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I'm looking for a exhaustive paper (or book) regardind a four (or two) wheeled robot trajectory control system in order to reproduce and fully understand the kinematics and control system equations.
My rover has four motor, one for wheel, and turns through a wheel speed control.
Would be amazing find the PID control design on the angle and speed control as well as the trigonometric equations of the robot trajectory.
Thank you very much
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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)
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Hi,
file name "sfun_ abcaaaaa.c" is not available in the folder mentioned.
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Hello, Can we find Kp, Ki, and Kd values of PID, Lead-lag, or Type2/Type3 compensator? I have designed a type2 compensator for my system but now I need a PID controller for the same system can I access Kp and Ki values from the Type2 compensator? Please guide me
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Hi, Can anyone guide me on how to use Loop Shaping PID Tuning for the buck converter?
I tried myself but stuck on step 4 as shown in the figure attached.
Thanks
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Dear Esteemed Researchers,
I have a mathematical model of a Plant. I want to implement two different controllers and see the response of system in tracking a specific reference. I would like to analyze the transient time response of the system for both the controllers. I don't mean to just check the response in simulation I want technical analysis using tools such as eigenvalue analysis. What tool can help me build up the evidence for best transient time response.
Thank you.
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Dear Zahoor Ahmed Thank you so much for the informative response. I will look into these references.
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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?
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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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I am working on a project in which I need to control the duty cycle of the pulse given to mosfet in an AC to DC converter.The mosfets are connected to LCL filter to give a regualted 5V.The output voltage and a reference of 5V error is taken and a compensator is connected.The output is compared using PWM and then sent to mosfet.Do we need mosfet driver in between?What kind of mosfet driver should I use in multisim?Can I get any reference?Should we solve this using bode plot?Should I use PID controller to decrease the error and should I simulate in MATLAB using PID controller ?As I find it easy
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Hi,
It would be that this reference can help:
PD: Matlab implementation codes are available.
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Hey! I'm in the work of designing a controller for a zeta converter, it is a fourth-order system.
I tried ways like the Ziegler-Nicols method, Root locus method using Control System Designer in Matlab. But couldn't get any satisfactory outcome. My bad.
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You may check the followings:
2nd order approximation.
or
System approximation using the concept of dominant poles.
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I have two PI controller running in parallel both controls the same output variable, based predefined input conditions I would like to transfer control from Control A to Control B without any variation in the output response. would be great to get any suggestion on efficient way of doing it.
Using Matlab Simulink as implementation plattform
Thanks
Sreeraj A
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I have illustrated my idea for your problem, attached as an image to this comment.
In the image, t1, t2, t3, and t4, are discretionary, and you can set them to optional values. Even you may change the time signal to any shape you prefer, square wave, saw-toothed, sine wave, several pulses, with respect to your control-selector strategy. But beware that, the times of transfer from control A to control B, should not over-lap, because the control signal then becomes multiple-valued and hence you may encounter an error in Simulink simulation. You can as well modify the amplitude of the pulse, by multiplying it to a constant gain, or even multiplying it by a time-varying function described as another time-signal.
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I am working on a project where we are going to develop controller for batch fed biomass boiler.We have done some experiments in our lab setup and those experiments are time consuming.I want to know whether
there are software packages which we can model and simulate the biomass combustion and as well as the control system modelling.
I want know about both commercial and opensource software packages    
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Matlab (with Simulink) and or SciLab would be useful
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I am interested to simulate distribution networks with distributed generation utilizing custom controls. Simulink is quite versatile in control system design and is friendly for people preferring visual approach to programming. But I am not always satisfied with how it solves power flow for detailed network models.
Lets say that I am looking for more reliable power flow solvers, but with control system design versatility of Simulink (preferably with visual programming). Any suggestions?
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Hello,
Given a system with redundant actuators, what would be the names of techniques that I could research to use each actuator for different frequency bands?
To illustrate the problem with a simple 1-dimensional problem, consider the attached picture. We have a mass m moving in 1-dimension connected to two redundant actuators. We want to regulate the position x while rejecting a disturbance Wd. In addition, we want to use the first actuator U1 to reject low frequency disturbances and the second actuator U2 for high frequency disturbances only. In other words, we do not want to use the second actuator U2 at steady state.
So far, I have come across Härkegård's work, such as [1], that explores dynamic control allocation. This discrete-time technique provides a way to penalise both high and low frequency usage of an actuator by adjusting the weighting matrices in its quadratic-programming cost function. They illustrate this technique by designing an aircraft control system for a fighter aircraft with a delta-canard configuration. The controller is designed to result in no canard deflection at trimmed flight to achieve low drag.
I am currently looking for other techniques that could be used to 'partition' the frequency usage of redundant actuators in order to get a more holistic view of the topic before committing to a single technique. I am looking at both techniques that separate the controller design and control allocation problems and ones that combine both.
Any suggestions of technique names or terms I could research would be much appreciated.
Thanks in advance for any suggestions.
Kind regards.
References
[1] Härkegård, Ola. (2004). Dynamic Control Allocation Using Constrained Quadratic Programming. Journal of Guidance Control and Dynamics. 27. 10.2514/1.11607.
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Thank you very much for the quick answers and the literature recommendations. It does seem that this specific problem has indeed not been researched extensively yet, but these papers will be useful for my research.
Best regards,
Jérémie
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I some papers, the mean square error is considered. In some other, the mse is normalized by dividing the error by the (total sampling instants x the total length of the reference trajectory).
Which solution does represent the factual error?
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Dear Samira Eshghi,
The performance of the controller is generally measured using the following parameters such as :
1) Maximum Overshoot
2) Settling Time
3) Rise Time
4) Steady State Error.
Additionally, there are other ways to measure performance in literature. This includes integrated absolute error (IAE), the integral of squared-error
(ISE), or the integrated of time-weighted-squared-error (ITSE). These performance measures have their own advantages and disadvantages. For example, the disadvantage of the IAE and ISE criteria is that its minimization can result in a response with relatively small overshoot but a long settling time because the ISE performance criterion weights all errors equally independent of time. Although the ITSE performance criterion can overcome the disadvantage of the ISE criterion, the derivation processes of the analytical formula are complex and time-consuming. The formulas for these performance measures or the performance measure based on overshoot, settling time, rise time and steady-state error can be found in the paper given below.
In discrete domain, ISE refers to Mean Square Error. I am unfamiliar with normalized-mean-square-error .
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Dear Colleagues,
It is seen from that most of the control system design has to be done in time domain and frequency domain design is less preferred. Could you please put light on the reason behind it??
Thank you in advance..
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Following
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I am working in the field of control system design. So, I need human immunity dynamic model for further research in my domain. Please share the above one and also, collaborate in this work.
Thanking you in advance.
