9 votes
Accepted

Is nonlinear control slower than linear control?

"Linear" imposes a set of restrictions. "Non-linear" simply means there are no restrictions. Many non-linear control schemes can be faster than linear ones. Linear control schemes are restricted to ...
user avatar
  • 11.3k
5 votes
Accepted

Which course to take? Optimal control? Nonlinear control?

In nonlinear control theory, you will recognize most concepts such as controllability and observability where the linear case is often a special case of the nonlinear case. I would highly recommend ...
user avatar
  • 98
3 votes
Accepted

A clarifying question on Lasalle invariance principle

A set is invariant with respect to its dynamics if $x(t_0)\in M \implies x(t)\in M$, this is not the case for the set $E$. The set $E = \left\lbrace x\in \Omega \mid \dot{V}(x) = 0 \right\rbrace$ does ...
user avatar
2 votes
Accepted

High pass filter and differential equation relationship

It can be noted that the high-pass filter can also be written as $$ \frac{s}{s + \omega} = 1 - \frac{\omega}{s + \omega}, $$ such that $$ \frac{s}{s + \omega} Y(s) = Y(s) - \underbrace{\frac{\omega}{s ...
user avatar
  • 1,603
2 votes
Accepted

How do I study the frequency response of a physical system with Arduino?

The arduino does impose some limits. But a classical frequency identification is build from a few steps: As the other comments already suggest, the design of a suitable input. As mentioned, a ...
user avatar
  • 1,079
2 votes
Accepted

Input signal rescaling block

Input signal: ±U V. Scaled output signal: ±1 V. Required gain: $ \frac 1 U $. Figure 1. Possible solutions. If U > 1 then a simple potential divider may suffice. $ V_{OUT} = \frac {R_2}{R_1+R_2} $...
user avatar
  • 8,449
2 votes

A clarifying question on Lasalle invariance principle

The sets $M$ and $E$ can be different. The set $E$ only considers $\dot{V}=0$ while $M$ also considers $f(x)$. Namely, invariant set means that for all $x(0) \in M$ the solution $x(t)\in M$ for all $t&...
user avatar
  • 1,603
2 votes

Non-Linear Analysis Convergence Problem in Ansys

Your model contains a lot of nonlinearities, therefore achieving convergence is not easy. I would try gradually adding each nonlinearity to narrow down where the solver is struggling: turn off large ...
user avatar
1 vote

Non-Linear Analysis Convergence Problem in Ansys

You should be able to see Newton-Rapson residuals and element violations. Just turn them on in the 'solution information' field: Choose a value bigger than zero, like 4. You should also be able to ...
user avatar
  • 156
1 vote

Non-Linear Analysis Convergence Problem in Ansys

First of all, you didn't even mention distinctly that what does the first image that you have inserted here illustrate and represent. What is X axis and what is Y axis. There are numerous graphs ...
user avatar
1 vote

How could I verify the stability of a real system with non-linearities?

Simple answer: tune the controller such that it avoids saturation / rate limits at all cost, then use standard stability analysis techniques. Complex answer: Stability techniques like bode and nyquist ...
user avatar
  • 1,079
1 vote

Zero overshoot criterion from the initial point $x_0$ to the final $x_*$, $x_*$ unknown in advance

Im going to step out of the comment section as it is fairly limited. The quickest answer to the question: Is it possible to somehow form a transient process (with given properties) if the steady ...
user avatar
  • 1,079
1 vote
Accepted

Which way of solving from nonlinear control to choose?

Taking the time derivative of $y$ yields: $$ \dot{y}=\frac{\partial f}{\partial x}(f(x)+u) $$ We need $y(t)=y(0) e^{-\beta t}$ but this is possible if and only if $\dot{y}=-\beta y $ , if the hessian ...
user avatar
  • 126
1 vote

High pass filter and differential equation relationship

You can show it with Laplace transform. Let's say Y = ℒ[y], H = ℒ[η], and ω_p is the filter pole. (Let's not simply call it ω -- when omega is used as a parameter rather than a variable, a subscript ...
user avatar
  • 1,367
1 vote

Changing the quality of the transient process in a nonlinear system (Part II)

The problem is complicated by the fact that the function f(t) and the point at which its minimum/maximum x∗ is located, generally speaking, are not known to us. So if I understand it correctly: $f(t)$...
user avatar
  • 1,079
1 vote
Accepted

Numeric quadrature vs summation of running costs in model predictive control

MPC finds the optimal input $u^*$ which is the input that minimizes the cost function $J$ or $c$. This means that regardless of what this actual value is, its proven to be its minimum. As such, ...
user avatar
  • 1,079
1 vote
Accepted

Fixed end points optimal control problem

I think I have found an answer and please correct me if there are any other reasons apart from the following justification. Since $x^{*}(t)=\{x(t)\in\Omega|J(x)<\min J(y), \forall { y \in \Omega}\}$...
user avatar
  • 215
1 vote

Adding phase error to a system based on phase margin

Being able to check the response of a system, particularly of a MIMO system, to a bunch of unknown external disturbances is very crucial when designing a controller. These external unknown ...
user avatar
1 vote

Control of a nonlinear static MIMO System

Based on your comment, it seems like you are trying to control a dynamical system to track some reference trajectory subject to Gaussian disturbances. Suppose you have some kind of model for the ...
user avatar
1 vote
Accepted

Bounds to prove exponential stablity for given Lyapunov function

You don't necessarily have to find exact constants $k_1,k_2,k_3$, only need to show that there exists some positive constants. In your example above, I can say that $$ \dot{V} \leq -\bigg(\frac{x_1 +...
user avatar
1 vote

Which course to take? Optimal control? Nonlinear control?

In control systems, the main focus is the design of a controller for machines or robots, here we mainly deal with linear systems application of linear control theory. While non-linear systems is an ...
user avatar

Only top scored, non community-wiki answers of a minimum length are eligible