Questions tagged [nonlinear-control]
For questions regarding the control of nonlinear dynamical systems with known or unknown nonlinearities.
22
questions
2
votes
1answer
62 views
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 ...
1
vote
0answers
22 views
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 ...
0
votes
1answer
50 views
Input signal rescaling block [closed]
The input signal is limited and lies in range $[-U;+U]$. $U$ - unknown.
The output signal must be rescaled to be in the range $[-1;+1]$, i.e. is $+1$ if the input is at steady-state $+U$, and $-1$ if ...
0
votes
0answers
44 views
Nonlinear system with time-optimal control
Given nonlinear system:
\begin{cases} \dot{x_1}=x_3+u \\ \dot{x_2}=-x_2+\dot{f} \\ \dot{x_3}=-x_3+x_2 \cdot \alpha \sin(\omega t) \\ \dot{x_4}=-x_4+x_2 \cdot (\frac{16}{\alpha^2}(\sin(\omega t)-\frac{...
0
votes
1answer
36 views
Zero overshoot criterion from the initial point $x_0$ to the final $x_*$, $x_*$ unknown in advance
Suppose a system is described by the following ODE:
$$\dot{x} = f(t,x)+u$$
where
$x$ denotes the state of the system
$f(x,t)$ is an unknown nonlinear function which meets the following condition:
$$ ...
0
votes
1answer
49 views
Which way of solving from nonlinear control to choose?
I have a nonlinear system:
\begin{cases} x'=f(x)+u \\ y=f(x) \end{cases}
where $f(x)$ - gradient of some one-extremal function (for example $f=e^{-(x)^2}$), i.e. $\frac{df}{dx}$.
Task:
I want ...
1
vote
2answers
60 views
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 ...
0
votes
0answers
39 views
Optimal control of the gradient type PDE
I recently encountered the following optimal control problem.
The purpose of the system is to find the parameter $x$ at which the maximum or minimum of the function $f$ a is reached. $x$ is unknown to ...
0
votes
0answers
37 views
Controlling the dynamics of nonlinear systems with an unknown steady state
On the one hand, the question is simple, on the other hand, I need the help of specialists in control theory.
Let's take a simple gradient dynamical system:
$\frac{dx}{dt}=\frac{df}{dx}$
where $f=e^{-(...
0
votes
1answer
54 views
Changing the quality of the transient process in a nonlinear system (Part II)
My question is a continuation of the topic.
https://math.stackexchange.com/questions/3910814/changing-the-quality-of-the-transient-process-in-a-nonlinear-system-in-mathemat
Unfortunately, last time I ...
0
votes
0answers
45 views
Changing the quality of the transient process in a nonlinear system (in Mathematica)
I urgently need advice and help.
I have a system of differential equations like this:
$\begin{cases} \frac{dx}{dt} = y[t] \cdot \alpha \cdot sin(\omega t) + \frac{d}{dt}(\alpha \cdot sin(\omega t))
...
0
votes
1answer
57 views
Numeric quadrature vs summation of running costs in model predictive control
Usually, an MPC consists of discretizing the optimal control problem in time using some numerical quadrature scheme. So the infinite-dimensional OCP reads
$$\begin{aligned}J(\vec{u}) &= \varphi\...
1
vote
1answer
31 views
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}
...
0
votes
0answers
44 views
Research of transients in nonlinear systems with linear dynamic links
I am having difficulties of this nature. There is a nonlinear system of the following type:
I need to analyze analytically the transient process in such a system. The analytical study of the ...
2
votes
1answer
41 views
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 ...
6
votes
2answers
133 views
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 $...
-1
votes
2answers
69 views
Control of a nonlinear static MIMO System
I am currently writing my master thesis and trying to design a controller for my system. However, the system is somewhat unconventional.
It has a large number of inputs and outputs, is static, non-...
2
votes
0answers
67 views
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:
$$ \ddot{y} + \frac{mg}{a} \sin(θ) -\frac{m}{a}y\dot{θ}^2 = 0 $$
$$ \ddot{θ} + \frac{2m}{b}y\dot{...
1
vote
1answer
40 views
Bounds to prove exponential stablity for given Lyapunov function
Problem 3.6 in Khalil's Nonlinear Control: Use given Lypunov candidate function to prove that the origin is exponentially stable. The system is
$$\dot{x}=\begin{bmatrix}x_2\\-h(x_1)-2x_2\end{bmatrix},...
0
votes
2answers
154 views
Which course to take? Optimal control? Nonlinear control? [closed]
I have tried to compare two courses, and there seems to be some overlap, but not as much. Which method is better when controlling a nonlinear system? Also, what is the main difference between the two?
1
vote
0answers
58 views
What are some practical applications of nonlinear control and multivariable control in the industry?
All the books I've used in my control systems class give a definition multiple-input, multiple-output systems and nonlinear systems, but all the techniques covered in the folloing chapters apply only ...
1
vote
1answer
128 views
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 ...