With Regards
Mahendra Kumar
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Though these articles are not conducts with Covid 19 but you can still get your information from this....
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What analysis tool is most suitable for transient-state analysis and designing control to mitigate those transients in power distribution system? I am planning to carry out transient analysis caused by sudden increase in load on distribution feeder and want to control those transient by charging/discharging the battery storage system. Our load has a high ramp rate and high magnitude which could cause these transients in the distribution grid voltage profile.
Regards
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Mechanical to Electrical to Mechanical ( Generator/Motor) are via electromagnetic(reactive power)....
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Your project sounds very interesting - maybe a weight change system like this can be modified to serve pigs? https://youtu.be/MniFOpO3jws
This very durable and autonomous device can support fluid flow/percolation while measuring mass, and I propose that this could be beneficial to your PigSys. regards Stephen
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i have reported you to Reserach Gate for activities incompatible with the scope of RG
Please do not distrub me again
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Should they be designed for predefined socio-technical functionality or for context-dependent utilization of stimulated/acquired social, cognitive technical affordances?
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Dear Azam,
Your last question is very relevant and makes a lot of sense for me. The circumscribed issue is far not so trivial as it seems at the first sight. Smart systems will be adaptive (actually, self-adaptive). Therefore, their functionality cannot be described exhaustively in the design phase. (As I wrote somewhere: part of the task of designing will be delegated to the intellectualized systems themselves). This is actually that raises the question about the relevance or appropriateness of functions-centered design. When a system self-adapts (as a consequence of certain system states, behavioral performance, or envirinmental circumstances), it may rely on the affordances offered by the system 'design' as well as on the available and utilizable (un-bound) system resources (built-in or acquired at run-time). Some recently completed PhD studies suggested to me that, in the case of run-time self-adaptation, the system affordances and their exploitation play an important role. The current knowledge is insufficient concerning this complicated (multi-faceted) phenomenon. Further explorative/experimental research and speculations seem to be indispensible ...
Best regards,
I.H.
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Hi
As I have implemented in the attached picture, I'm making a simulink model and it keeps on giving an error:
Error in default port dimensions function of S-function 'FeedbackLinearization/Controller'. This function does not fully set the dimensions of output port 2
I toggled the signal dimensions display on and then I noticed that for my "error" signal, the output is of dimension 3 but it somehow transforms in dimension 1. (See the picture)
Can anybody please help me? I'm very confused
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After 3 channel to 1 multiplexer, you need to use demultiplexer to send . As further you are finding xdot , so 1st channel represents x state, so derivative of 1st channel will give xdot. But what you are doing is output of multiplexer is 3 so it is having all x,y,z states , further demux them to get 1x3 array and then individually find derivative of x state.
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In your opinion, what are the main challenges currently for the design of autonomous vehicle systems? Answers can be related to hardware, software, controls, societal impact, etc.
Secondarily, what are the main considerations that can be relaxed or approximated (to save design time and cost) for systems that will not directly interface with humans?
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I conclude that the idea that one can transfer control of the almost autonomous vehicle to the human occupant when the going gets too complicated for the system is fatally flawed. Driving skill assumptions about the hapless occupant are bound to be inaccurate and far lower than a well designed electronic system. If the situation is starkly perilous, the "operator" may well have fainted dead away. The closer the development process gets to the completely autonomous (level 5) design, the more insurmountable the handover. Even a moderately well designed level 5 system will be able to outperform 99% of the anticipated human operators. The user experience in the autonomous vehicle will, of necessity, be that of a train ride with no user concern for the technical or practical matters of the vehicle. The user experience in the almost autonomous (level 4.8 or so) vehicle may be so disconcerting as to prevent anyone who is informed of the control transfer situation from acquiring such a vehicle, or taking a ride taxi style.
John M. Kirkwood, CHFP
2208 Hunter Street Cinnaminson, NJ 08077
Phone: 609-828-2045
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Hi everybody,
I have a question about the circle of friction or Kamm circle. This circle is used in vehicle modelling, but I did not understand this well. I say my own opinion, please let me know if I am mistaken.
vehicle friction force at tire contact patch divided into two forces, lateral and longitudinal forces. As the coefficient of friction is u and the normal force is N, then the maximum of friction force is F_tot = uN. Now F_tot is the radius of the Kamm circle (?), then F_x and F_y are longitudinal and lateral forces, so ( F_x^2 + F_y^2 )^0.5 is lower or equal to F_tot.
If I was right, please tell me what is the use of Kamm circle?
Thanks in advance.
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Friction circle (based on the assumption that a tire can develop equal limiting longitudinal and lateral forces) gives you:
- The maximum longitudinal force that the tire can develop while it is developing a specified lateral force, or
- The minimum lateral force that the tire can developed while it is developing a specified longitudinal force.
Consequently, the maximum longitudinal force in the absence of lateral force generation and the maximum lateral force in the absence of longitudinal force will both be equal to adhesion coefficient*normal tire load.
For tires developed for emphasized traction or cornering capability, "friction ellipse" may be more suitable.
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Kindly help me with the parameter selection of the value of gains of the PR controller.
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Mathematically, the commonly used PR controller is not equivalent to PI controller. It can be deduced using the theory presented in the appendix of [1] that the controller in stationary frame shown in the attached figure is equivalent to a PI controller in synchronous frame.
[1] D. N. Zmood; D. G. Holmes. "Stationary frame current regulation of PWM inverters with zero steady-state error," IEEE Transactions on Power Electronics, 2003, 18(3): 814 - 822.
You can find in the attached figure that there exist coupling terms between the alpha axis-controller and the beta-axis controller. The commonly used PR controller in stationary frame does't include such coupling terms. The coupling terms come from the controller itself, not from the plant. If completely decoupled controller is required, the coupling terms generated by the plant model (e.g. the typical R-L model) should also be included.
I have done some test in matlab/simulink some time ago that such a controller performs exactly the same with the PI controller in stationary frame, if the parameters Kp and Ki have the same values.
However, in practice, the performance difference between the commonly used PR controller and PI controller may not be so obvious.
In addition, I would like to recommend the an advanced resonant controller, i.e. the vector-proportional-integral (VPI) controller. Its expression is s(Kps+Ki)/(s^2+w^2). Its numerator could be used to cancel the pole of the R-L plant. VPI controller could eliminate undesired peaks in the bode plot. According to my experience, it performs really better than the common PR controller. More information about the VPI controller could be found in [2] and other literature.
[2] Alejandro G. Yepes; Francisco D. Freijedo; Jesús Doval-Gandoy; Óscar López; Jano Malvar; Pablo Fernandez-Comesaña. " Effects of Discretization Methods on the Performance of ResonantControllers," IEEE Transactions on Power Electronics, 2010, 25(7): 1692 - 1712.
