two facts are clear: there is a minimum sampling time (or total loop time) of
around 13 ms, such that the system simply will not run faster than that; and the distribution of sampling times permits occasional outliers: loop times that are substantially longer than the mean but
statistically rare. In the parlance of dynamic equations on time scales, the sampling times form an
ordered discrete subset of the real numbers known as a time scale T ⊂ R, and the sampling periods
are known as the time scale graininess µ(tn ) = tn+1 − tn where all ti ∈ T. The basics of time scale
theory appear in a volume by Bohner and Petersen [6], and recents works on the application of
time scale theory to discrete-time control appear in the bibliography[5, 7–9].
The upshot of the time scale analytical framework is that any linear, time-invariant, open-loop
system expressed in continuous-time state space form ẋ(t) = Ax(t) + Bu(t), with t ∈ R, can be
discretized onto an arbitrary time scale and expressed as a closed-loop time scale state space system
x∆ (t) = A (µ(t))x(t);
t ∈ T,
(1)
where x∆ is the Hilger dynamic derivative (similar to a forward difference operator). Here
A (µ(t)) = expc(µ(t)A)Acl
(2)
where expc(X) = I + 21 X + 16 X 2 + ... + n!1 X n−1 is a convergent power series and Acl is the closedloop system matrix.; for example Acl = A − BK for a state feedback controller. (Readers will
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160
140
occurances
120
100
80
outliers
60
40
20
0
0.013
0.014
0.015
0.016
0.017
0.018
Period µ (seconds)
0.019
0.02
0.021
Figure 6: A histogram of 1000 ADC/DAC conversions executed in a ML loop running in Windows
7. The hardware interface is a NI USB-6009. Period µ(t) is clearly non-constant, with some
statistically rare outliers. (Taken from [5])
note we are assuming the closed-loop system is autonomous and neglecting any reference inputs
without loss of generality.) The new time scale state space representation is no longer time invariant
in general; however, if the timing variance is small compared to the mean, as is the case in Figure
6, it is reasonable to use a constant coefficient system
x∆ (t) = Āx(t);
t ∈ T,
(3)
where Ā = E[A (µ(t))] is the expected value of A considering the graininess as a random variable.
With this in mind, Poulsen, et. al., showed that the discretized closed-loop system will uniformly
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Figure 7: The complex plane showing the circular region Hδ (T) for a time scale with gammadistributed graininess. The larger shaded area is the largest region of stability that is possible for
a constant-coefficient system. This region is difficult to compute and does not guarantee uniform
exponential stability. (Taken from [7].)
exponentially stabilize if its eigenvalues fall within the region Hδ (T) , where
)
(
2
1
1
Ha =
λ ∈ C : λ + < 2 ,
a
a
(4)
Z T
µ(t)∆t
δ (T) = lim sup
T →∞
t0
T − t0
.
If we are armed with knowledge of a fixed statistical distribution for graininess µ, then δ (T)
simplifies to
E[µ 2 ]
δ (T) =
,
(5)
E[µ]
which is very easy to calculate.
Regions of the form Ha are known as ”Hilger circles”. In particular, the specific region Hδ (T) is
the largest Hilger circle that can be subsumed by the (generally non-circular) region of convergence
for a system of the form of (3). Figure 7 illustrates this concept, and leads to a key observation:
loop timing may be best modeled using a ”long-tail” distribution function, for example a gamma
or exponential distribution, because of the possibility of outliers as illustrated earlier. As long as
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these are statistically rare – such that δ (T) exists – a closed loop system will tolerate them and
maintain uniform exponential stability. This is not a guarantee of ”nice” performance, but simply
a way to ensure that the controller will in fact work in the presence of variable timing.
Returning the discussion to its pedagogical purposes, there are two main takeaways. First, instructors will need to ensure that the dynamics of the plants and controllers chosen for student
experiments place the closed-loop eigenvalues of (3) within Hδ (T) , or there will be no guarantee
of control stability. Second, some knowledge of the worst-case statistical distribution of the system
is needed, which will require tests across a variety of computing platforms likely to be used by students. Weighed against ease and simplicity of operation (no target microcontrollers or compilers,
no real-time system concerns, use of off-the-shelf and widely supported USB interface hardware,
portability to any sufficiently fast computer running MATLAB), the need for careful experiment
design may be a good tradeoff.
