A Systematic Approach for Development and Simulation of Digital Control Algorithms using SIMULINK

Matthew G Feemster

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Conference: 2013 ASEE Annual Conference & Exposition
Location: Atlanta, Georgia
Publication Date: June 23, 2013
Start Date: June 23, 2013
End Date: June 26, 2013
ISSN: 2153-5965
Conference Session: Laboratory Experiences in Signal Processing and Controls
Tagged Division: Division Experimentation & Lab-Oriented Studies
Page Count: 12
Page Numbers: 23.119.1 - 23.119.12
DOI: 10.18260/1-2--19133
Permanent URL: https://peer.asee.org/19133
Download Count: 635

Paper Authors

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Matthew G Feemster U.S. Naval Academy

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Matthew Feemster received his Ph.D in Electrical Engineering from Clemson University in 2000. From 2000 to 2002, he was the lead Controls Engineer at WaveCrest Laboratories based in Dulles, VA. In 2002, he accepted a position at the U.S. Naval Academy where he is currently an Associate Professor. His current research interests include nonlinear/adaptive control techniques applied to marine applications.

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Abstract

A Systematic Approach for Development and Simulation of Digital Control Algorithms using SIMULINK I. ABSTRACTWith much of the department’s faculty research aligned with autonomous aerial, ground, marine, or underwatervehicles, students tend to emulate these areas by proposing related capstone projects (see Figure 1 for samplestudent driven projects). Figure 1: Student autonomous (a) aerial (b) ground (c) marine vehicleSince these vehicle related projects are developed for outdoor operation, the utilization of a micro-processor for lowlevel control algorithm implementation is frequent. In direct response to the numerous vehicle driven projects, acustom, inertial measurement unit (IMU) has been developed by our Technical Support Division based around theRabbit single board computer (SBC) (see Figure 2). Rabbit SBC 3-axis gyro/accelerometers Magnetic compass GPS receiver underneath board Figure 2: (a) WSE IMU (b) IMU integrated in autonomous surface vesselWith the development of the above IMU board, measurement of the vehicle state (position, heading, and associatedvelocities) is greatly simplified. As a result, students need only to focus on the calculation of the proper actuatorcommands to control/steer the vehicle within a C like software environment (Dynamic C). However from review offinal capstone reports and attendance of presentations, students expressed having major difficulties whenimplementing even simple PID based control algorithms. This difficulty in C based implementation seems surprisingin light that all students are required to take a two hour lab based course dedicated to the design and implementationof control algorithms on the Rabbit single board computer. Specifically this course targets the design of classicalcompensators KGc s  for a typical DC motor with implementation of the algorithm on the Rabbit SBC. Theconversion of the continuous time compensator to the corresponding digital compensator KGc z  is accomplishedvia Tustin’s Transformation (utilizing the c2d command in MATLAB). From the structure of KGc z  , studentssubsequently developed the corresponding difference equations that can now be transferred to the Rabbit SBC forimplementation. The major oversight here is that students did not simulate their difference control equations toverify that the conversion from KGc z  to equations was performed properly. If the control experiments did notperform as expected as compared to the continuous time simulation, students were unsure 1) if there are hardwareproblems (bad connections, improper sensor calibration, etc) or if 2) their control algorithm was not developedcorrectly to difference equations.In response to this observation, this paper will present a sequence within the MATLAB/SIMULINK softwareenvironment (outlined in Figure 3) to provide students with assurance that the structure of their control algorithm iscorrect. Specifically, the recent ability to utilize embedded function blocks (as opposed to previous S-functions)within the SIMULINK modeling environment has facilitated an easy method for verifying digital control algorithms.In addition, these embedded functions allow for simplified execution of non-linear models; therefore, ourundergraduate students can now also better predict experimental performance by simulating against the higherfidelity nonlinear models (as opposed to limiting themselves to linear transfer functions or linear state spacemodels). This paper will also present the translation of the MATLAB difference equations in to the Dynamic Cenvironment for select plants such as the fluid system shown in Figure 4. A student questionnaire will also beadministered this semester to gauge opinion of the process. Responses from this questionnaire will be discussed. The student must illustrate that KGc s  1 KGc Gp ea theta meets all performance specificationsConstant Continuous time Linear model simulated against the linear plant model compensator G p s  before simulating against the nonlinear model contained in the KGc Ea theta embedded MATLAB function. ea theta fcn Continuous time Nonliner model compensator (Embedded MATLAB function) KGcz Gp ea1 theta1 Digital compensator Linear model Once the student is certain that their continuous time controller is effective, they then simulate their corresponding digital controller KGc z  against the KGcz Ea theta linear and nonlinear model. ea theta fcn Digital compensator Nonliner model (Embedded MATLAB function) Pulse Generator theta ea Gp ea2 theta_2 Difference equations Linear model Utilizing the rising edge triggered subsystem block to emulate an interrupt driven service routine, students can now simulate their difference equations against Pulse Generator1 the linear and nonlinear model at a theta ea Ea theta specified sample time. ea2 theta_2 fcn Difference equations Nonliner model (Embedded MATLAB function)1 Figure 3: SIMULINK simulation process to promote confidence in control algorithmFigure 4: Rabbit SBC controlling fluid tank system