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Can there be a system which has unstable closed loop behaviour and a stable open loop behaviour ? Do they form a separate class of system?
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There are plenty of open loop stable systems. However we need feedback not for stabilization only but for several other reasons such as robustness to parameter uncertainty or correction of the static characteristic (especially for systems with steady state error - the "static" systems). In such cases an open loop high gain is introduced and the closed loop system can be de-stabilized. The Nyquist-Bode theory has been created firstly for such cases.
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Sir,
I am unable to solve second ramp response. I need the derivation with partial fraction.
Thank you
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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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Hello,
I work now about the integration of PVs panels in a distribution system, but to do that i need to calculate the PI parameter controller for voltage outer loop and current inner loop in the Vsc Control.  but I don't know how calculate  the value of this parameters. I am looking forward to your help! Thank you very much!
The voltage outer loop and current inner loop are attached to this mail.
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Properties and performance of Control system are important in control system analysis and design
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Is it possible to drive a piezoelectric stack with just DC.. ie. if you want to use a piezo to move something a set distance can you just apply a constant voltage to keep the piezo "activated" at the desired length, or do you always have to drive them sinusoidally. For example with the piezo microscope stages are they AC driven with some complicated synchronising stuff to only take images when they are at the right place, or fixed in a position with a DC voltage?
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I'm trying to design a controller for a flexible arm. The dynamic equation which describes the system is
T (t) = (I + 1/3 ρ*L^3) θ¨(t)+ρ Integration from (0 to L) x ¨ y(x, t) dx
+ m*L*(L ¨ θ(t)+ ¨y(L, t )).
Where:
I, ρ, L, m are constants
The variable y(x, t) is the deflection of the arm at a point located a distance x from the beginning of the arm
θ: the rotary angle of the arm from its reference position.
My question now is how to transform this equation in frequency domain using Fourier transform
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Can you provide information on your controller's design procedure, so that we can help you in different way?
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Detailed Description :
I am working on steering wheel angle sensor that measures absolute angle of steering wheel. As steering angle sensors uses gears and several joints which is totally hardware related so in spite of calibration in start with the passage of time due to usage of mechanical parts and also due to some environmental and road conditions some errors occurs in the values of sensors (e.g. offset, phase change, flattening of signal, delay).
In short due to these errors in the measurements our aim gets distracted means If I am viewing velocity vs time curve so if in the original or calibrated sensor in short close to ideal condition sensor my velocity shows a peak in amplitude but due to error (hysteresis) in measured signal I am not getting peak in velocity curve or I am getting flattening of curve so it will affect my final task.
I have a tolerance let say 1.20 degree for hysteresis so that’s why I am having detailed idea about my signal and want to observe my signal if some changes means offset, delay, lowering has occurred in my signal or not. This will not only provide me an idea that whether to lessen the amount of sensors used for my task or made some changes in hardware of sensor to lessen the amount of hysteresis or do some other actions to reduce it.
What I have done uptill now in which uptill now I am not sure that whether I am right or wrong. I am getting some values for hysteresis but I have few questions regarding those techniques. If someone provides me an idea about it how to improve these techniques or provide me a better approach then it will be nice and great guidance.
I have an ideal sensor signal (under ideal conditions which we want) and values from 1 sensor I have data of 6 different drives from car. I am explaining just 1 example of my first drive and its relation with my reference sensor data.
Given the data reference signal and sensor signal data of size 1x1626100 and 1 x 1626100 double for one reading from sensor but in all readings values from Ideal and measured signal w.r.t to time are same.
In short I want to find out the Hysteresis difference of sensor signal from measured signal.
I have applied few data estimation techniques to accomplish my goals.
1-      I have applied Gaussian Technique to estimate error in my data but I am not satisfied with it as I am not getting some good values or expected values with it may be due to outliers or some other errors.
I have subtracted (Ref – measured value of signal). Calculated mean of difference signal after applying my limitations, Standard Deviation of difference signal after applying my limitations, then make a Gaussian Curve along with mean and standard deviation. Made 2 lines one for mean+ standard deviation and 2nd one is with Mean – Standard Deviation and distance between +ve Mean_std and –ve Mead_std is called Hysteresis (Loss).
Please have a look at the attached figure. I have attached figure for 3 modal Gaussian curve but in some diagrams just like picture 3 my data is shifted. Can anyone tell me the reason why it is so and how to erase it because it is occurring in all diagrams but in this figure 3 it was clear.
2- In this method I have applied Regression lines Technique (On upper and lower values of difference signal).
I took difference of my signals (Ref – measured value of signal after applying my limitation on signal).
Applied regression technique above and below the difference signal means on upper values and on lower values separately and difference between upper and lower values regression lines is called as Hysteresis (Loss). Please have a look at figure 3 and 4 for clear view.
The Problem here with this technique is that I define the values for upper and lower regression line by myself after looking into data like up= 0.08  , low= -0.08.
3-      I have also applied RMSE technique but have few questions that are confusing me.
As I am dealing with static data so I considered my Reference signal as actual valued signal and my measured valued signal from sensor as measured values and apply RMSE formula on that.
    RMSE=    square_error = (sig_diff_lim).^2;
    mse =  mean(square_error)
    msedivided = mse/numel(drv(2))
    rmse = sqrt(mse)
4-      I have also applied correlation function but I think it is not working well with my data.
But it gave me some good insight about data.
Some Questions that also need clarification if possible:
1-      What is difference between RMSE and MSE means I know basic stuffs but I want to know that what are the applications where we use RMSE or MSE and which will work in my case for my data.
2-      I have now explained Gaussian, Regression technique, RMSE. Just one Request .Can someone explain me which Technique is the best to use because I have mentioned my issues in Gaussian and Regression Technique above. Just some explanation will work for me .Means Pros and cons of above mentioned technique.
I hope that I remained able to provide you the clear idea and detailed review what I want to do and what I am expecting and I hope to get some positive and valuable response from people.
Sorry for providing a long story but As I am not too expert in these as I am still learning so if I will get some useful responses it will improve my knowledge and also help me to accomplish my task/Goal.
Thanks for cooperation in advance.
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What type of hysteresis sensor are you studying?
Magnetic?
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i plan to do hardware project on self tuning PID model reference adaptive controller for bldc motor. i simulated with help of matlab ,but how to implement hardware for MRAC controller ?
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I am working on high bandwidth controller design for high speed scan mirror mechanism for satellite. The structural frequency (or vibrational frequency) for this system is coming within the desired bandwidth for attaining the high speed motion.
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I would like to analyse the stability of a closed-loop system in which the controller is built around a Smith predictor. I am interested in particular with the stability analysis with respect to uncertain time-delay in the plant. Thank you.
