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Questions tagged [nonlinear-control]

For questions regarding the control of nonlinear dynamical systems with known or unknown nonlinearities.

Nonlinear control is the tool used to force certain desired behaviors directly into nonlinear plants which in general provide an enhanced and more accurate description of the physical dynamic processes. Nonlinearities can be considered known, unknown or even approximated through certain mathematical tools such as neural networks, basis functions etc. The designer should take into consideration these knowledge regarding the system in order to design a proper nonlinear controller. More information can be found under this link: Nonlinear Control.

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A clarifying question on Lasalle invariance principle

Given a nonlinear system \begin{equation} \dot{x}=f(x),~x(0)=x_0 \tag{1} \end{equation} where $f\in{\mathcal{C}^{1}}:D\to\mathbb{R}^{n}$. The Lasalle invariance theorem statement goes as follows: Let $\Omega\subset{D}$ be a compact set that is…
jbgujgu
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Non-Linear Analysis Convergence Problem in Ansys

I am currently conducting a static structural analysis study in Ansys and encountered convergence prolems. I have a very large thermal gradient (almost 600°C) as input from a precedent transient thermal analysis which I apply gradually. I am looking…
hansophyx
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PI or PID-regulator for control system with hysteresis relay in inner loop

I have such control system (sorry for rough drawing :) ) $G(s)$ - stable object with proper transfer function. $1/s$ - integrator. I need to clarify, how synthesized PI or PID controller for such object, that include inner-loop with…
ayr
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Is it theoretically possible to control an continuously flexible inverted pendulum?

We can control an inverted pendulum relatively easily with PID. We can control a double-inverted pendulum with more sophisticated methods. Lately, a triple inverted pendulum was controlled, with 56 transition states mapped. So, how far can this go?…
sebzuddas
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How do I study the frequency response of a physical system with Arduino?

I am a control engineering student and I am studying the frequency response of a system, so the Laplace domain, the Bode plot, poles, zeros,etc. ... I have clear grasp of their meaning, but if I think about the practice it is hard to grasp, at least…
dcr
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Adding phase error to a system based on phase margin

I have a MIMO transfer function and referring to a research work, I have found a phase margin for this MIMO system. I want to check and see the system blow when a phase error greater than the phase margin is introduced to the system. But I cannot…
Aniket Sharma
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Converting nonlinear system into equivalent nonlinear of the Byrnes-Isidori normal form

I have a nonlinear system (Ball & Beam) which is described by the following equations of motion: $$ \ddot{y} + \frac{mg}{a} \sin(θ) -\frac{m}{a}y\dot{θ}^2 = 0 $$ $$ \ddot{θ} + \frac{2m}{b}y\dot{y}\dot{θ}+\frac{mg}{b}y\cos(θ) = u $$ where the letters…
Teo Protoulis
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Is nonlinear control slower than linear control?

Is there any scientific comparison between linear and nonlinear systems? I often hear that Nonlinear control is more sluggish than linear control. which makes sense. But is there any research or any claim based on practical experience which…
user15940
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Linearization about equilibrium point 0 in the presence of unknown input

Consider a SISO non-linear system $$\dot{x} = F(x,u)$$ in which $\vec{0}$ is an equilibrium point. In the process of determining that it is indeed an equilibrium point, the input did not matter at all. It was completely independent, due to the term…
Anonymous
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What's a real life example of linearization of a system around a fixed point

I'm tasked on finding a example of a real non-linear control system. a real paper or publication on a website like the IEEE thats describes the model of the system so I can then linearizy it around a fixed point an simulate it. I'm having trouble…
Enrique Cisneros
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How could I verify the stability of a real system with non-linearities?

For a closed loop system, I could do the stability margin analysis using linear method like bode diagram, but in reality there are non-linear elements in the system like saturation/rate limits inside the control loop, so is the computed stability…
LHX
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Increasing convergence rate using Optimal Control and Pontryagin Maximum Principle

My question is in addition to Tuning the optimal control synthesized according to the Pontryagin maximum/minimum principle and choosing the cost function, but requires help from the mathematical side of view. Given system of ODE: $F=\begin{cases}…
ayr
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High pass filter and differential equation relationship

Consider the problem stated as follows: A signal y passes through a high pass filter $\frac{s}{s + ω }$. A high pass filter with cutoff frequency ω isolates the variations of this optimized variable from its average value. The state that represents…
Tee
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Fixed end points optimal control problem

Given two points $(t_0,x(t_0)=x^{0})$ and $(t_1,x(t_1)=x^{1})$ in the $(t,x)$ plane, the objective is to find an optimal trajectory $x^{*}(t)$ such that the cost function \begin{equation}\label{eq:1} J(x) = \int_{t_0} ^ {t_1} g(x,\dot{x},t) dt…
jbgujgu
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Bounds to prove exponential stablity for given Lyapunov function

Problem 3.6 in Khalil's Nonlinear Control: Use given Lypunov candidate function to prove that the origin is exponentially stable. The system is…
drC1Ron
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