Modeling, Identification, Control (A. Sala)
Modeling, Identification, Control (A. Sala)
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Gaussian Processes: covariance between position and speed (2), example, prediction
This video uses position/velocity joint covariances from a Gaussian process to make velocity predictions given position measurements in a numerical Matlab example. The second part of this example discusses how to incorporate mixed measurements of position and velocity to make statistical predictions of both position and velocity (interpolation).
The variances and covariances themselves are calculated with the first and second derivatives of the covariance kernel between two `positions', as detailed in the video th-cam.com/video/b6aSbUXR544/w-d-xo.html , which you are advised to watch before this one for better understanding.
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PDF/code/notes at: personales.upv.es/asala/YT/V/gpvel2EN.html
#gaussianprocesses #kalmanfilter #machineleearning #statistics
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Antonio Sala
Full collection of videos at: personales.upv.es/asala/YT/indexEN.html
มุมมอง: 71

วีดีโอ

Force estimation uncertain mechanical system: h2-hinf-musyn performance analysis in frequency [3/4]
มุมมอง 2616 ชั่วโมงที่ผ่านมา
This video continues the case study of the design of an ``estimator of an internal variable'' (observer) of a system with an uncertain model, which began in the video th-cam.com/video/nhLZCRbxJxM/w-d-xo.html (modelling), continuing in the th-cam.com/video/lHEG0O50hPk/w-d-xo.html (eneralized plant and optimal design h2, hinf, mu). Formally, the theory pursues guarantees in the frequency domain; ...
Force estimation in an uncertain mechanical system: h2, hinf, musyn Matlab example [2/4]
มุมมอง 58วันที่ผ่านมา
This video addresses the design of an optimal estimator (in a certain sense) of the force acting on a mass-spring-damper system with uncertain damping coefficient. Although it's quickly reviewed here, a more extensive explanation of the uncertain LFT modeling part is covered in the video th-cam.com/video/nhLZCRbxJxM/w-d-xo.html , which you might want to watch, prior to this one, depending on yo...
LFT modelling of a system with uncertain damping for force estimation [robust control] [1/4]
มุมมอง 4814 วันที่ผ่านมา
This video presents the modeling of a mass-spring-damper system with an uncertain damping coefficient, subject to an unknown force input with limited bandwidth (that is, it will be the output of a first-order filter). The LFT modeling is detailed, leaving the uncertainty separated from the plant. The outputs that will be necessary to solve a problem of optimal design of force estimators will be...
Gaussian Processes: covariance between position and speed (1), example
มุมมอง 4214 วันที่ผ่านมา
This video discusses a specific case of statistical relationship between `position' and `velocity' of a 1D Gaussian process. This video brieflly states the theoretical formulas for calculating covariance between position and speed and autocovariance of speed. The detailed discussion and proof of these formulas is discussed in the videos th-cam.com/video/GMS-h06DpjI/w-d-xo.html and th-cam.com/vi...
Feedback linearization/decoupling: two-input two-output example (hand-made, no Matlab)
มุมมอง 5721 วันที่ผ่านมา
This video discusses a simple academic exercise to calculate the decoupling and feedback linearization equations of a 2nd order system, with 2 inputs and 2 outputs, relative degree 1 in both of them (inputs appear with first derivatives of outputs). The system also has no singularities or ``zero dynamics'' to analyze. The equations are just an invention, they do not model any actual physical sy...
Phugoid mode dynamics: equilibrium, linearization, stability (simplified 2nd order equations)
มุมมอง 4121 วันที่ผ่านมา
This video discusses calculation of equilibrium points, their linearization and the local stability analysis, of the simplified phugoid mode (or "fugoid") dynamics model (2nd order) of an aircraft. The detail of obtaining the model based on principles of Physics is discussed in the video youtu.be/M\_VhFU29nj4 , and different simulations with {ode45} and animations are covered in the video th-ca...
Hidden tiger 7: recursive Bayes formula (simulation, Matlab)
มุมมอง 43หลายเดือนก่อน
This video presents a simulation of the recursive Bayes filter in the hidden tiger problem that we have analyzed in several previous videos. Specifically, the theory of the recursive filter was discussed in the video th-cam.com/video/hfLmZRtOIPQ/w-d-xo.html (well, only adapted to this particular case study). Here, the code to carry it out is detailed, and its results are discussed, which obviou...
Robust stability margins [robstab, wcgain, robgain]: 2nd order system with uncertain damping, Matlab
มุมมอง 66หลายเดือนก่อน
This video outlines the meaning of the robust stability (or robust performance) margins given by the {robstab} (robust stability margin), {wcgain} (worst case gain) and {robgain} (robust performance margin) commands of Matlab's Robust Control Toolbox. For simplicity, the case of a second-order uncertain open loop system (mass-spring-damper with uncertain damping) is addressed, although the most...
Aircraft phugoid mode: simulation, animation code (simplified equations, Matlab ode45)
มุมมอง 69หลายเดือนก่อน
