Science topic

# Control Systems Engineering - Science topic

Control engineering or control systems engineering is the engineering discipline that applies control theory to design systems with desired behaviors.
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Hello, I have a PWM signal having a variable frequency. I need to remove high frequencies from PWM. For example, I want to stop frequencies above 20kHz and can pass frequencies below 20kHz. Any idea how to design this technique in MATLAB Simulink?
Thank
Yes, you can use a Triggered Subsystem in MATLAB Simulink to implement a low-pass filter on a PWM signal. The Triggered Subsystem allows you to execute a block of Simulink model when a specific condition is met, which in this case would be the PWM signal exceeding a certain frequency threshold.
A high-level overview of how you can design this technique in MATLAB Simulink is:
1 - Generate the PWM signal: Start by generating the PWM signal that you want to filter. You can use appropriate blocks or functions in Simulink to generate the PWM waveform based on your requirements.
2 - Measure the frequency: Use a frequency measurement block or algorithm to measure the frequency of the PWM signal. This could be achieved using techniques such as zero-crossing detection or FFT analysis.
3 - Compare with the threshold: Compare the measured frequency with the desired frequency threshold (20 kHz in your case). You can use a Comparison block or an if-else condition to make this comparison.
4 - Triggered Subsystem: Inside the Triggered Subsystem block, design the low-pass filter. You can use standard Simulink blocks, such as a Discrete-Time Integrator and a Discrete-Time Transfer Function block, to implement a simple low-pass filter. Adjust the filter parameters based on your desired cutoff frequency.
5 - Connect the subsystem: Connect the output of the Triggered Subsystem to the appropriate output in your Simulink model, so that the filtered PWM signal can be utilized for further processing or analysis.
6 - Configure the Trigger: Set up the trigger condition for the Triggered Subsystem. In this case, the trigger condition would be the comparison result from step 3.
7 - Simulate and analyze: Simulate the Simulink model and observe the filtered PWM output. Verify that the frequencies above 20 kHz are effectively attenuated while the frequencies below 20 kHz are passed through.
It's important to note that the specific details of your implementation may vary depending on your PWM signal source, sampling rate, desired filter characteristics, and any other additional requirements. Experimentation and fine-tuning may be necessary to achieve the desired filtering behavior.
By utilizing the Triggered Subsystem and appropriate filter blocks, you can implement a low-pass filter on a PWM signal in MATLAB Simulink, removing high frequencies above the specified threshold while allowing frequencies below it to pass through.
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Background:
In control theory we often develop new methods for analysis or controller/observer/filter design and usually evaluate them with numerical simulations. In many papers only a few selected examples are considered.
I think it would be desirable, if there was a catalogue of potential example systems which contains a variety of system models from one could select those which are suitable for a specific use case. A colleague and I are working on such a catalogue (see https://ackrep.org for more information).
After establishing the framework, a basic ontology ("Ontology of Control Systems Engineering") and some preliminary examples (e.g. cart pole system, Brockett integrator, some PDEs and DAEs), we now look for more content. Another colleague recommended http://www.compleib.de/ which contains > 100 linear state space systems.
I am also aware of some other small collections of nonlinear/mechanical systems (available only as PDF file) such as :
Differential Flatness of Mechanical Control Systems: A Catalog of Prototype Systems, 1995 Murray, Rathinam, Sluis
Question:
Are you aware of other catalogues or collections of dynamical systems? Preferably, the equations (and potential metadata) are available in a machine actionable format, but this is optional.
With respect to electric motors / drives, we have collected a database of 500+ different parameter sets describing the first principle dynamics of permanent magnet synchronous motors which are publicly available here: https://github.com/upb-lea/meta_RL_PMSM
The parameter set originates from real-world, industry grade motor series. In addition, we offer an upsampling scheme to produce additional ‘artificial’ parameter sets if desired.
For simulation, the parameter sets can be loaded and processed using the following framework: https://github.com/upb-lea/gym-electric-motor
Although this model set only describes one specific kind of ODE structure, the dynamics of the covered motors (from few watts to hundreds of kilowatts) varies strongly.
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I hope this message finds you'll well. My name is Onyero Walter Ofuzim. I am reaching out to express my interest in collaborating in the field of Electrical/Electronic Engineering mainly in Control Systems Engineering, Dynamic Networks, Machine Learning, IoT, and/or Robotics.
I am deeply passionate about these areas and have been actively involved in research and projects related to them. I firmly believe that collaborating with others in this field will not only increase my chances of getting into a foreign-funded Masters or Ph.D. program, which is my ultimate goal but also help drive innovation and advancements in the field.
I am eager to share my ideas and knowledge and learn from others to contribute to the growth and development of these cutting-edge technologies. I am confident that my skills and experience will be a valuable asset to any team, and I look forward to the opportunity to work with anyone who will be nice to have me.
Thank you for considering my request for collaboration. I look forward to hearing about a possible invitation.
Feel free to explore my profile as I am optimizing it to make my chances high.
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I admitted as an undergraduate to multiple universities in Arizona and Colorado! I have been actively looking for admission to the university to continuously prepare me as an investigator/innovation scientist in mineral exploration by building my foundational knowledge in metallurgy, chemistry, control systems engineering, geochemistry, geophysics, etc. These might be included in my coursework. My focus may be on "control system engineering" compared to "geoscience," as I want to spend my effort investigating sensor innovation using metallurgy, geophysics, chemistry, etc. for mineral exploration. Precisely, investigative research will be on creating "detection technology for purposing of Mining exploration and extraction" So, I'm confused with two queries: 1. Which university would be the best option based on my research interests? 2. Which major and region for internship/ real time research job corresponds to what I'm actually looking for?
Hope you already understand I’ve applied many universities with getting rejection that didn’t also find exact research team yet I’m looking. Thank you so much.
Dear Saifur Rahman Khan and Al,
lI wish you Happy New Year: success in your spiritual achievement, good health and prosperity for it!
I found the next on the facbook (https://www.facebook.com/USGSVolcanoes):
'A volcanologist is a person who studies volcanoes, but there are many different specialties within the field of volcanology. Which interests you and what steps should you take to achieve your goal? Find out more in #VolcanoWatch.
Earthquakes are one primary tool used to study volcanoes. A volcano seismologist studies the earthquakes that are generated as magma moves through Earth’s crust.
A volcano geodesist studies the deformation, or change in shape, of a volcano caused by the movement of magma and gases beneath the surface. Many features of volcanoes can be studied from space, as well, using satellite sensors. Tools like these provide clues about the state of the volcano.