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interesant question, I want to proof stability with nonlinear smith predictor. I think is necessary to use Lyapunov method
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I have a question on observer design . I am working on a state space controller that involves an observer . I started with designing a state feedback controller without and observer . It works and meet my design requirements. But some of the states are not measured, I need to include an observer to estimate the states . But the problem I am having is my observer is able to estimate states without L matrix , meaning open loop observer working excellent , which seems too good to be true. My understanding is Luenberger observer uses system output which includes extensive infor abou the states and involves calculating gain L. I have not solve for L I think my gain will come out to be zero , as my states match exactly with open loop observer . Is that possible ?
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In the standard Luenberger observer theory the observer error dynamics is given as
edot=(A-LC)e
When L=0, we get the error dynamics
edot=Ae
Hence, when the matrix A is Hurwitz (all eigenvalues have real parts strictly less than zero), then the error would still go to zero whatever the initial error is. This means that your observer would still estimate the states perfectly as t->infty. Hence if your open loop system is stable (i.e., if A is Hurwitz), then a Luenberger observer with gain L=0 would still work. Please note that if the open loop system is stable but A has eigenvalues close to jw-axis (still in the open left half plane), then the convergence of your observer would be really slow and this might not be good for control purposes. So the performance of your observer, although its estimates would converge to the correct states as t->infty, is limited with the open loop system poles.
On the other hand, if A is not Hurwitz, then the error might remain constant, oscillate or even diverge. Hence if the open loop system is not stable, then this observer (L=0) would fail, in which case you would need to choose L a nonzero vector to make the matrix A-LC a Hurwitz matrix again.
As a result: The Luenberger observer with L=0 might work when the open loop system is stable and it will not if the open loop system is not stable. On the other hand, such an observer might have a very slow response than what is usually required by the state feedback controller. A rule of thumb in observer design is to put the observer error system poles (eigenvalues of A-LC) to significantly far away to the left of the controller poles (eigenvalues of A-BK). When L=0, the observer error poles are at the eigenvalues of A which are logically to the right of the controller poles (eigenvalues of A-BK) (otherwise there is no need to do control, your open loop system would be better than the closed loop). Hence a basic design requirement is not satisfied when L=0 although the observer error still goes to zero when the open loop system is stable. This issue would manifest itself in the fact that your observer would be too slow to converge to the correct state than what your controller would require, which will reduce the performance of the overall control system.
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I acquired some input and output data sets from a PID closed loop control biological system which the input is brain stimulation and output is the measured blood flow. I tried to use system identification toolbox of matlab. The results turned out that a second order process model can model it pretty well.  
I have heard Model Predictive Control can provided better control outcome under two condition the model should be accurate enough and the plant needs to have delay.
First question I have is how to define the accuracy of modeling/system identification and how accurate it needs to be for MPC to have better control outcome?
Second question I have is how can I measure the delay of a system by using input output data sets? 
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Dear Rex,
You must realize that the sampling is different for PID and MPC. In petrochemical industry the sampling period for PID control loop (depending on the process and controlled variable) might be in seconds, but in MPC the typical execution time for MPC is one minnute.
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Bode plot, plots the magnitude and phase of the open loop transfer function. Nyquist plot, plots the Real and imaginary parts of open loop transfer function. In principal, both have the same information. But for stability analysis, mainly for systems with zeros and non-minimum phase systems, Nyquist plot is preferred.
Using Nyquist plot, one can tell the number of right half plane poles. But is there a similar method available while using Bode plots?
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Dear Debasish,
The Bode plot is a graphical representation of a complex function, just as the polar plot (also known as the Nyquist plot) and Nichols chart (gain in decibles versus phase in degrees). These are used in different context. It is perfectly valid for us to display the Bode plot for a CLOSED LOOP (that is one of the ideas behind Nichols chart), so your first assertion is of course biased towards a particular application.
If we interpret the Bode plot as a graphical representation of the system (either open loop or closed loop), then, in principle it ca only refer to stable systems (no right plane poles allowed) for the simple reason that an unstable system does NOT have fequency response (e.g. the steady state response to sinusoidal excitation is NOT sinusoidal). Mathematically you can see this by the fact that the Fourier transform is not defined for signals that are not absolutely integrable (like the impulse response of an unstable system). Or still, what is the gain (at a certain frequency) of a system for which the output diverges to infinity when excited at that frequency? So, perhaps we shouldn't search for unstable poles in a Bode diagram after all.
Having said that, let me add that a diagram (Bode, Nyquist or decibel-degrees) can be seen just as a graphical tool to display a complex function in the frequency domain, without any physical interpretation (in fact, this seems to be the case with some software packages that will provide plots even for unstable systems). In that case, comparing the relation of magnitude and phase it could be possible to detect when the original transfer function was unstable.
Reading the answers given by Pandiyan and Prof. Lafif it seems that they interpreted your unstable poles to be in the closed loop, given that the plot analyzed refers to the open loop (as in classical control design). In that case, as they point out, the aswer is conventional: in the Bode plot, if the phase is more negative than -180 when the gain is 0 dB then THE CLOSED LOOP WILL BE UNSTABLE. If the gain is larger than 0dB when the phase is -180, then THE CLOSED LOOP WILL BE UNSTABLE. In both cases it is assumd that the open loop is stabe. This totally agrees with Nyquist criterion.
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In designing an unknown input observer for the system, first, we need to show that the invariant zeros of the system must lie in the open left half complex plane and the observer matching condition is satisfied.
How can I check the first condition about the invariant zeros of the system?
Thanks in advance for any help.
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For a given linear system, e.g. in Laplace domain, zeros are the roots of the numerator while the poles are the roots of the denominator. Zeros which are located on the left hand-side are minimum-phase, while on the right-hand side are nonminimum-phase. In a feedback control system, the right-half plane (RHP) zeros cannot be cancelled out by any stable controller law, so these zeros remain at the locations as they are in the open-loop regardless of the controller used. Any attempt to cancel out one of the zero will lead to an unstable controller form and as such suffers from internal instability. On the other hand, if the zeros are on the left-hand plane (LHP), they might be cancelled out or alter by a controller in the closed-loop system - in this case, the controller does not need to have unstable poles; it can cancel the stable zeros using stable poles. Observer often uses known inputs and outputs to estimate the system states, which latter will be used in control. Supposed the system has at least one RHP zero, when there is an inversion calculation involved, the RHP zero will become RHP pole (i.e., unstable pole), which is not desired in any stable observer. Thus, it is important to be assertive that the system zeros are LHP so that any inversion involved will not lead to unstable observer.
Please note that, this explanation is from the layman point of view with minimum mathematical knowledge, But you need a basic feedback control knowledge.
