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# Dynamic Systems - Science topic

Explore the latest questions and answers in Dynamic Systems, and find Dynamic Systems experts.

Questions related to Dynamic Systems

I am working on dynamic state estimation of power system for IEEE 14 bus system using Kalman filter.

1. I was taking F as unity matrix, but estimation was very poor when compared with RSCAD measurements data. However, it works when i took simulated measurements, estimation was better.

2. Is there any method to get F matrix of the dynamic system.

3. Is there any other error problem might be there.

Please Suggest.

Thanks

Sumanta Nanda

I need to use mathematical software program for mathematical modelling such as; modelling of dynamic systems etc.

I have a dynamic system including some nonlinearitoes, and want to control its output (Y). The concept of the control is to use MPC for reference output signal (y*) planning then another controlller will be utilized to provide an input (u) to track the reference output (y*). The process should be completed within 300 ms.

There are a wide variety of control method avaliable in the literature, and for a non expert in system control and control theory, it is not an easy task to choose from.

I am looking after a control method that can be combined with MPC to produce a stable controller and perfume the task within the alloted time.

I created Electric vehicle dynamic model in Matlab Simulink.IT is showing the perfect result. But I am facing the difficulties when I am integrating that EV in any system or MG. Its either not running or its taking too much time to run.How to solve this issue,can anyone find the solution please let me know.

It is known that in order to quantify chaos in a dynamic system, the maximum Lyapunov exponent must be detected, but before applying Lyapunov detection, is there any way to know at a glance a dynamic system is chaotic ?

Is it enough to see that the phase space is fully and disorderly filled up? It happens that in a dynamic system I am computer simulating I get a fully and completely disordered state space. I want to know if this is an indication of chaotic behavior.

Thanks in advance to those who answer !!!

Regarding the analysis of a dynamic system without wavelets and with wavelets, I obtained values. My question is, if I want to find the optimal answer from the obtained values(D parameter), what optimal methods or references are used for the dynamic system?

Also, if I want to analyze the error according to the values obtained (D parameter), what are the methods or references for error detection in dynamic system?

Hi,

I am doing research on differential equations but came around the term dynamic system and dynamical system. Some papers says dynamic systems and some other says dynamical systems. I can't figure what the exact technical difference between these two terms or are they just two different words used with the same meaning. Thanks in Advance

When the solution of a dynamic system is obtained in time series, to analyze that solution in the frequency domain, we can use the power spectrum (one of the system displays in frequency), but MATLAB does not have a Fourier transform signal plot like power spectrum plot for the time domain,

Chaos is a long-term non-periodic behavior in a deterministic system that is dependent

Shows sensitivity to initial conditions.

The operating environment of chaos is dynamic systems. A dynamic system consists of a single phase space or a fuzzy state whose coordinates determine the dynamic state of the system using dynamic laws.

A dynamic system can be Intermittent or chaotic. Dynamic systems (Lorenz-Rossler) are called strange attractors because they are a set of all paths that converge toward a fixed point, a finite loop, or so on.

Attractors are highly sensitive to initial conditions and are called strange because they consist of a fractal set.

Can any body suggest me a straightforward way with low computational cost, for obtaining LCO amplitude and frequency for multi-dimensional phase space?

With Fourier relations, the Lorenz and Rossler dynamic system was formulated (alpha) based on fixed parameters, and analyzed with fixed parameters to describe the chaotic behavior,

Is it possible to create an image of dynamical systems to analyze the the concept of fractals and chaotic behavior?

I am looking for Python packages which represent a good alternative to Matlab's System Identification Toolbox (or at least for parts of it). It would be great if you could recommend Python packages for linear and nonlinear system identification where you have already gained extensive experience. What are your experiences with e.g. SIPPY or SysIdentPy? Are there better and more comprehensive Python packages?

I especially plan to use the identified models for MPC and NMPC. Thanks in advance!

Best regards,

Günther

I have two matrices

**and***U***, each containing the eigenvectors of two respective and independent dynamic physical systems. In other words,***W***and***U***each span respective subspaces (***W**eigenspaces*). My scope is to show that**and***U***belong to some mutual vector space***W**V.*More specifically:

a) what does the angle between subspace

**and subspace***U***tell me about their relationship in terms of a hypothetical mutual vector space***W***?***V*b) if

**and***U***are intersecting, how do I compute the subspace in which the intersection lives?***W*c) if

**exists, how do I compute its basis?***V*How do I approach a), b) and c) in Python?

Apologies if these questions may overlap eachother. Many thanks in advance!