Experimental Results
Figure 8 demonstrates the capabilities of the current system. The plots will be explained moving
from left to right, top to bottom. The first plot shows the DAQ ouput/amplifier input and amplifier
output/motor input voltages. The DAQ output voltage is specified in ML and is not measured. The
motor voltage is being measured using two DAQ analog inputs in a differential configuration. The
amplifiers are setup in a non-inverting configuration with a nominal gain of 3. The DAQ output
voltage is set at ±3 V, and it can be seen that the motor voltage is approximately ±9 V, as expected.
Next is motor speed. A basic backward difference is being used to compute speed. Rotations are
being measured by the internal DAQ counter driven by the quadrature clock converter. ML’s ”tic”
and ”toc” functions are being used to measure actual sample time, which is then used in the speed
calculation. For this example, the signal is not being filtered.
In the middle are two different plots of motor position. On the left is the actual binary count value
being stored on the external binary counters (and read periodically by the DAQ unit). One can see
that the counters ”wrap around” when they reach a maximum value of 212 = 4096. On the right is
an ”unwrapped” version which has also been converted to angular position in degrees. The speed
plot appears to be the derivative of this position plot, as would be expected.
On the bottom left is a plot of the two current sensors presently on the unit. There are two for the
sake of comparison. The final design will have only one. There are several issues with the current
sensors which will be resolved in the future, including the difference in polarity, the amount of
noise present in the ”Vac” sensor, and verifying the accuracy of the measurements.
On the bottom right is a histogram plot of the sample times, exactly like Figure 6. As stated previously, on these DAQ units, the sampling time increases as more I/O channels are included. Thus,
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the mean of this distribution is higher than the previous one, but the general character remains the
same—most of the samples are gouped around the mean with a few outliers.
Figure 9 shows a SL diagram with a control loop that includes the hardware and motor (top) and a
loop that is simulation only (bottom) using a first-order model of the motor. Zero-order hold blocks
have been placed on either side of the simulation model to imitate the discrete behavior of the DAQ
system. Figure 10 shows the motor and DAQ voltages (left) and the actual and simulated speed
cuves (right). The performance of the motor is reasonable; however, there is some discrepancy in
the transient response, the cause of which is still to be determined.
Future Development
The next step is to continue to improve the hardware design to a state where it is ready to provide
to students. The students will be asked to try some basic DC motor experiments with the new
system and provide feedback about their experience. Moving forward, additional peripherals can
be developed to expand the types of experiments that can be performed. For example, it would be
possible to do a temperature control system with a small enclosure, resistive heating element, fan,
and one or more thermocouples. It would also be possible to use this system with the ”aeropendulum” referenced in [1].
Another idea for future development is to integrate this platform into other undergraduate engineering classes in addition to introductory controls. The hardware system’s modularity (DAQ
unit/amplification and signal processing board/peripheral plant modules) is one of the key features
that makes this platform so versatile for multi-class use. As was stated in the introduction, one of
the benefits of using this system for teaching a controls course is that it is target-free and does not
require compiling code or an external microcontroller. For a controls course, this is very appropriate because it keeps the students focused on applying the theoretical aspects of controls.
For other classes, however, a different approach can be taken. For example, when teaching a microprocessors class, the students are focused on learning how to write and compile code and not
focused on learning control theory. The system could be used for a microprocessors class by having the students replace the DAQ unit with the microcontrollers that they are learning to program.
They could then apply their microprocessor programming skills to implement either an HIL or
embedded control system. In addition to learning how to compile code, this would also be a good
application of learning how to process microprocessor input/output data. Processing sensor feedback, for example, would teach them about working with microprocessor input data and creating
an output signal for motor control could teach them about output. Because they would be interacting with the amplification and signal processing board, they would also learn about methods to
interface a microprocessor with mechatronic systems.