Citation
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Feemster, M. G. (2013, June), A Systematic Approach for Development and Simulation of Digital Control Algorithms using SIMULINK Paper presented at 2013 ASEE Annual Conference & Exposition, Atlanta, Georgia. 10.18260/1-2--19133

TY  - CPAPER
AB  -     A Systematic Approach for Development and Simulation of Digital                 Control Algorithms using SIMULINK                                                    I. ABSTRACTWith much of the department’s faculty research aligned with autonomous aerial, ground, marine, or underwatervehicles, students tend to emulate these areas by proposing related capstone projects (see Figure 1 for samplestudent driven projects).                           Figure 1: Student autonomous (a) aerial (b) ground (c) marine vehicleSince these vehicle related projects are developed for outdoor operation, the utilization of a micro-processor for lowlevel control algorithm implementation is frequent. In direct response to the numerous vehicle driven projects, acustom, inertial measurement unit (IMU) has been developed by our Technical Support Division based around theRabbit single board computer (SBC) (see Figure 2).                                       Rabbit SBC      3-axis gyro/accelerometers                        Magnetic compass                GPS receiver underneath board                         Figure 2: (a) WSE IMU (b) IMU integrated in autonomous surface vesselWith the development of the above IMU board, measurement of the vehicle state (position, heading, and associatedvelocities) is greatly simplified. As a result, students need only to focus on the calculation of the proper actuatorcommands to control/steer the vehicle within a C like software environment (Dynamic C). However from review offinal capstone reports and attendance of presentations, students expressed having major difficulties whenimplementing even simple PID based control algorithms. This difficulty in C based implementation seems surprisingin light that all students are required to take a two hour lab based course dedicated to the design and implementationof control algorithms on the Rabbit single board computer. Specifically this course targets the design of classicalcompensators KGc s  for a typical DC motor with implementation of the algorithm on the Rabbit SBC. Theconversion of the continuous time compensator to the corresponding digital compensator KGc z  is accomplishedvia Tustin’s Transformation (utilizing the c2d command in MATLAB). From the structure of KGc z  , studentssubsequently developed the corresponding difference equations that can now be transferred to the Rabbit SBC forimplementation. The major oversight here is that students did not simulate their difference control equations toverify that the conversion from KGc z  to equations was performed properly. If the control experiments did notperform as expected as compared to the continuous time simulation, students were unsure 1) if there are hardwareproblems (bad connections, improper sensor calibration, etc) or if 2) their control algorithm was not developedcorrectly to difference equations.In response to this observation, this paper will present a sequence within the MATLAB/SIMULINK softwareenvironment (outlined in Figure 3) to provide students with assurance that the structure of their control algorithm iscorrect. Specifically, the recent ability to utilize embedded function blocks (as opposed to previous S-functions)within the SIMULINK modeling environment has facilitated an easy method for verifying digital control algorithms.In addition, these embedded functions allow for simplified execution of non-linear models; therefore, ourundergraduate students can now also better predict experimental performance by simulating against the higherfidelity nonlinear models (as opposed to limiting themselves to linear transfer functions or linear state spacemodels). This paper will also present the translation of the MATLAB difference equations in to the Dynamic Cenvironment for select plants such as the fluid system shown in Figure 4. A student questionnaire will also beadministered this semester to gauge opinion of the process. Responses from this questionnaire will be discussed.                                                                                                        The student must illustrate that KGc s    1                                          KGc                              Gp                                                           ea                                  theta    meets all performance specificationsConstant                             Continuous time                    Linear model                    simulated against the linear plant model                                      compensator                                                                                                        G p s  before simulating against the                                                                                                        nonlinear model contained         in   the                                              KGc                         Ea           theta                                                                                                        embedded MATLAB function.                                                           ea                                  theta                                                                                 fcn                                     Continuous time                   Nonliner model                                      compensator                (Embedded MATLAB function)                                          KGcz                                 Gp                                                           ea1                                 theta1                                   Digital compensator                  Linear model                                                                                                         Once the student is certain that their                                                                                                         continuous time controller is effective,                                                                                                         they then simulate their corresponding                                                                                                         digital controller KGc z  against the                                          KGcz                            Ea           theta                                                                                                         linear and nonlinear model.                                                           ea                                  theta                                                                                 fcn                                   Digital compensator                 Nonliner model                                                                 (Embedded MATLAB function)              Pulse             Generator                          theta               ea                         Gp                                                     ea2                                 theta_2                          Difference equations                    Linear model                           Utilizing the rising edge triggered                                                                                                         subsystem block to emulate an interrupt                                                                                                         driven service routine, students can now                                                                                                         simulate their difference equations against             Pulse           Generator1                                                                                                         the linear and nonlinear model at a                        theta            ea                        Ea          theta                                                                                                         specified sample time.                                                   ea2                                 theta_2                                                                         fcn                    Difference equations                          Nonliner model                                                            (Embedded MATLAB function)1                         Figure 3: SIMULINK simulation process to promote confidence in control algorithmFigure 4: Rabbit SBC controlling fluid tank system
AU  - Matthew G Feemster
CY  - Atlanta, Georgia
DA  - 2013/06/23
PB  - ASEE Conferences
TI  - A Systematic Approach for Development and Simulation of Digital Control Algorithms using SIMULINK
UR  - https://peer.asee.org/19133
DO  - 10.18260/1-2--19133
ER  -