As I know, the ordinary differential equation (ODE), xdot= -x^3+u, where x is the state variable, and u the control variable, is the control system associated to a falling object in atmosphere with viscous drag. I am not sure to be correct on that! Please comment on that!.

**Update 1**: xdot= -x^3+u, is called the hyper-sensitive system.

c.f.: A Collection of Optimal Control Test Problems: John T Betts.

Another example is velocity control for aircrafts in horizontal flight, which has an ODE evolution:

xdot=-x^2+u. Notice the attachment picked from:

Optimal Control with Engineering Applications; By: Hans Peter Geering.

I want to also know the real model associated to the control system described by the ODE: xdot= x^3+u. I guess more probably, this is associated to electrical systems.

**Update 2:**My own intuition says, positively damped systems as:

x_dot+x^3=u

are mechanical. Meanwhile, negatively damped systems as:

x_dot-x^3=u

are electrical.

You can yourself find some other examples in this regard.

What are temporal limits in determining brain metastability? In other words, how long does the minimum length of the scan segment using fMRI have to be for the result to be of any value?

I'm particularly interested in measuring metastability during decision making. If I have two different decision conditions, which are shown alternately in the fMRI paradigm (so let's say condition A and B, and paradigm look like it: ABABABAB....), will "slicing" the data and combining them later produce reliable results in the context of metastability estimation (so I could calculate metastability for A and B condition separately)?

I came across a publication where a similar operation was performed (Alderson, TH, Bokde, AL, Kelso, JS, Maguire, L. and Coyle, D., 2020. Metastable neural dynamics underlies cognitive performance across multiple behavioral paradigms. Human brain mapping, 41 ( 12), pp. 3212-3234.). However, it concerned cutting out fixation elements between trials and joining whole blocks. I, on the other hand, want to cut and join the trials, then compare the level of metastability between the two conditions. Is it possible, or not really good idea?

I want to know that we have a real system with fractional order state space model

Dear colleagues, friends, and professors,

As we know, we have very strong analytical approaches to control theory. Any dynamic decision-making process that its variables change in time could be characterized by state-space and/or state-action representations. However, we see very few control viewpoints for solving electricity market problems. I would like to invite you to share your thoughts about the opportunities, and limitations of such a viewpoint.

Thank you and kind regards,

Reza.

Hello everyone, I hope you have a good day,

As we all know, the lateral dynamic system of vehicles has two output, lateral error and heading error, and we have one input, which is steering angle, I always have one big problem:

**How to Design a Controller to have zero steady-state error, when I have XY reference path?**

I designed a controller to track the heading, but when the vehicle gets departed from the path, as it does not have any sense of lateral error, it will not come back to the path, it will just follow the heading with some offset.

I read a lot of papers in this area, but none of them talked about XY reference paths.

I add a photo to clear up some points, please check the attached file.

Thanks in advanced,

Arash

I am working on system identification for general dynamic systems.

The idea is that I think it can be well-presented using regression using the input and output data.

Do you know anyone who worked on this before, or maybe, you can direct me to published work of something similar?

Thank you very much

Measuring dependency of chaotic systems on initial values by Lyapunov exponent, an original trajectory along with a perturbed one is needed, but I cannot understand the connection with the following article, (fig.3 of the article).

Nature or the earth is not static but dynamic in nature. I am very interested to the possible reason behind this.

Whath does a pair of equal floquet multipliers signify in stability analysis

In the paper which is attached in simulation results section, four sigmoid activation functions are introduced but all of them are for scalar input (and using such sigmoids the method just works for systems with one state variable ) so if one decides to apply this controller (Neuro-adaptive controller) to a dynamic system with higher orders(2,3,....),what should be the form of sigmoid activation functions?

What's the similarity of these systems? How can I identify them?

How could we calculate the zero dynamics of a MIMO nonlinear system with non-zero initial condition?

I am dealing with a nonlinear system in which having a positive value on the inputs (cable tension) is one of the necessary condition for the system to be active. I would like to know how can the zero dynamics of the system be calculated in a non-zero initial condition.