Geologists and geochemists study the composition of lavas and gases to understand the source and style of the eruption. Measuring gas emissions is especially important, as the vog (volcanic air pollution) caused by toxic volcanic gases can contribute to breathing problems, acid rain, and agricultural problems downwind, especially during long-lived eruptions.
If you are interested in becoming a volcanologist, you’ll need to work toward a bachelor’s degree, preferably in a STEM field (Science, Technology, Engineering, and Math). Volcanologists frequently pursue degrees in geology, chemistry, physics, and/or mathematics, but that is not always the case. Oceanography, computer science, engineering, environmental science are all potential pathways, and the list goes on. Explore different fields to find what interests you most.
After achieving a bachelor’s degree, consider options for advanced degrees like a Masters or Doctorate. Many advanced degree programs in the sciences are funded, meaning tuition may be waived, and you might get a stipend for doing the work. Basically, you get paid instead of having to pay for school, and you gain valuable work experience at the same time.
You might consider working for the USGS or other agencies and companies. You have seen many photos of HVO scientists working during the eruptions of Mauna Loa and Kīlauea. The National Park Service also offers a variety of positions for people with either bachelor’s or advanced degrees, such as park geologists, archaeologists, botanists, guides, interpretive rangers, and law enforcement rangers. Science writing and journalism are also excellent ways to explore the excitement of volcanology, natural disasters, and cutting-edge science, while encouraging those passions in others. Similarly, eco- and geo-tourism are great ways to get close to the action and work outdoors, while also meeting, educating, and inspiring people from all over the world. Careers in emergency management will have you helping people stay informed during crises.
Check out usajobs.gov for positions within the federal government. There is even a special section for students and recent grads.
#MaunaLoa is not erupting. Webcam imagery shows weak, residual incandescence intermittently in the inactive Northeast Rift Zone fissure 3 lava flow at night. Seismicity remains low and ground deformation rates have decreased. Sulfur dioxide (SO2) emission rates are at background levels. For Mauna Loa monitoring data, see: https://www.usgs.gov/volcanoes/mauna-loa/monitoring-data.
#Kilauea is not erupting. Lava supply to the Halemaʻumaʻu lava lake in Hawai‘i Volcanoes National Park ceased on December 9. Sulfur dioxide emission rates have decreased to near pre-eruption background levels and were last measured at approximately 200 tonnes per day (t/d) on December 14. Seismicity is elevated but stable, with few earthquakes. Over the past week, summit tiltmeters recorded several deflation-inflation (DI) events. For Kīlauea monitoring data, see https://www.usgs.gov/.../past-week-monitoring-data-kilauea.
There were three earthquakes with 3 or more felt reports in the Hawaiian Islands during the past week: a M3.3 earthquake 14 km (8 mi) S of Fern Forest at 7 km (4 mi) depth on Dec. 27 at 4:33 a.m. HST, a M3.4 earthquake 7 km (4 mi) WSW of Volcano at 2 km (1 mi) depth on Dec. 24 at 8:31 p.m. HST, and a M2.5 earthquake 1 km (0 mi) S of Mountain View at 11 km (7 mi) depth on Dec. 24 at 9:57 a.m. HST.
In the photo, an HVO technician adjusts a volcanic gas analysis instrument that was specifically designed for this Unoccupied Aircraft System (UAS) unit, which carries three one-liter analysis bags. The instrument transmits gas concentration information in real-time during the flight at Kīlauea summit. USGS has special use permits from the National Park Service to conduct official UAS missions as part of HVO's mission to monitor active volcanoes in Hawaii, assess their hazards, issue warnings, and advance scientific understanding to reduce impacts of volcanic eruptions. Launching, landing, or operating an unoccupied aircraft from or on lands and waters administered by the National Park Service within the boundaries of Hawai‘i Volcanoes National Park is prohibited under 36 CFR § 1.5 - Closures and public use limits.
USGS image taken January 14, 2022 by M. Warren.
#USGS #HVO #HawaiianVolcanoObservatory'
Regards,
Laszlo
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With this question, I want to know that proper systems exist? or they are just theoretical systems?
Hi Marco, you have already received good answers, all complementary, check Silvano Meroni and Yew-Chung Chak 's responses.
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How long does it take to a journal indexed in the "Emerging Sources Citation Index" get an Impact Factor? What is the future of journals indexed in Emerging Sources Citation Index?
Clarivate announced that starting with 2023 ESCI-indexed journals will also be assigned an impact factor. See: https://clarivate.com/blog/clarivate-announces-changes-to-the-2023-journal-citation-reports-release/
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In his name is the judge
Hi everyone
In order to use controller for structure with absorber, have to connect matlab and opensees in real time :
it means in each loop in opensees data must send to matlab and then matlab do some prossess with controller like fuzzy then send back data to opensees
Relying on researching and consulting the only way is use hybrid simulation (like openfresco),
do you have any other idea or way to connect these two programs without using openfresco?
Translation results
star_border
Consult
Wish you best.
Take refuge in the right.
Use TCP/IP communication.
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I already saw some examples of GA (genetic algorithm) applications to tune PID parameters, but I (until now) don't know a way to define the bounds. The bounds are always presented in manuscripts, but they appear without great explanations. I suspect that they are obtained in empirical methods.
Could Anyone recommend me research?
Dear Italo,
In general, the bounds selection is made empirically because the "suitable range" of a PID controller is problem-dependent. The way I use to select the bounds is: 1. I tune a PID controller that produces a stable response to the closed-loop system. Then, 2. I choose a range around this "nominal" value large enough such that the GA has still some degree of freedom to search in the optimization space. Finally, 3. if the GA converges, I start decreasing/increasing this range till I got a more or less good behavior of the GA, i.e., the GA doesn't stick in a sub-optimal minimum or so.
If you want to use a more rigorous approach, I would suggest computing the set of all stabilizing PID controllers for the particular system. Then, I would establish the bounds for the GA search space to be the this computed set. In that way, you would search for the optimal controller only within those producing a stable closed-loop response.
Best,
Jorge
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As IEC 61131-3 standard for PLC programming languages defines a few of them, it will be useful to learn what our colleagues apply for PLC programming.
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Does anyone know if I can connect the attached DAQ (CASSY type) to MATLAB real time simulink for controlling purposes?
It depends on your sample frequency, which is limited for performance of DAQ. another issue should be concerned is the number analog of a processing control system. the quality of data will be bad or real-time data might be good if you collect as much data in process as possible.
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Hi
How can i correct this error?? I think it's about matrix dimensions for port e.