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In relay auto tuning of PID controllers, controllers are replaced by a relay in closed loop. For step change in setpoint,  process variable oscillates and their period turns out to be a close approximation of the ultimate period -Pu,  that Ziegler and Nichols (ZN) used for their tuning rules. And the amplitude of the process variable's oscillations relative to the amplitude of the control effort's oscillations approximates the process's ultimate gain - Ku, when multiplied by 4/π. Then  ZN tuning rule is applied.
But theoretically, how a pure first order system (linear, no time delay - maximum phase lag will be only 90) oscillates at ultimate period (resulting from a phase lag of 180)? It oscillates in relay auto tuning method, but how it will be Pu? 
Note: Also ZN ultimate gain method is not valid for pure first order systems - no ultimate gain possible here?
Thanks in Advance.
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Lalu,
My opinion is that we can not take it to be ultimate period. The oscillations in this case are due to the original first order system together with the relay nonlinearity.
So we are making measurements for the relay + original system, not exclusively the original system !
There is only a sort of "compromise justification" that I can think of, though! (Almost as an afterthought.)
In most PID controllers, the control signal as generated by the PID combo is passed through a pair of saturation limits that avoid what is known as the integral windup or integrator windup. If the saturation limits are decided before application of the ZN rules, and included with the system block, then the tuning is automatically for the saturation + original system!
But even if we accept this argument, there are two riders to it:
  1. The saturation limits are (ideally speaking !) not open to modification once the PID parameters have been set according to ZN.
  2. Saturation limits are equivalent (not exactly the same !) to relay strictly without hysteresis. So all this only justifies involvement of a relay without hysteresis, not one that includes the latter.
-Sanjay
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Dear All,
Could some explain the difference between the controller and compensator in control system design?
Since similar behavior is there for the Proportional Integrator and Lag compensator?
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Hi Manoj,
A controller is an element whose role is to maintain a physical quantity in a desired level. For exemple we have a Temperature controller, pH controller, speed control, PID controller. In other words, aim of controller design is to reduce the error between the reference and the output signal which is fed back to the controller with input (reference) signal.
A compensator : modification of system dynamics, to improve characteristics of the open-loop plant so that it can safely be used with feedback control. For exemple to improve stability, uncouple a system, to a 'lead/lag compensator, phase compensator. In case of Lead and Lag compensator which are often designed to satisfy phase and gain margins, these bode plot of the system itself changes after the insertion of compensator, bode plot indirectly represents system dynamics.
Good understanding
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Question 1:What is the reason for a BIBO stable LTI system that all the roots of the characteristic equation have negative real parts?
Y(s)=T(s)*R(s)= N(s)/D(s), where T(s) is closed loop transfer function and R(s) is input to the system. For y(t) to be bounded, all the roots of D(s) should lie in left half of the s plane. It can have roots on imaginary axis (but not multiple root on same point). According to BIBO output it should be bounded for every bounded input. So poles of system transfer function should lie in the left half of the s plane(excluding imaginary axis as bounded input can have poles on imaginary axis). Is the laplace transform table only proof for this?
Question 2:
It is the same thing extended for Polar and Bode also.They both are not complete plots. For an unstable open loop system, they cannot predict the stability of a closed loop system. In books they mention polar and bode can be applied to minimum phase systems, but stable open loop systems may have zeros in the right half of the plane. So in polar and bode open loop transfer function restricted to minimum phase systems or systems only with poles only in the left half of the plane?
In Nyquist it is clear that it is an extension as it comes from Cauchy's argument principle.
For closed loop systems having repeated roots on the imaginary axis is the Nyquist theorem valid?
Please elaborate and correct me if I'm wrong somewhere.
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1. Ignore the input for a moment. If the poles of the closed-loop LTI system are in left half plane (LHP), the plant is asymptotically stale. In other words, the plant will go to zero from any nonzero initial conditions.
It is because if it has the factor 1/(s+a) with a>0, its time response, its impulse response (Laplace transform of impulse is 1)  is exp(-at). For a couple complex conjugate poles, you get something like exp(-at)sin(bt+fi). Both are converging time functions. If the transfer function (TF) contains a product of many LHP poles, the decomposition gives you a sum of converging time functions.
Then, if the plant without inputs is asymptotically stable, we can show that it is also BIBO.
If you have a bounded input, such as step (for simplicity) which gives you 1/s, it only gives you another factor to the product and, after decomposition, this factor gives you a term which results in a bounded time-function, while all "stable" poles give you vanishing terms.
2. If you know the closed-loop poles, you don't need any plots.
Bode, Nyquist (polar) and Nichols plots allow you to plot the open loop G(s) and "think" about closed loop T(s)=G(s)/(1+G(s)).
Bode is the best and simplest plot exactly then, when the plot is simple, almost straight lines. When gain and phase start jumping up-and down, however, it is almost impossible to get any conclusion about any stability.
Nyquist is always right. However, in real systems, the gain that may go from 0 to 1000 makes it difficult to get all results from one plot.
Nichols plot is like Nyquist, only the dB scaling allows you to get all results from one plot (-40 to 40 dB makes an easier reading). Nichols is less intuitive in the beginning and maybe less taught then the others, yet these days, in MATLAB  you just write nichols(sys) and, after playing with it and digesting it for a while, you may reach the conclusion that nichols is the best.
I hope it helps. If not, please feel free to come back with any question, comment or objection.
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The seventh order transfer function is [-1496.8 (s^2 + 7.942s + 21.66) (s^2 + 0.6747s + 142.9) (s^2 + 119s + 4991) ] / [(s+2.681) (s^2 + 21.06s + 192.9) (s^2 + 1.836s + 147.7) (s^2 + 47.69s + 9205)].
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If the system is not oscillating then 1st order approximation is fine. If it is oscillating, then 1st order reduction is not good and you need a 2nd order approximation.  For second order, if you have dominant poles while the other poles have large real parts then you many not need to add delay and you are good to pick the 2 dominant poles as a starting point and tweek them. If the other poles are not negligible, then add some delay and iterate with it until you get satisfactory FRF approximation or time response. For 1st order, you can either find what is the approximate time constant and dead time of your response, then the dead time is the time delay and the time constant is the first order Tau!
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As I understand, stability of such a closed-loop system is discussed in two steps.
1- observer error dynamics must go to zero exponentially fast.
2- state variables must always remain in the attraction region of the controller. 
Khalil ("Nonlinear Systems" 3rd edition, page 617) has explained this in a very complicated way.
Can anyone give a better and formal explanation?
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You are only asking about nonlinear high-gain observer, yet you enter the nonlinear systems stability issue, which may not be simple at all.
All above mentioned books are excellent and good to read (and I myself also see Slotine and Li as most readable). Still, all stability proofs for nonlinear nonautonomous systems (i.e., where the time appears explicitly, either via input commands or as time varying parameters) are based on Barbalat’s Lemma and require strong conditions of uniform continuity.