Hi, Is it possible to implement these algorithms for dynamic state problem where the values are not static and continuously changing with respect to time?

And which algorithm is most suitable for dynamic state problem?

Please provide me your valuable answers. Thanks

When the system is not full state feedback, it contains inner state and outer state. The outer state is stable by a feedback gain, like u = -kx. Question: 1. How can I prove the inner state is stable or unstable?2. If the simulation results of the outer state is stable, can it prove the stability of zero dynamics? 3. I'm interested in the equilibrium point(not zero), and is it right that the zero dynamics of the system is $\dot_\eta = f(\eta, \xi=\xi_d)$, ?

I have a nonlinear model that I have applied feedback linearization to. However, the llinearized model no longer had valid physics. Can this issue be avoided? Could this issue be resolved if the dynamics of the system are represented in a different coordinate system?

Change is nature, and climate is changing. Human capacity in boosting and controlling climate change is still a debatable issue and has the scope of investigation. Whatever the level of human intervention in boosting climate change, human capacity of controlling climate change is very limited. We may slowdown the rate of changing climate but for sure, we cannot prevent it. Climate change is inevitable. The only realistic way to fight against climate change is adaptation.

For a sustainable adaptation, we must understand both positive and negative effects of climate change. Earth is a complete dynamic system and always trying to keep the system in a balance. Hence, when climate change is bringing future challenges for us, it is also bringing equal amount opportunities. For a better future, we must identify both challenges and opportunities.

Can you see any opportunities in climate change?

In "Simultaneous Stabilization and Tracking of Nonholonomic Mobile Robots: A Lyapunov-Based Approach", the authors stated that the nonholonomy of mobile robots allows control of the system with less control inputs. A mobile robot is underactuated in nature, and it's often controlled with less number of control inputs than the system's degree of freedom (if dynamic is ignored). How does the nonholonomy of the system helps with that?

I'm writing a project of energy reduction in a base station. Please I need guide on how to model a base station with respect to its energy consumption.

I have thermal dynamic system for shell and tube heat exchanger but i dont sure wheather from thermal dynamic system can design a form of shell and tube heat exchanger transfer function or not. Can someone help me with these confusion?

**A)**As evolutionary-NeoSchumpeterians (or complexity-oriented) economists, we conceive the economy as a dynamic system in which scattered heterogeneous and boundedly-rational agents interact. Local and global interactions involving feedbacks and domain-specific connections involve producing, investing, consuming, distributing incomes, trading in general, learning, innovating, entry/exit, etc. And the ongoing development of the specifc dynamics we propose to explore a problem generate "EMERGENT PROPERTIES".

**B)**The methodologies we use range from verbal logical arguments (which of course can be genuinely complex) to complex ABMs, passing through non-linear highly stylized models, replicator dynamics and evolving complex networks with the afore-mentioned components.

**C)**The specific methodology used is not innocous. Thus, whereas verbal arguments involving real complexity are often almost inestricable, ABMs are a bit more enlightening (the less so the higher the scale), and, in my opinion, the subset of low-scale ABMs, enriched-replicator dynamics, networks and non-linear styled complex models are the best. They often even allow for closed-form quasi-exhaustive analysis.

**D)**The problem is how should we pass from the results we obtain in our theory, to the posing of policy recommendations to be implemented within a reality which we perceive as emerging from a complex system?

Notice that there are two sources of complexity (2 complex realms involved):

**1)The inherent complexity of the real system**under scrutiny.

**2)The often black-boxed complexity of the theory we propose**.

We know that even small differences between two evolving complex systems can make a huge difference in their outcomes. If we assume (as we should) that we can never access the "real complex mechanism underlying reality" (just we should aspire to approach it, at least in social sciences), we should be very prudent in our policy prescriptions.

**E)**The

**solution**prescribed by those using simple models (mainstream economic models or simple statistical models) is not valid, since they begin by assuming that

**reality is SIMPLE**(instead of complex), and they falsely avoid the problem. Why should social reality be simple in its functioning? The historical record of crisis and social distorsions, and the analogies with natural systems point out to a clear failure of the standard approach. Thus, if we accept complexity:

How do you address

**the issue of double complextity 1) and 2)?**Dear colleagues,

I am trying to design a recurrent neural network to predict patients' length of stay as output. I have different types of data (numeric, categorical, free text, etc..) and I want to present the data as a time series( to capture the temporal dynamic of the system). It means I want the model to know when each piece of information is collected.