This video presents the detail of the Matlab code necessary to make simulations and animations of the 2D phugoid flight mode (longitudinal dynamics) of an aircraft (also called "fugoid mode" in other sources). The first two minutes review the state equations to be simulated (further details in video th-cam.com/video/M_VhFU29nj4/w-d-xo.html ). A theoretical analysis of the equilibrium points and...
Hidden tiger 6: RECURSIVE Bayes formula, any number of roars (proof)
มุมมอง 35หลายเดือนก่อน
This video reviews the theory behind the recursive Bayes formula for the N "hidden tiger roar" problem. The NON-recursive formula was discussed in the video th-cam.com/video/U23HJSN0pKA/w-d-xo.html . Here, we verify that applying N times the Bayes formula with the `1 roar conditional table' gives the same final posterior probability as applying the `N roar table' just one single time. In both c...
phugoid mode: simulation/animation examples, simplified flight dynamics, Matlab
มุมมอง 71หลายเดือนก่อน
This video presents simulations and animations with different lift/drag coefficients and thrust values of the simplified fugoid mode of flight dynamics model whose derivation was discussed in the video th-cam.com/video/M_VhFU29nj4/w-d-xo.html . The detail of the Matlab code to run these examples is presented in the video th-cam.com/video/2uad_enY1Qc/w-d-xo.html . The chosen examples are the fol...
Maximum volume ellipsoid inside polyhedron and other ellipsoids: 2D example, Matlab (LMI/SDP)
มุมมอง 49หลายเดือนก่อน
This video discusses the problem of obtaining the maximum volume ellipsoid inside a convex body defined as the intersection of polyhedra and ellipsoidal sets; well, as we are detailing a 2D example, we will actually speak abput polygons and maximum area ellipse, but the ideas efficiently generalise to higher dimensions in a trivial way. We use Matlab YALMIP SeDuMi to solve the associated semide...
Sampling Gaussian processes with observations (sampling the posterior), Matlab example
มุมมอง 57หลายเดือนก่อน
This video discusses how to compute realizations of a stochastic process when you have observations of its value at a set of `measurement' points. For example, the stochastic process may be the speed of each car at different points on a highway, and you want to 'interpolate' for a specific car the most likely speed trajectories as a function of time knowing that, in two positions where there wa...
Distance between ellipses: semidefinite programming, linear matrix inequalities [SDP/LMI]
มุมมอง 52หลายเดือนก่อน
This video explains how to compute the distance between two ellipses (minimum distance between any pair of points in them), by optimizing a function subject to linear matrix inequalities (LMI), that is, semidefinite programming (SDP). The example is a 2D (ellipse) one, but it trivially generalizes to ellipsoids in 3D and higher dimensions. The basic idea is to express the ellipses (x_i-c_i)^TQ_...
Time response, RCR circuit: pulse train, Laplace transform techniques for circuit analysis
มุมมอง 28หลายเดือนก่อน
Time response, RCR circuit: pulse train, Laplace transform techniques for circuit analysis
Sampling Gaussian processes (realizations of stochastic process): Matlab example
มุมมอง 372 หลายเดือนก่อน
Sampling Gaussian processes (realizations of stochastic process): Matlab example
Longitudinal phugoid dynamics of aircraft/glider (2nd order ODE, simplified flight dynamics)
มุมมอง 162 หลายเดือนก่อน
Longitudinal phugoid dynamics of aircraft/glider (2nd order ODE, simplified flight dynamics)
Time response RCR circuit: single sinusoidal pulse (2: piecewise, Laplace), circuit analysis
มุมมอง 252 หลายเดือนก่อน
Time response RCR circuit: single sinusoidal pulse (2: piecewise, Laplace), circuit analysis
Hidden tiger 5: Bayes formula for ANY number of roars (non-recursive) heard by zookeeper
มุมมอง 192 หลายเดือนก่อน
Hidden tiger 5: Bayes formula for ANY number of roars (non-recursive) heard by zookeeper
Time response of RCR circuit to single sinusoidal pulse (1: Laplace, superposition) circuit analysis
มุมมอง 2.2K2 หลายเดือนก่อน
Time response of RCR circuit to single sinusoidal pulse (1: Laplace, superposition) circuit analysis
IMC control of fast process: constant Q [internal model control]
มุมมอง 352 หลายเดือนก่อน
IMC control of fast process: constant Q [internal model control]
Laplace transform: sinusoidal pulse (1 semiperiod)
มุมมอง 652 หลายเดือนก่อน
Laplace transform: sinusoidal pulse (1 semiperiod)
Hidden tiger 4: conditional + Bayes rule, TWO roars
มุมมอง 482 หลายเดือนก่อน
Hidden tiger 4: conditional Bayes rule, TWO roars
RC circuit + leakage resistance: state space + Laplace domain model (Symbolic toolbox)
มุมมอง 1222 หลายเดือนก่อน
RC circuit leakage resistance: state space Laplace domain model (Symbolic toolbox)
Mathematical and computational (digital twin) models of physical systems: motivation, practical use
มุมมอง 923 หลายเดือนก่อน
Mathematical and computational (digital twin) models of physical systems: motivation, practical use
Hidden tiger 3: marginal, conditional, Bayes rule, graphical interpretation
มุมมอง 153 หลายเดือนก่อน
Hidden tiger 3: marginal, conditional, Bayes rule, graphical interpretation
Interactive simulation of a liquid tank: Matlab class, source code detail
มุมมอง 313 หลายเดือนก่อน
Interactive simulation of a liquid tank: Matlab class, source code detail
3 mass 4 spring mechanical system: modal analysis, free response oscillations (damped)
มุมมอง 483 หลายเดือนก่อน
3 mass 4 spring mechanical system: modal analysis, free response oscillations (damped)
Hidden tiger 2: joint to marginal and conditional; direct/inverse conditional tables
มุมมอง 173 หลายเดือนก่อน
Hidden tiger 2: joint to marginal and conditional; direct/inverse conditional tables

