Questions tagged [nonlinear-control]

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

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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 ...
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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 ...
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SMC: Is there a way to control two sliding surfaces with just one control input?

This is a question related to Control Systems. I've been searching papers all over the internet with very little success. I know that traditionally we want one control per sliding surface but If ...
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Stability properties of controllers with independent control laws applied in underactuated systems

I am interested in designing a GNC controller for a 3DOF underactuated vehicle that follows a path in 2D space. The two available control inputs are the thrust force in the surge direction and a ...
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How do I find the tracking error when simulating spacecraft motion?

I have been studying Control of Nonlinear Spacecraft Attitude Motion and I would like to solve the following question. I have created the following MATLAB code that works for similar questions, but ...
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Best Techniques to design a cascaded precision position controller

I'm looking to design a cascaded controller to transform a BLDC into a servomotor. The system has a motor current controller in the inner loop, which is controlled by a torque controller, which is ...
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Block-diagram combining two controlled subsystems

I have two subsystems which are shown in the picture below. One of them is a system of stable and controlled differential equations of a mechanical system. Second is a block that implements a function ...
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Linearizing nonlinear system for PID control

I have a system where y = 1/x. (y=output, x=input) If I calculate the PID error not by reading y, but by reading 1/y (so linearizing the system), will my system be nicely linearized, and the PID ...
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2 answers
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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 ...
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Definition of BIBO stability of a nonlinear system

I am studying an electric motor whose state-space equations are nonlinear. I am trying to control the system through a closed loop and I would like to verify the BIBO stability. For linear systems, ...
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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 ...
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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 ...
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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 ...
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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 ...
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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{...
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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: $$ ...
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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 ...
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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 ...
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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 ...
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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^{-(...
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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 ...
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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)) ...
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65 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\...
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1 answer
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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} ...
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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 ...
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2 votes
1 answer
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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 ...
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7 votes
2 answers
179 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 $...
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-1 votes
2 answers
72 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-...
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2 votes
0 answers
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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{...
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1 vote
1 answer
43 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},...
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0 votes
2 answers
230 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?
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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 ...
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2 votes
1 answer
169 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 ...
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