Here is my question:

1- What are the methods to feed the data into the model?

2- What are the advantages and disadvantages of each method?

Imagine we have an ODE system

x_dot=[f1(x,u), f2(x,u), f3(x,u),....fn(x,u)]

where f1,..,fn are nonlinear functions of control input u and states x,

x is member of R^n and u is member of R^m

under which conditions we can change the dynamic of the system to arbitrary dynamic x_dot=[f1_des(x) f2_des(x),...,fn_des(x)]

where f1_des(x) f2_des(x),...,fn_des(x) are arbitrary pre-defined nonlinear functions.

is input to state controllability enough to do that?

*Example*

*consider the 2-D system:*

*x1_dot=f1(x1,x2)+g1(x1,x2)*u1*

*x2_dot=f2(x1,x2)+g2(x1,x2)*u2*

*by choosing*

*u1=(f1_des(x1,x2)-f1(x1,x2))/g1(x1,x2)*

*u2=(f2_des(x1,x2)-f2(x1,x2))/g2(x1,x2)*

*we can change the dynamic of the system to*

*x1_dot=f1_des(x1,x2)*

*x2_dot=f2_des(x1,x2)*I am trying to use Model Reference Adaptive Control (MRAC) based on Lyapunov's rule on a system. My question is: should the reference model be assumed or is there a systematic procedure for determining its parameters in relation to the dynamism of the system in question.

It is clear that a dynamic system might exhibit

*chaotic behavior*(complexity), if internal feedback loops (nonlinear dynamics) exist among its interacting components for a certain range of*control parameter values*and the system is far from thermodynamic equilibrium (e.g. oscillating reactions). My question is:**Is there a systematic methodology (algorithm) to find the ranges of values for which the system exhibits chaos?**If I have a dynamic system, what are the differences between linear and rotational disturbances (single and multiple)? Also, what are the differences between disturbances on the dynamic system and disturbances on the motor torque system?

In a simplest case imagine we have a continuous finite-dimensional dynamic system described by and ODE

x_dot=f(x) (1) ,

Is it possible to prove the asymptotic stability of (1) by investigating the discrete time version of (1)

x(k+1)=F(x(k)) (2)

((2) might be written by RK4 discretization, Euler first order descretization or any other descretization scheme)

if it is possible to do that, what about infinite dimensional system resulting from space descritization of PDEs?

Task allocation problem is of critical importance in manufacturing industry, and determines the eﬀectiveness and eﬃciency of advanced manufacturing systems. In order to be adaptable to the needs and future challenges that industry are facing, like rapid changes of demands and requirements, the cost of the entire production system have to be minimized. This performance start by optimizing the sequences of tasks and resource allocations through the system, and this can be handled by using computers optimization algorithms.

Does this problem have a clear and straightforward algorithmic solution or

the resolution of this problem involve the use of heuristics?

My work is mainly experiment-based research. Moving a step further in the advanced analysis, can you please help me with the following questions?

1- Do you think this topic is linked with dynamic systems analysis? if yes: how this analysis should be done?

2- What kind of theoretical analysis (based on differential equations formulation) could be added to my research (especially to the vortex's stability and/or stochastic factors)?

3- What's your best suggestion for making sure that the results obtained (from experiments) are dependable? (Validation by CFD?)

Every single answer is important to me.

Thank you very much.

How can we characterize a chaotic system having two equilibrium points with a negative and two zero eigenvalue?

\lambda_1=-A and \lambda_{2,3}=0.

Is it a non-hyperbolic system? or there is another class of such systems?

As we know, coherent groups of synchronous generators can be identified and converted to an equivalent dynamic model to simplify a given power system and still maintain the dynamics of the system. However, the Type-3 and Type-4 wind farms do not possess much inertia and hence cannot replicate the behaviour of synchronous generators. What approaches can still be made to aggregate the wind farms present in a region and connect it to a single transmission bus, such that the dynamics of the system is still maintained? Any help on this would be much appreciated.