ความคิดเห็น

  • @mmoa1997
    @mmoa1997 17 วันที่ผ่านมา

    Thanks for the video. What happens to the pressure variable inside the tank?

    • @ASalaControlEN
      @ASalaControlEN 17 วันที่ผ่านมา

      I am not modelling pressure. So, this extremely simplified model is intentionally useless to compute pressure drops and pumping power needs: I am just modelling thermal energy balance under incompressible and constant specific heat assumptions. Regards!

  • @59vijaiyaaravindthsr39
    @59vijaiyaaravindthsr39 28 วันที่ผ่านมา

    thanks for making this video sir

    • @ASalaControlEN
      @ASalaControlEN 28 วันที่ผ่านมา

      Thank you for the comment. Best, Antonio.

  • @rezah336
    @rezah336 หลายเดือนก่อน

    it's better than nothing but it is still assuming the system is a 2nd order system, if the system is not 2nd order which is the case if you cant model it correctly with a 2nd order the whole concept falls

    • @ASalaControlEN
      @ASalaControlEN หลายเดือนก่อน

      Indeed, you are right, thanks for the comment. Of course, this is a "toy example": a system with a single uncertain real parameter, plus the fact that it is in "open loop", which makes things even simpler. The true reach of uncertainty descriptions in robust control is usually apprehended in closed-loop configurations, also adding some "ultidyn" (uncertain LTI dynamics) with no prescribed order in order to encompass that "unmodelled dynamics" in the uncertainty description, or using small-gain results to probe robustness even in front of sector-bounded nonlinearities... In summary, this video is just a first glance to the idea, oriented to students that were taught what damping and overshoot is, in order to motivate them towards the interest of more ellaborate approaches, Regards!

  • @rodericksibelius8472
    @rodericksibelius8472 2 หลายเดือนก่อน

    A seasoned experienced Electronics Technician can breadboard and explain it's workings and troubleshoot the circuit using simple 'algebra and trigonometry' without using Laplace jargon and complex mathematics, using calibrated, oscilloscopes, high quality parts, voltmeters, ammeters, and even with the aid of a spectrum analyzer, Vector Network Analyzer etc...etc... I have great respect for Engineers and Physicist who can derive equations from complex theory, using mathematical software, and predict the behavior of circuit designs, and apply it to a design to practicality in the real world.