Error in default port dimensions function of S-function 'FeedbackLinearization/Controller'. This function does not fully set the dimensions of output port 2
I'm running a simulation based on feedback linearization control method that comes from a paper attached below.
the model is also attached.
Anyone help me, helps a poor student. (if it makes sense lol)
Hi,
file name "sfun_ abcaaaaa.c" is not available in the folder mentioned.
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Assuming that no motion in the normal direction, how would you propose a system of hardware and interconnection as well as the control strategy that will drive the system?
Sounds analogous to an inverted pendulum. Here is one way to construct something with closely similar dynamics. Take a knee (90° angle) connector for sewage pipe, cut it nicely and mount it on a toy car such that the knee is pointing straight upwards. Place a small ball (i.e. from a roll-on bottle) on top of the knee and try to keep it there stably by moving the toy car back, forth, and sideways (hard to do manually without automated feedback control loop). I guess many feedback control schemes would keep the ball at the top of this curve subject to micromotion.
Aside: If the knee was facing down, mounted on a motor, and the ball is placed inside the 90° curve while the motor is rotated at some angular frequency, the resulting dynamics would resemble Mathieu equations whose stability analysis could be checked from Floquet theory. Incidentally, these are the same dynamics exhibited by a single ion trapped in a linear Paul trap.
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Suppose we have a lipschitz nonlinear system with a disturbance input. The disturbance is of decaying exponential like nature with an upper bound known.
System: x_dot = f(x) + g(x)u(t) + d(t)
where, x:state; u(t): control input; d(t): Disturbance input
How can we design nonlinear observer for such system?
Disturbance is sometimes helpful while dealing with multicollinearity. Also helpful may be keeping the number of degrees of freedom minimum.
Maybe you can alernatively consider the recursive least squares algorithm (RLS). RLS is the recursive application of the well-known least squares (LS) regression algorithm, so that each new data point is taken in account to modify (correct) a previous estimate of the parameters from some linear (or linearized) correlation thought to model the observed system. The method allows for the dynamical application of LS to time series acquired in real-time. As with LS, there may be several correlation equations with the corresponding set of dependent (observed) variables. For the recursive least squares algorithm with forgetting factor (RLS-FF), adquired data is weighted according to its age, with increased weight given to the most recent data.
Years ago, while investigating adaptive control and energetic optimization of aerobic fermenters, I have applied the RLS-FF algorithm to estimate the parameters from the KLa correlation, used to predict the O2 gas-liquid mass-transfer, hence giving increased weight to most recent data. Estimates were improved by imposing sinusoidal disturbance to air flow and agitation speed (manipulated variables). The power dissipated by agitation was accessed by a torque meter (pilot plant). The proposed (adaptive) control algorithm compared favourably with PID. Simulations assessed the effect of numerically generated white Gaussian noise (2-sigma truncated) and of first order delay. This investigation was reported at (MSc Thesis):
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Hi!
I have started working on a project "floating sensor networks (FSN) for continuous water quality monitoring". For which I need simulator to measure Like, pH, Turbidity, Salinity, Temperature, DO, EC, etc. Rather than going with real time deployment of FSN for measuring water quality sensors.
Objectives of the Project:
A. Water Quality Measurement
B. Reliable Data Transform
C. Congestion Control
D. Deployment Strategy
E. Energy Harvesting
All objectives should be carried out simulation based. Kindly suggest whether this work will done via simulation design (either partially or whole)
Dear Sarang, did you find any suitable simulation software? We also need it for a small project we are working on
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Hello everyone,
I'm looking for some short courses (not online) in the field of CE (more interested in Automotive control) in Europe.
My field of interests are,
- Robotic Control Systems
- Vehicular Dynamics Control
- Motion Control
- Data-Driven Control
- Optimal Control
- System Identification
- Reinforcement Learning Control Design.
I can participate by Self-Fund but I will be happier if there will be a scholarship or something,
Yours cordially,
A. M.
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We can avoid dq transformation by using PR controller. Why don't we use PR controller in industry? Why do we prefer PI controller?
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it means the oil pump to be sometimes able to turn off during the driving cycle, and if it is possible, how efficient would it be? (more particularly in heavy vehicles like a bus).
It depends upon the size of the accumulator, and the flowrate required. If you calculate the flowrate required for the PAS pump you could work out the accumulator volume required. See link below for typical (but a little old) energy consumption info.
However, many modern vehicles are moving to electric PAS systems, so the traditional hydraulic system may not be required in future.
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I am designing a flight controller for a quadrotor.
At first I am designing a nested/cascaded controller consisting of only proportional controllers Kp . Now, if i tune the rate controller for 10 rad/s cross-over frequency, what should be the cross-over frequency for the angle, velocity and then the position loops. Also, what else do i need to know while designing a flight controller for practical implementation purposes?
Secondly, How do we implement a own flight controller such as observer based via arducopter?
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I am trying to discretize a continuous time state space model using the following code
s=tf('s');
G=1/(Iyy*(s^2))
Gs=ss(G)
Gd=c2d(Gs,0.01,'zoh');
Now, when i use this discretized model 'Discrete State-space Model' in simulink, my close loop system goes unstable. Same is happening with observer, like discretized observer is making close loop system unstable. Can someone help me here?
Your system is basicly a double integrator, so a borderline stable system. If you look at your phase value of the bode plot for the continious system (bode(G)), you will see that it has a phase of -180° over all frequencies. Since any kind of delay causes the phase of a system to drop, if you introduce an arbitrarily small amount of delay on your continious tf G, and use the command "margin(G)", you will find that your system will always have a negative phase margin. And since discretizing will always introduce delay into your system, closing the loop on it will automatically destabalize it. You can use 'tustin' as you discretizing method, which essentialy uses trapezoidal integration, a more stable integration algorithm, and simulink should probably get your discrete system stable this way.
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Optimal control and nonlinear control system.
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Consider a system with relative degree two with respect to a chosen sliding output function s. If twisting controller is applied for control, what are the expected drawbacks in control performance and steady state behaviour? You may consider that $s$ and $\dot{s}$ is available.
1. Historically twisting have been designed to substitute a discontinuous controller with Lipschitz continuous one keeping the finite-time theretically exact convergence to the sliding output for the systems with relative degree one affected by Lipschitz perturbaitons(see Levant A. IJC, 1993 https://www.tau.ac.il/~levant/slorder93.pdf).
The only adavantage of the twisting controller is that if this algorithm is applied for the systems with relative degree two it ensures theoretically exact finite-time convergence of the sliding output and its derivative to zero in finite-time.
But from the viewpoint of chattering the twiating controller is the worst one because his gains are at least twice bigger, than the upper bound of uncertainties.