Hi,

I have a 3D figure of around 1000 points and the shape of the figure is very similar to a bifurcation. The question is how can I generate the related dynamic equation of these points?

Please let me know if you have any idea about using MATLAB codes as well.

Thanks

Dear Dr ,MARIUS-F. DANCA

I wonder I if I can have a thertical backround or Matlab code of Lyapunov exponents of (combined / hybridization /coupled) dynamic systems (Chaotic)

Best regards

Karima. Amara Korba

To verify if the system satisfies the observability property. Several techniques and tools have been developed to study whether a nonlinear system is observable or not. Generally, the observability property study of a nonlinear system are depended values when the expression of determinant (D) are canceled for limited points but not for all operation modes such as in the case of

*complex*expression of determinant.differences of dynamic systems with system thinking

I used the lagrangian energy methods and reach the ODE equations of motions and want to submit them to numerical integration in MATLAB to model the dynamics of the system.

Hello,

This project aims are to address the theory of dynamic systems from the pedagogy point of view or these intend to study the possibilities for the reformulations, for the re-conceptualizations ... of pedagogy from the perspective of the theory of complex systems?

In any cases, I thing that this project is very interesting and useful too for the knowledge society.

If I misunderstood, please give me some details about the objectives of your proposed project.

Sincerely,

Bogdan Nicolescu

How can I make a optimization code in Matlab for tuned mass damper?

Hi guys,

As you know when predicting multi step ahead if there is even a small error between actual and predicted one at the beginning, this error will be propagated through all predicted values so i want to know if there is any way to reduce this error.

Thanks

Hello Guys,

Suppose that we have a data from a chemical process. There are some inputs and one output, the output depends on those inputs and also the time. I am gonna identify this process. So what is the difference between using simple MLP with Lagged output as an input (lagging the output as an input to the model, like 5 step before) and using recurrent neural network such as ELMAN or JORDAN without lagging the output, because i know JORDAN is just feeding back one step before as an input.

Thanks

One of the central themes in Dynamical Systems and Ergodic Theory is that of recurrence, which is a circle of results concerning how points in measurable dynamical systems return close to themselves under iteration. There are several types of recurrent behavior (exact recurrence, Poincaré recurrence, coherent recurrence , ...) for some classes of measurability-preserving discrete time dynamical systems. P. Johnson and A. Sklar in [Recurrence and dispersion under iteration of Čebyšev polynomials. J. Math. Anal. Appl. 54 (1976), no. 3, 752-771] regard the third type („ coherent recurrence” for measurability-preserving transformations) as being of at least equal physical significance, and this type of recurrence fails for Čebyšev polynomials. They also found that there is considerable evidence to support a conjecture that no (strongly) mixing transformation can exhibit coherent recurrence. (This conjecture has been proved by R. E. Rice in [On mixing transformations. Aequationes Math. 17 (1978), no. 1, 104-108].)

Time constant is important in control engineering applications. Is there any mathematical concepts that can be used to calculate time constant from system mathematical model?

I am new to membrane dynamics simulation. In recent days i learnt to build a membrane dynamics system, but i doubt whether my system is properly made or not. I checked results of energy minimization, NVT, NPT and solvation layer too, everything is fine. But when i am performing a protein of 300 residues in lysozyme in water, the efficiency of my workstation is it can run 7.5 ns per day. For the same protein, when i am making the membrane simulation system, the efficiency of my workstation becomes it can complete 12 ns per day. Is this a common thing or a strange situation, where i might have commited some mistakes in preparing the system. Hoping for good suggestions and thanks in advance.

I am interested in studying the dynamics of a lipid vesicle. Surface Evolver seems to be a great program and quite extensible. However, as I understand it, the program only minimizes the total energy of the surface, and cannot be used to study the evolution (ironically) of the surface over time.

Are there any available programs, packages, or even libraries for programming languages, with similar capabilities as Surface Evolver to model the surface dynamics of systems with various topologies, and types of energies?

How far is it feasible to use an optimally tuned proportional-derivative controller to control a system with fast dynamics?

I understand PD controller suits best for the slow dynamic system.

Let's assume we have a dynamic system and we want to identify its unknown parameters in a real time procedure. Observability and identifiability are important for convergence of the estimation process. How can we ensure these two important characteristics?

