Questions tagged [nonlinear-control]

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

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Scaled Relative Graph Analysis

The drug concentration levels $c_1$ and $c_2$ in two compartments are modeled by the following differential equations: $V_1\dot c_1=-\rho_1(c_1)-\alpha_{12}c_1+w_1$ $V_2\dot c_2=-\rho_2(c_2)-\alpha_{...
BeNavon's user avatar
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Analyzing shear stress of plate

I would like to conduct a nonlinear analysis to obtain the stress-strain curve of a plate subjected to shear force, as depicted in the figure below. However, I am encountering difficulties in setting ...
moong's user avatar
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Linear and nonlinear model outputs are different using the same input

I'm working on something in nonlinear control, and we want to compare the output of the obtained linear model (state space form using steady state data) w.r.t the nonlinear model. Attached is a ...
Chek Mate's user avatar
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What is the relationship between classical control: transfer functions/frequency domain and the swing-up problem of an inverted pendulum

I am still pretty new to control theory, but I have been studying both classical and modern state space/optimal control ideas. I am having trouble understanding what the frequency domain/transfer ...
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Type of Lyapunov surfaces corresponding to a specific Lyapunov function

Consider the following Lyapunov candidate function: $$ V(x,y,q_i) = \frac{1}{2}x^2 + \frac{1}{2}y^2 + \sum_{i=1}^{n}\ln\big(\cosh(q_{i})\big) \tag1$$ where $q_{i} = \sqrt{(x-x_{i})^2 + (y-y_{i})^2} - ...
Teo Protoulis's user avatar
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Why the control input for in the operating point is not considered in the control?

One method of controlling a nonlinear system is linearizing the model in an operating point and gain scheduling the controller. The operating point includes a state and an input (the trim input) so ...
user45799's user avatar
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Control with variable delay plus inverse relationship

As we all (should) know, PID controllers are pretty bad when the system they control isn't linear. In my case, I have a water heater and a pump. I want to control the pump so that the output is at a ...
Matthias Urlichs's user avatar
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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 ...
sebzuddas's user avatar
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Control a plant with a general logistic function like characteristic

I have a "real" plant, which is basically a light bulb, with a characteristic curve which matches the shape of a generalised logistic function I need to control that plant dynamically over ...
Pj Toopmuch's user avatar
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Use feedforward to control a simple pendulum open loop system

I am currently simulating a simple torque controlled pendulum in simulink (friction accounted for). This and all works like a charm. Now for the control of the system am using the system's ...
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How could Adrian Bejan's 'Constructal Law' be formulated mathematically?

Adrian Bejan is known for having devised a very interesting theory for the hierarchical and aesthetic structure found in nature, from the branching tree shape of river deltas to the tree shape of ...
ariejdl's user avatar
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Real examples of complex PID regulators

I am currently developing the C library for easy implementation of PID controllers. Can you give some examples of complex PID controllers from real life? I don't mean a simple DC motor with a speed ...
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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....
Anonymous's user avatar
3 votes
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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 ...
hansophyx's user avatar
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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 ...
Enrique Cisneros's user avatar
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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 ...
Meeron's user avatar
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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 ...
Rodrigo de Oliveira's user avatar
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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 ...
dtn's user avatar
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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 ...
Asdasd34's user avatar
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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 ...
dtn's user avatar
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2 votes
1 answer
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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{...
dtn's user avatar
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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: $$ ...
dtn's user avatar
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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 ...
dtn's user avatar
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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 ...
dtn's user avatar
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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^{-(...
dtn's user avatar
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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 ...
dtn's user avatar
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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)) ...
dtn's user avatar
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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\...
link's user avatar
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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 ...
dtn's user avatar
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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 ...
Aniket Sharma's user avatar
7 votes
3 answers
304 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 $...
jbgujgu's user avatar
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2 answers
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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-...
David Zanger's user avatar
2 votes
0 answers
91 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{...
Teo Protoulis's user avatar
1 vote
1 answer
78 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},...
drC1Ron's user avatar
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330 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?
Superman's user avatar
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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 ...
JuanEsteban Valdez's user avatar
2 votes
1 answer
237 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 ...
user15940's user avatar