Moreover, the amplitude of chattering produced by twisting controller is bigger than the amplitude of chattering produced by relay controller with a linear sliding surface see attached file, table 3
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PID controller is reportedly widely built and used in control systems engineering for industrial applications. The PID-controller has a transfer function as: (Kd*s^2+Kp*s+Ki)/s.
Therefore, it seems such a transfer function box, could be built in terms of an electronic circuit component.
Meanwhile, the order of an observer-based controller is higher than a PID-controller, as for example you see in the snap-shot from Ogata control engineering book, attached. Since Ogata is a practical engineering text-book, therefore I guess such an observer-based controller could be practically built as an electronic circuit and then embedded as a controller.
Moreover, we usually build transfer function blocks, simply in Matlab Simulink. But is it possible, practical, simple, and convenient to build such blocks as an integrated electronic element in a circuit, while they are of high order?
My main question:
There is a controller, with a transfer-function:
H_controller(s)=N(s)/D(s),
Where:
N(s)=b0*s^m+b1*s^(m-1)+b2*s^(m-2)+…+bm,
And:
D(s)=a0*s^n+a1*s^(n-1)+a2*s^(n-2)+…+an.
Moreover, m=10, n=10, or, n=11.
The digested question:
Is it possible, and practical to design an electronic circuitry for a box, with the transfer function: H_box=H_controller(s)=N(s)/D(s)?
Warning: I have no experience to build a real electronic circuitry, and my question is only the possibility and practicality of designing a circuit for such a transfer function box. Do not mind about the performance of the controller or any other stability concern with regard to that. Only the possibility and practicality of designing an electronic box which has an equivalent transfer function: H_box=H_controller(s)=N(s)/D(s).
The box is in feed-forward path.
The transfer function H(s)= N(s)/D(s)
has the form of filter characteristics.
Such general transfer characteristics has zeros and poles.
The filter which contains zeros and poles are elliptic filters.
Such filters can be implemented by using op amps+ discrete RC elements
They can be built completely integrated using switched capacitor filters
They can be also implemented by using gm-C filters.
For such filter design using active filters please follow the reference: https://www.sciencedirect.com/book/9780750675475/analog-and-digital-filter-design
Bestwishes
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I want to know that we have a real system with fractional order state space model
Dear Professor Sabatier
First, I'd like to thank you so for asking these kind of challenging questions. These kinds of questions are very important for advancing this field. As you said, our life is full of doubts. Now this question arise that: How can we trust to different integer differential models? The only sin of fractional derivative is that it has been introduced after integer derivative. Why should we accept that the first derivative (u') denotes the velocity? Why another fractional derivative (such u^{0999}) is not?
As we can check in many considerable works, fractional derivatives modify many old results in integer derivatives. As you said, you often use fractional models to build and implement very physical and useful systems (eg: battery state observers, hydrogen generator, ...). We need a comparison in study of these different natural phenomena and so a standard basic theory for the comparison which is usually integer derivative models while we can doubt it. I fee that we could improve our initial mental attitude. Again, I appreciate you.
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I'm studying digital control by myself, and I would like to know if has available on the internet the solutions manual of "Digital Control of Dynamic System 3rd edition"?
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For example, the first order Laplacian measures the difference between the local and average values of a quantity in an infinitesimal neighborhood of the point in question. So, for a flexible string, the acceleration is proportional to the Laplacian (wave equation).
For plates, the acceleration is proportional to the double Laplacian. Also, the double Laplacian occurs in the modification of the wave equation for a stiff string. Therefore, what is the double Laplacian a measure of? Thanks.
We have:
Applications of Double Laplace Transform to Boundary Value Problems DOI: 10.9790/5728-0925760
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I only have acces to historical data recorded over the course of a few years. However the data is of a closedloop proces that has already been tuned with PID. The values of P, I and D are known.
How can I determine the openloop transferfunction usign only this data?
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Why the results are not optimal?
difficult to infer all performance values? why
1- PID Tuning of Plants With Time Delay Using Root Locus
Greg Baker ,San Jose State University
2- A revision of root locus method with applications
September 2015, Journal of Process Control 34:26-34, DOI: 10.1016/j.jprocont.2015.07.007
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Is it theoretically possible, that after discretization by using Talyor Series Expansion, a non-observable nonlinear system will became an observable?
It was proved, that used continuous model of PMSM is non-observable (see attached). I want to know, if resulting discrete system is observable or not. Any comment appreciated. Thanks.
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the dc-dc converters has two transfer functions , control to output and line to output TF. which one is used when design a controller? and which one is used to test step response?
I agree with Aparna Sathya Murthy
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How can I implant ANFIS as a controller in MATLAB/SIMULINK simulation for sit to stand movement supported with functional electrical stimulation in paraplegics. I think it will be inverse dynamic model and I should use model base controller
Best regards
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I'm a beginner in control engineer, what books or websites you could recommend?
T. Bauer, J.T. Betts, W. Hallman, W.P. Huffman, K. Zondervan, Solving the optimal control problem using a nonlinear programming technique, Parts I and II, 1984.
A.E. Bryson Jr.Optimal control – 1950 to 1985
IEEE Control Systems (1996),
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Suppose a six degree of freedom simulation of an aircraft, which some aerodynamic parameters (e.g: stability derivatives), mass configuration (e.g center of mass) and etc, are randomly choose within known bounds. From the Monte Carlo sample those simulations are split in two groups: with instability (any time during the simulation) and without instability during the flight.
My question is, How could I find the more important combination of random parameters the caused the instability in flight?
I have already done a sensitivity analysis, so I have an idea how each one influence individually. What I really one to find is how the combination of parameter is causing the instability.
For more details, we have:
Monte Carlo Simulation of Real Dynamic Systems :
Best regards
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Hi every one,
here I have a problem in MATLAB, when I want to solve the following equation, relative to PI in the photo, or tau in the code, MATLAB will send me this error: Warning: Unable to find explicit solution. For options, see help.
I attached the question and the code below (in code, I rewrite pi in the photo with tau).
If you have any idea to solve this problem, analytically or numerically, I will be happy to hear it out.