Dear all,

I am trying to stabilize an inverted pendulum on cart. I was able to derive the dynamics of the system using Lagrangian mechanics and have a working simulation (I'm using LQR controller for stabilization). However, I have a question when it comes to actually implementing my code using a microcontroller. Here is what I am trying to do:

The laptop implements the LQR controller and passes the control information (u(t)) to the microcontroller (via serial communication). Now, this is where I have a problem. How do I relate the torque information to some appropriate PWM signal so that the microcontroller could pass it to the motor attached to the cart? Am I supposed to do torque control or speed control here? Any help will be much appreciated. Please feel free to ask questions for any clarification.

The delayed dynamical system is as follows:

dx/dt= -Betta*x(t)+F(x(t))+(Betta-1)F(x(t-d)),

x(t)=Phi(t) for t in[-d, 0] where d is delay and F(x(t)) is a projection function. I have Matlab code (using ODE45) for this delayed dynamical system without delay, but when the delayed added I don't know how I can insert the delay.

I would be very grateful if someone could help me to design Matlab code for such delayed dynamical system?

The scope of environmental risk assessment has been expanded from the traditional chemical and accident assessment to the inclusion of the potential harm from artificial introduction of species, both natural and genetically modified, into an ecosystem. Thus major categories of environmental hazards include chemical, physical, biological, and/or their combinations. Environmental entities can be more complex with respect to system structure and functions, although the methodologies are largely transplanted from human health risk assessment. Environmental risk assessment processes would involve problem formulation, characterization of exposure and effects, and risk characterization. The assessment can be made retrospective or predicative, depending on the risks involved and management requirements. Thus, is it possible to implemented the dynamic system methods to risk management in order to prevent environmental damage?

If xdot=Ax+Bu is a state space representation, what would a column of zeros in the A matrix depict in particular other than the system being singular in nature.

In control theory field, the rank of the controllable matrix is for investigating the control ability of the dynamic systems, and that the matrix is full rank means that the systems is the fully state controllable, and then the bigger the rank is, the stronger the control ability of the systems is. Up to now, no precise concept on the control ability is presented.

In fact, the rank of the controllable matrix and the controllablilty are not good measures on the control ability. For example, for the uncontrollable matrix pair (A,B), a little perturbation on the matrix A or B may lead to that the matrix pair is controllable. So, there isn't exist a distinct line between the controllability and uncontrollability concepts and the two concepts are fuzzy. Considered that the modeling error for the system models of the practical dynamic systems, the rank of the controllable matrix and the controllability aren't appropriate for investigating precisely the control ability of the practical dynamic systems.

In the studying on the precise measure on the control ability of the dynamic systems, the volume value of the controllable region under the unit input energy is propose as a new precise measure on that in my paper arXiv1705.08064(On Controllable Abundance Of Saturated-input Linear Discrete Systems). A new theorem on the positive relations among the volume value, the diversity of the control laws (i.e., the size of the solution space of the control laws) in the controller designing, and the performances and robustness of the closed-loop control systems is presented and proven in the paper. That is, the bigger the volume value of the controllable region, the richer the control laws, and then t the closed-loop control systems may be with he better performance and robustness. The volume value is a good measure on the control ability.

How to name the new measure? Which name is appropriate for that, controllable (or controllability) power, controllable (or controllability) abundance, controllable (or controllability) richness, or others? Which colleague gives some helpful suggestions.

Hello!

As a part of my research on urban transportation, I am using System Dynamics as a tool. If anyone has experience in System Dynamics / Systems Thinking, software tools for System Dynamics or its application on transportation systems, please get in touch with me.

Main Purpose -

1. Make friends from same working background :)

2. I want to engage in discussions with a peer

3. Get some inputs on selecting suitable software package

Thanks,

Madhur Jain

Following a good tradition of asking for examples of specific systems (non-lin., non-min-phase etc.) I'd like to ask if somebody could give me an example of a simple but still physically relevant LTV system.

Most textbooks contain examples with terms like t*exp(-2t) and so on, which are clearly artificial. Students are normally not very excited about dealing with such problems (which I find completely reasonable). I thus wonder if there are any examples which stem from real problems, but can be addressed within the framework of a class.

I'd be particularly interested in non-periodic cases, but the periodic ones are also welcome. Any references will be very helpful.