This is based on the fact that, when these books and people in general mention LaSalle’s (or Krasovsky-LaSalle) Invariance Principle, they all mean 1950-1960 works, which only cover autonomous systems of the form xdot=f(x) (i.e., where time does not appear).
However, at least for LaSalle, those works are only an early advance to his REAL contribution and REAL Invariance Principle of 1976-1980, where he extended it to nonautonomous systems, yet , for some amazing reason, have remained unknown by the large nonlinear systems community, including those otherwise excellent books.
Besides, new works continue along the lines of those LaSalle’s latest works and simplify nonlinear systems analysis even more.
A discussion and the corresponding references can be found on Research Gate at
Hope it helps.
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so can we say that from above statement that a large resonance peak in frequency response corresponds to a large overshoot in transient response?
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talking about second order systems with a certain zeta, when zeta is >1, the system is overdamped. At zeta = 1, the system is critically damped, and will have no overshoot for step response. Decrease the zeta to any value less than 1, and you have an overshoot. All second order systems have a resonant frequency but zeta decides whether you will ever see the resonance, and higher gain at that frequency. A study of behavior of butterworth second order filters will indicate that if zeta is 0.707, it can be called Butterworth. That will have an overshoot for step response as zeta is less than 1. The criterion for no overshoot is that zeta be greater than or equal to 1. All second order systems have an wn , a frequency of natural resonance. This is apparent when you look at the transfer functions of second order systems. But they will have an overshoot for step response only if their zeta is less than 1. One can easily simulate second order systems  (e.g in circuit maker) with various zeta and study their step response. That will help understand the second order system better.....
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is there any book available regarding close loop control of electical machine(dc m/c, PMSM, BLDC, IM, SM etc) which includes machine modelling along with control system design like we have erickson maksimovic'in Converter control area???
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-High Performance AC Drives by Mukhtar Ahmad
-Induction Motor Control Design by Riccardo Marino, Patrizio Tomei and Cristiano M. Verrelli
-Vector Control of Induction Machines by Benoît Robyns, Bruno Francois,
Philippe Degobert and Jean Paul Hautier
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The signal y(t) = et+ e2t+e3t is a response of an autonomous LTI system, and my lecturer said that the order n of the system is n>=3. How can I derive the order of the system from this signal?
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You may determine the order of the system easier in the S-domain. The order of the system id determined by the number of poles. So, in order to answer your interesting question, then let us transfer the system equation from the time domain to S-domain using Laplace transform.
Then Y(s)  = 1/(S-1)  + 1/( S-2) + 1/ (S-3)
Then this system has three poles at 1 , 2 and 3 in the S-plane. Since the poles lies in the right side of the S plane, then the system is unstable.
wish you success
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how can I add low pass filter to my plant by using sisotool .
can anyone help?
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For example when you want to design a high speed response controller with minimum steady state error ( in network modem)  the choose of a high-gain is a good thing, but what are the caveats from the viewpoint in control theory?
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 The process of setting the optimal gains for P, I and D to get an ideal response from a control system is called tuning. There are different methods of tuning of which the “guess and check” method and the Ziegler Nichols method. I think The gains of a PID controller can be obtained by trial and error method...
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sensorless vector control drive How can I calculate speed of an induction motor from current and voltage vectors? please provide the equations if possible,how to impliment in matlab?
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As i want to add the simulink model of PMU to my simulation but From where I can get the PMU simulink model?or from and how I construct the simulink model of PMU in MATLAB?
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Dear Alok Jain,
Try tk search in the matlab file exchange website. You may find something.
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I would like to understand on how to use the Nichols chart. Can anyone please share any materials or any link to understand it  better.
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I am attaching two file below. They might help you understand it!!
Also have a look at this link
Hope these help!
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I have a Reaction Wheel hardware unit. I have been working on the estimation of internal parameters using RW outputs using Matlab and Simulink. Now I would like to be able to test it with hardware. The model I have from the RW is by Bialke. The hardware model is a little bit different but should be bale to manage the estimation process regardless. My challenge is how I can change/manipulate internal parameters change in the system so that I can test estimation algorithm with real hardware-in-the-loop.
If anyone has experience in this area please let me know. Also if you need more information please let me know.
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This is very interesting and will be useful for studies in fault-tolerance onboard spacecraft.
Mechanical degradation includes increase in friction and change in stiction. The build-in mechanical non-ideal mechanisms include rotor un-balance and associated induction of spacecraft vibrations. These could be a bit nasty in presence of high-precision optical sensors, since sampling would take place at lower frequencies that those induced by the wheel and aliasing could be an issue.
If you have access to the inner torque control loop in your hardware, you might superimpose the change in friction torque as a torque command add-on signal (delta Q), which is “unknown” to your control part. If you have only access at the speed reference level (omega), you might use the output of a simulation: delta omega = I^-1 delta Q, where I is the moment of inertia.
The basic idea is illustrated in a lecture note (a very basic model used for teaching a first course in spacecraft dynamics and control – no imperfections added) [1]
Simulating defects in the drive electronics is more difficult. In a project dealing with AC motors (not connected with space), we made a breadboard to be able to emulate faults including: IGBT bridge defects (short or open transistors) and winding short circuits. We made fault detection and fault-handling as described in:
However, the breadboard was only documented in an internal report.
Kind regards
Mogens Blanke
Technical Editor for Fault-tolerant Systems, IEEE Transactions on Aerospace and Electronic Engineering
References:
[1]  Blanke, M.: Satellite Dynamics in a quaternion formulation. Lecture note on satellite attitude dynamics and control. Automation and Control, Department of Electrical Engineering, Technical University of Denmark, Build. 326, DK 2800 Kgs. Lyngby, Denmark, latest version 2010, 22p
[2]  Blanke, M. and J. S. Thomsen: Electrical steering of vehicles - fault-tolerant analysis and design. Microelectronics Reliability Vol. 46 (2006) 1415-1420
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I have a previous knowledge of the system, so I've the lower and upper bound of the frequency response test.
I'm performing the response frequency test, as follow:
The input to the system is given one frequency per time, and after X cycles at the same frequency,the frequency is increased by a factor, F.
The X cycles are chosen appropriately to let the transient of the system vanish, and the increment F is chosen to have enough frequency to recreate the bode diagram.
To get the gain and the phase of the system for a given frequency, I've chosen only the portion that the system is in the steady state, and after I applied the least square method to the input and measurement (output of the system).
My doubts regarding about the implementation in the real world, because I cannot sampled the output and write in the input at the same time. Then, the input u(k) and output(k) are not synchronize.
I suppose the phase of the system in high frequency may be unreliable due to this problem. But, what is the correct sequence to minimize the undesirable effect on the test, without increasing the sampling frequency?