NOTE:
> PI_0.1(X,t) = tau
> X = [x(t),y(t),psi(t)]^T;
** PROBLEM: Find tau in terms of X and t in which solve the mentioned equation.
Arash.
code:
______________________________________
______________________________________
clc;clear;
syms x y psi tau t
c1 = 1;c2 = 1.5;lambda = 0.1;
x_r(tau) = 0.8486*tau - 0.6949;
y_r(tau) = 5.866*sin(0.1257*tau + pi);
psi_r(tau) = 0.7958*sin(0.1257*tau - pi/2);
x_r_dot = 0.8486;
y_r_dot(tau) = 0.7374*cos(0.1257*tau + pi);
psi_r_dot(tau) = 0.1*cos(0.1257*tau - pi/2);
phrase1 = c1/2*(cos(psi)*(x - x_r) + sin(psi)*(y - y_r))*(cos(psi)*x_r_dot + sin(psi)*y_r_dot);
phrase2 = c1/2*(-sin(psi)*(x - x_r) + cos(psi)*(y - y_r))*(-sin(psi)*x_r_dot+cos(psi)*y_r_dot);
phrase3 = 0.5*(psi - psi_r)*psi_r_dot;
eq = -2*(1-lambda)^2*(phrase1 + phrase2 + phrase3) - 2*lambda^2*(t - tau)
sol = solve(eq == 0 , tau , 'IgnoreAnalyticConstraints',1)
______________________________________
______________________________________
Pass x, instead of tau, as rightly pointed out by Saeb AmirAhmadi Chomachar
syms x y psi tau t
c1 = 1;c2 = 1.5;lambda = 0.1;
x_r(tau) = 0.8486*tau - 0.6949;
y_r(tau) = 5.866*sin(0.1257*tau + pi);
psi_r(tau) = 0.7958*sin(0.1257*tau - pi/2);
x_r_dot = 0.8486;
y_r_dot(tau) = 0.7374*cos(0.1257*tau + pi);
psi_r_dot(tau) = 0.1*cos(0.1257*tau - pi/2);
phrase1 = c1/2*(cos(psi)*(x - x_r) + sin(psi)*(y - y_r))*(cos(psi)*x_r_dot + sin(psi)*y_r_dot);
phrase2 = c1/2*(-sin(psi)*(x - x_r) + cos(psi)*(y - y_r))*(-sin(psi)*x_r_dot+cos(psi)*y_r_dot);
phrase3 = 0.5*(psi - psi_r)*psi_r_dot;
eq = -2*(1-lambda)^2*(phrase1 + phrase2 + phrase3) - 2*lambda^2*(t - tau);
eqn = rewrite(eq,'log');
sol = solve(eqn == 0 , x , 'IgnoreAnalyticConstraints',1);
pretty(sol)
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I want to know the exact definition of these four tests and I am wondering which of them could work in real time?
HIL or 'hardware-in-the-loop' testing is by its very nature a resource-hungry solution to testing, requiring multi-skilled teams able to set up and configure both the execution platform and the I/Os as well as the modelling environment.
Once your model is verified (i.e., MIL in the previous step is successful), the next stage is Software-in-Loop(SIL), where you generate code only from the Controller model and replace the Controller block with this code.
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I have the nonlinear systems of Khalil, however some definitions are no so clear, is there a newer book with Matlab examples
For Video tutorials , we have:
Introduction | Nonlinear Control Systems: https://www.youtube.com/watch?v=Xgnwn0G9qoo
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Hello everybody
Despite a few TMD cost models available in the literature, I am searching for more accurate initial and lifetime cost models of translational TMDs for Life Cycle Cost Analysis (LCCA) of TMD-equipped structures.
In fact, the provided cost model affiliated with one of the companies designs and manufactures transitional TMD (such as LeMessurier CO.), which this model consists TMD initial cost (construction and installation of the TMD) and TMD damage cost (maintenance and repair losses of TMD before structural collapse)
The effectiveness of tuned mass dampers (TMDs) in reducing the seismic response of civil structures is still a debated issue. The few studies regarding TMDs on inelastic structures indicate that they would perform well under moderate earthquake loading, when the structure remains linear or weakly nonlinear, while tending to fail under severe ground shaking, when the structure experiences strong nonlinearities. TMD seismic efficiency should be therefore rationally assessed by considering to which extent moderate and severe earthquakes respectively contribute to the expected cost of damages and losses over the lifespan of the structure.
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I design feedback close loop system with a robust static feedback controller using Hinf approach where control low is u(t)=Kx(t). What is the good method to show robustness for this type of system? What plots we can make to show robustness for designed system?
Regards
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How does one usually evaluate the robustness of a controller?
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Dear community,
I am trying to build a model of a Furuta pendulum in Simulink/Simscape. Unfortunately, when I try to linearize my model with the integrated Model Linearizer, I get an unexpected result. The evaluation of the linearized system shows, that it is only poorly controllable, although a classic Furuta pendulum should be fully controllable according to literature. Therefore I assume, that there must be something wrong with my model or the way I linearized it but I can´t figure out what it is.... I´d highly appreciate any help on that, as this is bothing me for quite some time now. The model is attached to this post. Furthermore I have attached a screenshot of the linearized system.
My controllability matrix (ctrb(A,B)) then looks like this with rank = 1, which I believe can´t be right...
Controllability matrix =
1.0e+26 *
0 0.0000 0.0000 -0.0000 0.0000
0.0000 0.0000 -0.0000 0.0000 -0.0007
0 0.0000 0.0000 -0.0000 0.0000
0.0000 0.0000 -0.0000 0.0000 -0.0015
0.0000 -0.0000 0.0000 -0.0000 9.2972
Thank you and best regards, Joo
Dear Joo ...
Regards
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Hello everyone, I hope you have a good day,
As we all know, the lateral dynamic system of vehicles has two output, lateral error and heading error, and we have one input, which is steering angle, I always have one big problem:
How to Design a Controller to have zero steady-state error, when I have XY reference path?
I designed a controller to track the heading, but when the vehicle gets departed from the path, as it does not have any sense of lateral error, it will not come back to the path, it will just follow the heading with some offset.
I read a lot of papers in this area, but none of them talked about XY reference paths.
I add a photo to clear up some points, please check the attached file.
Arash
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I'm writing my thesis and I am searching for good software to draw control block diagrams!
Any suggestion?
Thank you!
Tableau Desktop is also good one for drawing the scientific illustrations.
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.
Discrete-Time Systems:
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I want to find PID parameters to regulate my system.
Manual PID tuning is done by setting the reset time to its maximum value and the rate to zero and increasing the gain until the loop oscillates at a constant amplitude. (When the response to an error correction occurs quickly a larger gain can be used.
The best method for tuning PID controller parameters is depend of your system
Regards
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I want to know all the things related and necessary which help me in control system field.