Another course that the authors are involved in is called Avionics Systems Design. Here, students
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Motor Speed
Motor Voltage
4000
10
Motor
DAQ
3000
2000
Speed (RPM)
Voltage (V)
5
0
1000
0
−1000
−2000
−5
−3000
−10
0
1
2
3
Time (s)
4
5
−4000
6
0
1
2
Motor Position As Counts
16000
4000
14000
2500
2000
1500
6
5
6
10000
8000
6000
4000
1000
2000
500
0
1
2
3
Time (s)
4
5
0
6
0
1
2
3
Time (s)
4
Sample Timing
Measured Current
60
1.5
Vac T60404
HW CLSW6B5
1
50
# of samples
0.5
Current (A)
5
12000
3000
Angle (deg)
Position (cnts)
3500
0
40
30
−0.5
20
−1
10
−1.5
4
Motor Position As Angle
4500
0
3
Time (s)
0
1
2
3
Time (s)
4
5
6
0
25
30
35
40
45
50
Elapsed Time (ms)
55
60
65
Figure 8: Example 1: Open-loop operation of DC motor showing sensor measurements.
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Figure 9: Example 2: Simulink diagram. The upper loop interfaces with the DAQ unit. The lower
loop is a simulation using a first-order plant model with parameters from the motor’s data sheet.
Motor Voltage
Motor Speed
4
1400
3.5
1200
1000
Speed (RPM)
Voltage (V)
3
2.5
2
1.5
600
400
1
0.5
0
800
200
Motor
DAQ
0
1
2
3
4
Time (s)
5
6
7
8
0
Actual
Simulated
0
1
2
3
4
Time (s)
5
6
Figure 10: Example 2: Closed-loop operation of DC motor in Simulink.
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7
8
can benefit from this modular system’s ability to interact with peripheral modules. Avionics is a
senior elective so the students should already have experience in both microprocessors and control theory. They can apply this knowledge to avionics specific controls and signal processing
problems. Example problems might be applying a real time operating system (RTOS) to a control problem, learning about and applying advanced control concepts such as digital control, state
space concepts, and advanced signal processing algorithms such as Kalman filters. They could
even develop their own peripheral modules as part of their required major class projects. These
two course examples illustrate how this board can be re-configured in the future to help accomplish
different pedagogical goals of various classes.
References
[1] Eniko Enikov, Vasco Polyzoev, and Joshua Gill. “Low-Cost Take-Home Experiment on Classical Control Using Matlab/Simulink Real-Time Windows Target”. In: Proceedings of the
2010 ASEE Zone IV Conference (2010).
[2] Ryan W. Krauss. “Evaluation of a Low-Cost Microcontroller for Real-Time Control Education and Prototyping”. In: Proceedings of the ASME 2014 Dynamic Systems and Control
Conference (DSCC) DSCC2014-5846 (2014).
[3] Rebecca M. Reck and Ramavarapu S. Sreenivas. “Developing an Affordable Laboratory Kit
for Undergraduate Controls Education”. In: Proceedings of the ASME 2014 Dynamic Systems
and Control Conference (DSCC) DSCC2014-6046 (2014).
[4] Data Acquisition Toolbox. http://www.mathworks.com/products/daq/.
[5] Dylan Poulsen, Ian Gravagne, and John M. Davis. “Is Deterministic Real Time Control Always Necessary? A Time Scales Perspective”. In: Proceedings of the ASME 2014 Dynamic
Systems and Control Conference (DSCC) DSCC2014-6093 (2014).
[6] Martin Bohner and Allan Peterson. Dynamic Equation on Time Scales. Birkhauser, 2001.
[7] Dylan Poulsen, John M. Davis, and Ian Gravagne. “Stochastic time scales: quadratic Lyapunov functions and probablistic regions of stability”. In: Proceedings of the IEEE Southeastern Symposium on System Theory (SSST) (2013), pp. 98–103.
[8] Dylan Poulsen, John M. Davis, and Ian Gravagne. “Observer based feedback controllers on
stochastic time scales”. In: Proceedings of the IEEE Southeastern Symposium on System Theory (SSST) (2013), pp. 104–107.
[9] Ian Gravagne, John M. Davis, and Dylan Poulsen. “Time scale-based observer design for
battery state-of-charge estimation”. In: Proceedings of the IEEE Southeastern Symposium on
System Theory (SSST) (2012), pp. 12–17.
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