Do the calculation of the sine - Write at the Input of the system - Read the output
Read the output - do the calculation of the sine - Write at the Input
Second question.
I should compensate the zero-order-hold, during the phase estimation? I mean I should increase the phase by a factor ws*T/2, where ws is the sampling frequency?
Thank you in advanced.
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Dear Adolfo,
I would use a cross-spectral analysis for the estimation of the plant frequency response when dealing with linear system and wideband PRBS excitation signal. For example the Welch’s method of averaged periodograms proved to be a numerically robust tool, see
Welch, P.D. "The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging Over Short, Modified Periodograms".
The corresponding routine is available in Matlab Signal Processing Toolbox or you can implement it yourself easily using the Fast Fourier Transform.
As an alternative, you can use a swept sine wave (chirp) input signal with variable frequency, amplitude and DC component. This allows you to gain more control over the spectral power density of the excitation signal over the tested frequency range which may be beneficial to improve signal to noise ratio, avoid excitation of some types of nonlinearities, limit the range of the plant output and perform a closed-loop identification at the cost of longer experiment execution time. The plant frequency response can be estimated online or offline by means of an observer, see the provided links for more details.
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(like stationary signal, time correlation...)
Control system model identification using input and output signal.
Thanks a lot
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If you are  implementing only parameter  identification ( either with recursive schemes or with batch- type  off-line schemes)  so taht  you can choose the input, then the best solution is to take a periodic input with a sufficient numbrer of frequencies " sufficiently rich input" (  minimum number of frequencies:   one half of the parameters to be identified or  one half of the number of parameters + one). If the input is prefixed to one not being sufficiently rich , you can add a small  ( in amplitude) sufficiently rich signal  test to the convenient  input  for the problem. The combination of both input  signals would be an input being sufficiently rich in frequency.
If you are  combining identification and control  with an adaptive control scheme , the input is not of free choice since it has to be appropriate for the  control objective. But in this case , if the reference signal is sufficiently rich in frequency or if there is a  significant adaptation transient ,  the control input would be normally  sufficently rich in frequency ( note that abrupt tansients with quasi-oscillatory behaviors are also sufficiently rich in frequency- think conceptually  in  the  theoretical conclusion got  from  a Fourier analysis of such signals ). So , normally,  identification is also achievable even if it is not the central objective of the problem, or even if it has not been stated as an objective,  which is in this case the  asymptotic reference tracking.
If the objetive is just control but it is not relevant the identification of parameters then it is better to be careful just about the control objective which can be got ( i.e., tracking error tends asymptotically to zero) even if the parameter estimates  do not tend to the true values ( i.e. if identification fails). However, this can be problematic in the robustness  context since if the limit of the estimated vector is not the true parameter vector , small deviations of the various signals due to noise or computational errors would lead to  start run again the whole  the adpative scheme ( estimation + control)  with nonzero tracking errors). So , parametrical identification can be convenient in practice  even for  primary  control tracking objectives.
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How can I minimize J for finding K1 , K2 , K3 with de algorithm.according to photo 
Guidance: Due to the variable j in terms of k1, k2, k3 is optional comment plant should face denominators grade 3 or less than 3. Ss command values of A, B, C, D obtained initial values of X1, X2 .X3 is also optional.
A, B, C, D  is selected optionally.
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You can use riccati equation to find values of k1,k2,k3. From your fig. Your Q matrix is identity matrix of 3*3 and R is 1. You can also use matlab command riccati and get ans of k matrix. In this you should specify value of A,B,C,D,Q and R along with initial value of state.
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Dear friends,
I am implementing Kalman Filter on an Android device to get rid of noise generated due to double integration of accelerations from accelerometer. The aim of my project is to control the position of a model car so that it follows a specific trajectory. Kalman Filter predicts the position from some reference model to estimate the position in a recursive way. I can also take measuremets e.g from another sensor lets say, gyroscope, instead of car position from the physical model which could also be regarded as sensor fusion. The scenerio for first case could be as follows.
First step is to create the phycial model of the car. well as I am using an RC car. The input is the speed command to the wheels and output is the acceleration from the sensors. Which are the same as meaurements in the Kalman filter. I am not sure if this modelling approach is right? Does any one have experience in this area? The equations which I have created so far are as follows:
x(k) = x(k-1) + dt* derivative_of(x(k-1)) + velocity_of_car@(k)
derivative_of(x(k)) =   derivative_of(x(k-1)) + dt/2* velocity_of_car@(k)
Where derivative_of(xt(k)) and xt(k) are the only two states of the car under considerations. Please first tell me if these equations are correct. and then if my approach towards Kalman Filter implementation is correct.
Regards,
Zahid Raza
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The equations that you have written down simply seem like double integration itself, which is exactly what you want to avoid. In order for the Kalman filter implementation to work well, the actual model of the physical system (In this case the RC car) should be implemented. Now the model of the car is available in several resources, see for example chapter 2 of the following thesis,
specifically see Eq. 23. In your case the measurements should be \dot(v_u) which is the acceleration.
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Given a non-linear system, where outputs of the system are 4 of its state variables. We need to design a state (output) feedback control with its linearized model. Is it possible to design such feedback control ? if yes, How ?
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Being able to directly measure the states just means that you don't need to estimate the states. So this is a good situation!
In both cases you would design a gain vector K , to place the closed-loop poles (i.e. of the system with state feedback) at the desired place in the complex s or z plane (depending on whether you are designing a continuous- or discrete-time controller). Do this using Ackerman's method, for instance.  
In the latter, case you would also need to design an observer to estimate the states -e.g. a Luenberger observer. This design process would involve the design of a gain vector L, to place the poles of the observer (to obtain the desired transient and noise filtering properties).   
Have a look at "Linear State-Space Control Systems" by Robert L. Williams II and Douglas A. Lawrence for a very good introduction (continuous-time only).
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Whats is the solution for sunlight incidence on vision systems controllers?
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Hello Enrique,
Can you please elaborate the actual setup that you are talking about? Understanding the setup and the problem will help to devise the solution in a better way!
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Hi, would some one help me classify the different methods employed to determine the 3D pose of camera setup from images of captured object of interest?
Thanx
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hi
 Your q is interesting Some conjectures below .hope it helps.
1. Let us imagine  the ref axis is say x-y-z plane  fixed to image
2 Assume image lies on xz plane and camera is centrally placed  on y axis
3 Approx location of camera would be using focal length of camera fc and we have (some known dimensioned object in image) viz lobject/Limag . then ycord=lobject/Limag*fc .Now wrt object ref axis camera is located at(o,ycord,0).
4 Next if camera is also shifted upwards say by z0. then we tilt image around  xaxis and by suitable transformation on image get most acceptable image (aspect ratio?)'it should be possible to work out the angle of inclination and determine the zo value..requires some working
5. Alternatively there probably are codes with suitable transformations where you can just experiment and try.
Cheers
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Suppose that you have a sensor, that you can't change the sample rate or any other feature including the anti-aliasing before the signal be sampled.