You can use control methods in everywhere. Below, there are some areas:
1. Power systems (smart grid , micro-grid , power generation , power devices (motors,...))
2. Electrical drivers for electrical motors
3. Biological systems
4. Economic systems
5. Social systems
6. Robotics
7. Aerospace and aeronautical systems
8. Automobile industry
9. Chemical Process
10. Multi agent systems
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Hello everybody
I would like to link two topics, LCCA and BIM, each of which deals with "structural and earthquake engineering" and "construction management" in civil engineering, respectively.
I am trying to investigate on LCCA of a structure equipped with Tuned Mass Dampers (TMDs) based on principles of Performance Based Earthquake Engineering (PBDE) for different seismic hazard levels (this issue is related to structural engineering). So I intend to use BIM to create a more realistic cost model including other costs are related to this topic.
I suggest that you use the 5D BIM technology, which is related to the cost of construction elements. You need to model your project using software as revit, and then link the model's elements to the cost and time schedule using software like Naviswork. This will give you visualization for the construction phases and the project life cycle.
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In order to get a better conditioned A matrix, the absolute mean of the eigenvalues of the A matrix should be one (all eigenvalues are between -1 and 1, so within the unit circle and the absolute mean is 0.4389). This could be done by scaling the time.
For the following continuous-time state-space model:
dx/dt = Ax(t) + Bu(t)
y = Cx(t)
the state-space model will look like:
dx/dtau = (1/lambda_avg)*Ax(tau/lambda_avg) + (1/lambda_avg)*Bu(tau/lambda_avg)
y = Cx(tau/lambda_avg)
with
lambda_avg, the absolute mean of the eigenvalues of the A matrix
tau, the new timescale
tau = lambda_avg*t
However, I want to scale the time of a discrete-time state-space model in order to get a better conditioned A matrix:
xi+1|k = Axi|k + Bui|k
yk = Cxk
How could I do that in the same way as for the continuous model?
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Hello everybody,
I have observed a bit confusing behavior of my system response (or may be I am missing something).
I have a transfer function in S domain converted to Z domain with a 1kHz sampling frequency at the time of conversion using matlab, When I embed this discrete version of the transfer function to my system which is also sampling on the same frequency of 1kHz. The system works the way as expected (i.e. the step response is the same as that of the s-domain analogue controller).
But if I increase the sampling frequency of my system while using the SAME discrete transfer function that i just converted from s to z domain with a SAME conversion sampling frequency of 1kHz , the step response gets further faster.
My question is that, why the discrete system gets faster response than the analogue one, despite the transfer functions of the analogue controller and the discrete controller are the same.
What I understand, the step response of any transfer function should remain the same in either case (i.e. either the function is in s-domain or in z-domain) the response should be the same ?
Does this mean the digital controllers have the ability to fast the response of the same transfer function by changing the sampling frequency of the system?
It is important, not to confuse the system sampling frequency of my u-controller at which the u-controller is collecting the samples from ADC, with the sampling frequency that I used as a parameter required to convert the s-domain transfer function to z-domain transfer function.
I thank you all for your time.
Regards,
Iftikhar Abid
The conversion from the S-domain to the Z-domain can be accomplished by using the bilinear transformation.
- A transformation for S to Z
S= (Z-1) /(Z+1)
- And frequency prewarping
w analog = tan wd/2,
where wd= 2 pi f/fs
As one sees if one changes fs , one has to change w analog as a consequence of prewarping.
Best wishes
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Would anyone help me to understand the difference between energy signals and power signals (with examples to each of them), and what is the physical intuition behind the relation between the auto-correlation function of a signal and its power spectrum density?
When the energy of a signal is finite, but power is zero, such a signal is called energy signal. for example- a pulse has a finite energy, though power is zero.
On the other hand, if the energy of a signal is infinite, but it has a finite power, it is called as power signal., for ex- sinusoid is a power signal.
The auto-correlation function is simply the convolution of the signal with itself (not flipped), where delay/lag is the parameter. Here we try to find how much a signal overlaps with itself when lag parameter is varied over time. Its Fourier transform is power spectral density, which also does the same thing in frequency domain. So, at t=0, the auto-correlation function provides the energy or power of the signal x(t). (based on whether x(t) is a power or energy signal) which is same as the power in frequency domain obtained by integrating power spectral densities for all frequencies.
so, basically, both tell the same thing, one with respect to time, other with respect to frequency.
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I want to start to work on some stepper motors bipolar with arduino mega and ramps 1.4 but I don't know how to do it. Can anyone explain how to do this?
I don't understand exactly what you mean? What is your goal? What do you want to do?
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The specifications are in term of R, L, B, J, kv, kt
The max output force of  electromechanical  braking system is 3500N
Hi, I initially face a same problem in my research. It solved :)
Kindly refer my publication attached.
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What is the typical pitching speed of modern MW turbine blades and do this blades pitch fast enough compared to changing wind speeds?
Significantly very fast. Standing at the control panel of a Vestas 850 kw , I saw the display was showing the instantaneous power production and pitch angle. The display was updating either every second or half second and each reading gave different readings. so a time constant for the pitch of under a second, for 40 m blades is astonishing!
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I have a brushless gimbal motor (with 12N14P windings) whose rotor shaft position is measured by means of a high-resolution absolute optical encoder. (The motor has no hall-sensors)
The amount of current fed through the three field windings are independently controlled by 16-bit DACs. (i.e. not just PWM)
What control algorithm should be used to implement precise position control of this closed-loop system, and what auto-tuning technique should be employed?
I "think" that the 12N14P winding scheme means that one full rotation of the field winding signal produces one 1/14 of a mechanical rotation. (but I could be mistaken).
It is not known what the physical angular offset relationship is between the field windings inside the motor and the zero-datum of the absolute optical encoder attached to the rotor shaft. I suspect that the auto-tuning technique will need to perform an experiment to determine this angular offset if the control algorithm is to be able to produce a field vector that leads the desired position by 90 degrees to achieve maximum torque.
From the IMU we get position and velocity after sensor funsion. The input variable of the plant seems to be the speed of the gimbal motor (since its driven by 3 sine waves), not the voltage as usual in a brushed dc motor setup. So one can not just implement a torque control for holding the position. When I investigated the Storm32BGC, it looks like the PID does influence the position and the speed at the same time: Fast movements leads to fast speed corrections, but also the deviation from the stationary position leads to a given speed.
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On what parameters the selection of continuation method depends ?
We have proposed a numerical method (denoted as MEM) for solving the
Nonlinear Dynamic problems. If you would like, you can view our published articles in this field entitled "dynamic analysis of SDOF systems using modified energy method". By the way, the presented idea is also generalized to MDOF systems in another study, which is available on my research-gate account.