    • @ASalaControlEN
      @ASalaControlEN 2 หลายเดือนก่อน

      Thanks for commenting... and, yes, an experienced technician can do many things... and often be faster than an engineer in doing them... but somebody must invent/define what "phase angle" is, and what "spectrum" is before building the first spectrum analyzer, so everybody is needed: someone must know Maxwell equations to pass them to the next generation but he might have no idea on what a "ground wire" in a home is, and vice-versa, a technician can set up your antennae, fiber, grounding, etc. without knowing who were Laplace and Maxwell , and in a much better way than a Physicist!. Thanks God, all flavours of technical knowledge have its role. Regards, A. Sala.

    • @tybeedave
      @tybeedave หลายเดือนก่อน

      @@ASalaControlEN my fav sinusoidal waves are photons, may I offer these tidbits from the Popcorn Model of Nature's Reality. This is in the study of the Harmonics and the Harmony of Our Universe in the context of Everything: so, lets use a metaphor where 1 musical note, (*) , represents Nature's Reality; This note, (*) , represents the true existence of Nature's reality. This is the realm of the lord, the almighty GOOD (not a religion but an attitude). The real note in which everything resides. What follows are just harmonics of the supreme existence of reality. 1st harmonic of reality (hor)* the human mind and the MotherVerse. 2nd harmonic of reality * commonly referred to as our universe and where electromagnetic radiative force is dominant. 3rd hor * dark matter, the strong nuclear force dominates. 4th hor * the weak nuclear force dominates. 5th hor * gravity, where the popcorn really explodes. 6th hor * time, the here and now where the rubber meets the road. The 3rd, 4th, and 5th combine to create Dark Energy. This not everything. Undescribed harmonics extend, ad infinitum, above and below the note (*). The harmonics show that space that appears empty is never in fact empty. Between Nothing and Everything is Something :)

  • @ButchNews
    @ButchNews 2 หลายเดือนก่อน

    Don't do this stuff, but thanks, anyway. Physics nerd.

    • @ASalaControlEN
      @ASalaControlEN 2 หลายเดือนก่อน

      Thanks for your comment... From me, wannabe nerd, to actual nerd: if you are in particle physics, this is just a toy problem compared to Einstein, Dirac and the like whose intricacies I fail to comprehend. By the way, you've got quite an eclectic/unconventional channel: pride, Socrates, physics... thumbs up!.

    • @ButchNews
      @ButchNews 2 หลายเดือนก่อน

      @@ASalaControlEN It's quite nice and I taught myself basic electronics when I was 13. It's ALL connected, one way or another.

  • @theoryandapplication7197
    @theoryandapplication7197 2 หลายเดือนก่อน

    thank you very much

    • @ASalaControlEN
      @ASalaControlEN 2 หลายเดือนก่อน

      Glad it helped ;-)

  • @YOUSUPERTERIO
    @YOUSUPERTERIO 2 หลายเดือนก่อน

    10:10

    • @ASalaControlEN
      @ASalaControlEN 2 หลายเดือนก่อน

      Concise but intense 🙏

    • @YOUSUPERTERIO
      @YOUSUPERTERIO 2 หลายเดือนก่อน

      @@ASalaControlEN Thank you for your efforts

  • @darkside3ng
    @darkside3ng 3 หลายเดือนก่อน

    Amazing!!!!! Thank you very much for sharing this splendid content.

    • @ASalaControlEN
      @ASalaControlEN 3 หลายเดือนก่อน

      You are welcome. Thanks for the comment.

  • @maymetaylor9768
    @maymetaylor9768 6 หลายเดือนก่อน

    Thank you : 3 Helped a lot

    • @ASalaControlEN
      @ASalaControlEN 6 หลายเดือนก่อน

      I'm glad to be helpful. Thanks for commenting! Just added a link to the `matrix form' video in the description.

  • @rogeliomoisescastaneda7396
    @rogeliomoisescastaneda7396 7 หลายเดือนก่อน

    Nice example, thanks!

    • @ASalaControlEN
      @ASalaControlEN 7 หลายเดือนก่อน

      You are welcome!

  • @albertocuesta7054
    @albertocuesta7054 10 หลายเดือนก่อน

    Nice video, bro! Keep it up :)

    • @ASalaControlEN
      @ASalaControlEN 10 หลายเดือนก่อน

      Thanks 🙏 Gracias

  • @amaros2118
    @amaros2118 10 หลายเดือนก่อน

    My brain stops braining

    • @ASalaControlEN
      @ASalaControlEN 10 หลายเดือนก่อน

      Wow... Maybe power off, reboot and underclock your CPU at 0.75X . 😵‍💫