Beside this, suppose that, the control loop of the system runs with a slower rate than the sensor, and you cannot change the control loop rate, as well.
Now, assume that the sensor rate is multiple of the control loop rate.
Then, suppose that, after 5 samples of the sensor, the control loop runs once using the latest sample from the sensor (observation: the 5 five samples are stored).
As far I understand this characterized the down-sampling of the signal, and it produces the aliasing effects over the signal.
Then, how this effect can be minimized? Should I have to put a digital filter before the control loop?
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hi
1. Downsampling requires a pre-filter to eliminate aliasing  depending on the frequencies involved. A very simple example is say fsig=6hz  , fsampling= 36hz . D=2 then new fsamnew= 36/2= 18 . This is still > 2*6 =12hz (nyquist condn fsig  < fsam/2) so no filter is needed.No information is lost.
2. If we downsample  by D= 4 then fsamnew=36/4 = 9hz , here fsig=6hz>9/2 hz so we need a prefilter. We lose information.
3. Please see attached pdf..hope it is of help.
Cheers
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classical methods
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yo can use fuzzy logic based online tuning of PID controller
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firstly extracting the model uncertainties out of the nominal plant and use a weighting function to regulate the norm of the uncertainty block Delta within 1.Let's say z_inf to w_inf is Delta, and w_inf to z_inf is Tw_inf,z_inf(transfer function). According to small gain theory, the norm of Tw_inf,z_inf should be less than 1. Then the control goal is to design a controller(either output or state feedback) and make Tw_inf,z_inf less than 1. I'm wondering whether this controller always exist, or what are the requirements for its existence, Sorry if I made any conceptual misunderstanding. 
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No, the solution may not exists.  There exists a ultimate lower bound for the achievable H-infinity norm for a given problem, beyond which no solution exist.  For solution to H-infinity control problem, you may check the book by Başar and Bernhard.  
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In Ruth-Hurwitz algorithm one can determine how many unstable poles are in the system, due to the sign of the first column coefficients . I was wondering if there are any similar idea in Jouri algorithm.
thanks in advance,
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which link?
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sandeep
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I am interested to your question (similar to my case).and will explain in detail soon. Bit hurry for this time, please consult me.
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I would like load frequency control in power system consists of multi area.
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A very interesting article about this topic from a practical point of view is Tim Wescott's famous "PID without a PhD" (see link).
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I need an advice. What is the most efficient way to implement real-time control algorithm which needs to perform the following three steps every 5 minutes:
1. Read measurements from data base,
2. Based on measurements calculate control variables,
3. Write calculated control variables to database.
Thank you in advance.
Regards, Anita.
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Hello Anita,
I do not know whether you are looking for a MATLAB / Simulink based or a real-time hardware-based solution but my approach would be -
1) Use a timer based interrupt with 5 minute (300 seconds) interval rate.
2) When an interrupt is received perform the tasks as per your requirements as -
3) Read the measurement from (say an ADC or) your database
4) Do some processing / calculations
5) Write the result  to (say a DAC or) your database
6) Wait in loop for next interrupt to arrive/occur.
If you want to use only the database (or a memory array) instead of the ADC/DAC, you will have to modify (increment/decrement) the database pointers accordingly in each of the step above as needed.
I hope this addresses your question or else we can discuss further.
Thanks and best luck!
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we designed a controller for each loop individually for controlling the multivariable control system by allowing the interaction amid the variables. Now the question is how to measure the degree of robust stability of multivariable system. Is it measured individually to each loop or over all system. provide any supplementary document.
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Quote R. Hanuma Naik's question "how to measure the degree of robust stability of multivariable system?" There are a couple of approaches to achieve this goal.
(1) "Calculate the MIMO H-infinity norm for the closed-loop system." suggested by Zigang Pan.
A good reference book is
S. Skogestad, I. Postlethwaite, "Multivariable feedback control: analysis and design", Wiely, 2005.
(2) "measure by criterien an all over stability margin and see Lyaponov condition" suggested by Mohamed-Mourad Lafifi.
(3) "the stability margin of feedback loop" suggested by Lutz von Wangenheim and Osman Çakıroğlu.
Quote R. Hanuma Naik's question "Is it measured individually to each loop or over all system".
Each loop should be stable in order to make the whole system stable.
In addition to Lutz von Wangenheim's comments "the stability margin applies to one single feedback loop only. The worst margin determines the stability properties of the whole system."
the interaction with other loops will reduce the stability margin of each loop. In other words, the interaction makes the worst margin even worse.
Let us look at the simplest multivariable control system with only 2 loops (the simulation example in [HY05a]).
Assume that each loop has no interaction,
the phase margin of loop #1 is \phi_1,   
the phase margin of loop #2 is \phi_2,
both \phi_1 and \phi_2 should be positive in order to make the whole system stable. That is, \phi_1>0 and \phi_2>0.
However, taking into account the interaction between loop #1 and loop #2,
the real phase margins for both loops are {\phi_1}^' and {\phi_2}^' instead
 
Direct Nyquist Array (DNA) can be used to analyze the interaction of different loops over a system.
According to DNA stability theorem, {\phi_1}^'<\phi_1 and {\phi_2}^'<\phi_2
This means that the interaction between loops reduce the stability margin of each loop.
The following two papers apply Direct Nyquist Array to measure the stability margin of multivariable system.
Y. Hong and O.W.W. Yang, "Adaptive Multiloop PI Rate-based Controller Design for a MIMO IP Router Based on Phase Margin," Proceedings of IEEE Globecom, St. Louis, MO, U.S.A, November 2005, pp. 1070-1074.
Y. Hong and O.W.W. Yang, "Self-Tuning Multiloop PI Rate Controller for an MIMO AQM Router With Interval Gain Margin Assignment," Proceedings of IEEE HPSR, Hong Kong, China, May 2005, pp. 401-405.
The above two papers have been reviewed by the master thesis "Analysis of Stability and Stabilization for Second-Order Vector Differential Systems" written by Wen-Yan Huang. The master thesis (English version starts at Page #19) can be downloaded from the following link.
Discussion on control system design
"What are trends in control theory and its applications in physical systems (from a research point of view)?"
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I want to design a controller for a model that has an integrator.For this reason, i would to design a PD controller instead of PID and so on. almost of books and refs discuss about tuning rules of PI and PID controllers. Is there any rules about tuning of PD Controller?
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A simple PD controller design is the method of Cohen Coon (G. H. Cohen and G. A. Coon. Theoretical consideration of retarded control.Trans. ASME, 75:827–834, 1953.)
I enclose the implementation of this method in Matlab