Regards,
Jalili
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To design a controller for multi-degrees of freedom actuators which type of controller is better (Sliding Mode Controller or Backstepping Controller)?
There are 4 issues I have seen in this discussion:
1. Backstepping can compensate theoretically exactly only uncertainties decreasing together with the state variables. No comparison between backstepping and SMC in this sense.
2. Matched and unmatched uncertainties
For perturbed chain of integrators there are no unmatched perturbations. If you will differentiate the output till the system order all the perturbations will be matched! That is why the only reasonable to control the systems with unmatched uncertainties is a combination between backstepping and SMC, where backstepping compensates state dependent part and SMC(see Estrada et al IJRNC,27(4),2017,DOI : 10.1002/rnc.3590,Automatica 2010(11), TAC 2010(11), J. Davila TAC 2013, Ferreira et al Journal of Franklin Institute, 2014, 351(4),doi:/10.1016/j.jfranklin.2013.12.011, Automatica, September 2015, Vol. 59, 10.1016/j.automatica.2015.06.020)
3. SMC can not be smooth. Sliding mode (for definition!) is a motion on the sliding surface!
4. Chattering
4.a. There is no way to keep the sliding mode and eliminate the chattering.
4.b. It is wrong opinion that it continuous HOSM controllers (like super-twisting, Kamal et al DOI:10.1016/j.automatica.2016.02.001, Torres et al doi :10.1016/j.automatica.2017.02.035, Laghrouche et al TAC,2017) everytime produce less chattering that discontinuous ones (see https://www.researchgate.net/publication/317229996_Is_It_Reasonable_to_Substitute_Discontinuous_SMC_by_Continuous_HOSMC).
It is true for the systems with fast actuators only.
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Where can one get measurement data for ieee 34 bus radial distribution system ?
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I am making a small prototype, that consist of small compact size aerostatic bearing with active compensation. I have to control eccentricity of shaft by using active compensation. For this purpose I need a laser sensor to measure shaft eccentricity that varies from 0 to 100um. one possible suggestion is to use laser sensor of omron company but problem is that my current location is china and omron company said it will take you 5 month to receive it. Please suggest me some other possible ways so that I can finish it before time
If you want non-contact sensor, then proximity displacement sensor such as Bentley Nevada proximity sensors and Omega non-contact sensors can be used, they are cheaper than Laser sensors and have excellent accuracy:
If contact is permissible then you have wider options and LVDT sensors can be used, they have good accuracy and cheaper pices:
or search google or alibaba for LVDT sensor
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the coefficient of the plant should satisfy what kind of requirement ? and can you give some exampled?
It is generally difficult to stabilize unstable high-order non-minimum phase plants with the 'ideal' PID controller. Take Lakshmanaprabu's model as an example, which has a real pole and a real zero in the right-half plane:
Gp = (5⋅s − 1)/(16000⋅s4 + 41200⋅s3 + 2940⋅s2 − 152⋅s − 5).
It is possible to stabilize the plant with a cascading compensator
Gc = k1 − (k4⋅s2 + k3⋅s + k2)/(s3 + N3⋅s2 + N2⋅s + N1)
where
k1 = −4.4690e+04
k2 = 4.9923e+04
k3 = −2.6980e+05
k4 = 1.1096e+05
N1 = −1.1172
N2 = 6.0334
N3 = −2.4079
The closed-loop transfer function (Gc*Gp)/(1 + Gc*Gp) is a 7th-order system:
Gcl = (−2.235e+05⋅s4 + 2.793e+04⋅s3 + 4190⋅s2 − 139.7⋅s − 5.586) / (1.6e+04⋅s7 + 2674⋅s6 + 270.4⋅s5 + 17.88⋅s4 + 0.8151⋅s3 + 0.02545⋅s2 + 0.0004759⋅s + 4.249e-06),
which has two real zeros in the left-half plane and another two real zeros in the right-half plane. Cancelling the two real zeros in the left-half plane with a pre-filter
Gf = 4.249e-06/(s2 + 0.125⋅s + 0.0025)
applied to the input command outside of the feedback loop yields Gclf = Gf*Gcl
Gclf = (−5.934e-05⋅s2 + 1.483e-05⋅s − 5.934e-07) / (s7 + 0.1671⋅s6 + 0.0169⋅s5 + 0.001118⋅s4 + 5.094e-05⋅s3 + 1.59e-06⋅s2 + 2.974e-08⋅s + 2.656e-10)
Computing the DC gain of Gclf (−2234.5) and placing a reference scaling factor "1/dcgain(Gclf)" ensures the unity gain when a unit step input is applied.
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Hi,
Does someone have any experience of using PSVM for fault detection?
Thank you for the information
Dear Faeze Sdi,
Why proximal SVM are you using? You may try other algorithms for fault detection.
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Hello,
hoping that you will be in good health,
i have a 7-DOF independent wheel drive electric car model can be linear/nonlinear with longitudinal velocity, lateral velocity, yaw rate and angular rotation of the four wheels as the states of the system. the input to the system is the torque of each wheel .
i already designed a controller linear(LQR)/ nonlinear(SMC) which will turn the car with 90 degree yaw angle.
i want to find the trajectories/conditions that will achieve the control objective in minimum possible time/distance and minimum possible yaw rate, its kind of optimization "i think" can you please suggest any method or technique for doing this problem, or any starting point, i am using MATLAB/SIMULINK for my simulation ....
actually i am following the work done in this paper but they used some other tools for there work.
You can find a fully developed 14-DOF vehicle model in MATLAB with a time efficient suspension model and a reprogrammed full set MF tire model in https://arxiv.org/abs/1803.09411, in addition, this work formulated and solved the complicated optimal design and control problems of a 4-IWD electric race car on a given track in curvilinear coordinate system.
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Dear all;
1: I used SVM to fault detection, now I want to figure out effect of fault in 10 seconds time slot of 60 seconds such that I have a window of data with 10 seconds length like 0-10 seconds,0.005s-10.005 s, 0.01s -10.01s ...60s. and I want to use SVM for each 10 s window of data.
I have some data in excel file which is divided to two parts; upper section is normal data and lower section is fault data and I have 6 features. Entirely I have 24002 data. I wrote a piece of code but I'm not sure if it is correct or not and I want to know how can I correct it? 2:I would like to know how can I divide my data to train and test in for loop for each window?
clc;clear;close all;
T=2001; %length of data in 10s (Window Size)
K=(0.5*length(X))-T+1 % Number of repetitions
window=zeros(2*T,6);
for i=1:K
window=[X(i:i+T-1);X(i+12001:i+12001+T-1,:)];
%% Data Normalaization
m=length(window);
Mean_data=repmat(mean(window),m,1);
Std_data=repmat(std(window),m,1);
data_norm=(window-Mean_data)./(Std_data);
end
Dear Jiri Kovar,
I want to create motional time window in order to fault detection in each window.
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Sir,
I am unable to solve second ramp response. I need the derivation with partial fraction.
Thank you
See for paritial fraction i understand u want the values of a b or the way the roots will be arranged it is simple break roots and put s- a or s- b or whatever it be plus also then in one case put the value of one root in such a way the other root becomes zero and u will obtain value of a and b substitute back then take inverse laplace transform will obtain the transfer function in paritial fraction again the expansion of roots like repeated roots the method needs to differentiae the root once u obtaim the first root ur problem would be solved 100 percent by ogata it has detailed explanation modern control theory by ogata
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OpenDSS is a wonderful package, but it is not suitable for simulating some special features of railway traction network, it would be fantastic to have something similar related to Railway power systems. What do you think?
I totally agree with you in that
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I have designed a controller using Integrator backstepping method and that controller is based on Lyapunov Theory. I have a question How I can check stability of resulting controller?
Hi Waheed,
Since you have designed a Lyapunov-based integral backstepping controller for the 4th-order MISO system, what exactly is your difficulty in checking the stability of the control system?
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I want to know if there is any system that needs to operate on different variants (combinations of the P, I, D constants) of PID controller; like it operates on P-only controller first; then switches to PI and then may be to PD or PID alternatively or simultaneously or may be cascaded? Is there any need to have such a system? If yes where and if not why not?
thankyou all.
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I want to ascertain the level of interaction in a MIMO process and I am looking at various ways of doing that. I came across the SVD method in the book by Seborg and I would like to know how efficient it is. Is the relative gain array (RGA) method better than this ?
P.S. - I am asking the question strictly from a control system perspective.
The SVD precoding approach comes from Telatar's seminal work: http://web.mit.edu/18.325/www/telatar_capacity.pdf
He shows that it achieved the MIMO capacity. That paper is very nicely written, so I highly recommend it!
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IMC BASED FRACTIONAL ORDER PID
Anyway, you can consider derivative filter even in case of fractional PID controller in the design procedure, see e.g. But think carefully whether you really need fractional action at the controller side. It should be usually motivated by contradictory frequency domain requirements that cannot be fulfilled by classical integer order PID.
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all pole of the system are in left hand side of s -plane . But i m getting GM negative and phase margin(PM) as positive. Step response is also stable with 20 % overshoot and settling time as 6 sec. I m not able to conclude stability with tjhis results.
Dear Boris,
I hope I will be excused for writing a “long message,” (and people who are not interested can just ignore it) yet this to make sure that my messages are not misunderstood as puting “this method against the other.” Actually, I started with the claim that Nyquist theorem and Nyquist plot contain the entire information. The only problem is that, in realistic systems, where the amplitudes may go up quite a lot, even to infinite, when you need to decide what exactly occurs around 1, this could be a tough task in Nyquist plot. Here, Bode, with its logarithmic scale, is best… when it works, and, because of the two separate plots, this usually occurs in not too complex systems. Then, maybe only after some use, you learn that Nichols combines both advantages. Before Matlab (and other tools), plotting Nichols used to be a terrible task and this may explain why people might have remained reluctant to use it.
Please see my message about the Company which started with “No, we don’t use Nichols” and ended using Nichols as the main tool. So, maybe you just try to write (or ask students to write) Nichols along with Bode and just see what Nichols gives in all other than simple cases.
As you know, my main “academic” business has been (simple) adaptive control. However, as I use to tell, although I have been playing Prof. and Dr., all my years I have been mainly an engineer. In this context, first I actually refused to use adaptive control, because control practitioners do not think that, for a given specific case, one cannot find enough information to do a good fixed controller. Even when one has to fit parameters to a given specific plant, one can do it off-line. Actually, PID is so widely used because many systems are not too complicated; they could even be stable or close to stability to start with and then, you can safely fit the right parameters to give you the desired performance. If you don’t need too much, same controller can serve all machines of same type.
The problems start when you really need good performance, which usually means fast response and also very precise tracking. While doing manual tuning on one or two machines may still be not too difficult, when you produce 20, 100, or 400 machines per month, this becomes a very tough job, in particular when your customers, maybe thousands of kilometers away, may replace a motor or any other piece and the performance deteriorates. So, you may also have to keep sending your best guys all over the world.
The same complex systems and/or many not-exactly-identical systems are also the reason for my present use of adaptive control.
Same Company, which started with “we don’t use Nichols,” also responded to my idea of using automatic (adaptive) tuning with “Adaptive? Ha-Ha! You, Professor, please keep writing papers. We have real problems.” However, because the real problem was really too tough, they finally thought that they could not lose too much letting this funny Professor play for a little while.
The result? Now there is a button on each machine and all that they have to do at the end of production, or what the operator has to do when any change leads to deterioration of performance, is to push the button and wait a minute or so for the parameters to be adapted to the specific machine. Their technology, which was “dead” by 1994, is alive and kicking today and performance is something else.
This was only automatic tuning per machine, not what we understand by adaptive control, yet this was also what made me see that, when high performance is needed, on-line (simple) adaptive control is needed to maintain performance even for one given machine under uncertainty and under various and (real-time) changing operational environments. Results justify this and will still be seen.
With best regards, Itzhak
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Please read this two pictures in File, It is in Chinese I took it from a paper but the symbol and expression is worldwide and international. For a system, select sliding mode valuable as S=c1e1+c2e2......en.
What if I want to know the value of S' (dot(s)) ? In this paper, It gives the expression of S'. It derives from the error state space by letting en'=xn'-dot^n(yd)=f(x)+bu-dot^n(yd), But can I get it in an easier way?
Let see, e1=x1-yd| yd is the reference signal and x1 is the output of the system,y=x1. e2=dot(e1),e3=dot(e2)=dot(dot(e1))......So, in this way, we can get the value of S and its higher order time differentiates. I think it may work and the final value we get should be the same numerically.
What's your opioions? Thank you very much!
If you agree with me, I have another doubt.
In the simulink model of that paper, It calculated dot(s) by that expression it gave, Why didn't it use differentiator to get dot(s)? It seems it doesn't want to introduce more differentiators into its system.
Hi Dawn,
I can see where you're coming from. You are trying to generalize that
\dot{en} = \dot{xn} − yd(n) = x1(n) − yd(n) .
However,
\dot{xn} ≠ x1(n) because of
\dot{xn} = ∂(x) + β(x)u + η.
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